{ "claims": [ { "asserted_by": "arek", "certainty": "HIGH", "certainty_reasons": [ { "code": "machine_verified_computation", "direction": "upgrade" }, { "code": "survived_red_team_challenge", "direction": "upgrade" }, { "code": "single_source", "direction": "downgrade" } ], "challenged_by": [ "straz" ], "contradicts": [], "created_at": "2026-08-06T15:25:44Z", "depends_on": [], "derivation_refs": [ "compute/eq_energy_density_sign.py" ], "epistemic_status": "peer_reviewed_consensus", "evidence_ids": [ "E-0001", "E-0002" ], "id": "C-0001", "modality": "theorem", "note": "Wording corrected after X-0002. The paper says 'everywhere negative'; the equation gives non-positive, with zeros on the axis and outside the wall.", "regime": { "assumptions": [ "classical general relativity, no quantum corrections", "energy density as measured by Eulerian observers", "the shape function of the original 1994 construction" ], "invalid_outside": "semiclassical or quantum regimes, where the pointwise energy conditions are known not to hold in general", "metric_family": "alcubierre" }, "status": "GREEN", "supports": [], "text": "For the Alcubierre metric, the energy density seen by Eulerian observers is non-positive everywhere and strictly negative wherever the shape function varies off-axis, so the weak and dominant energy conditions are violated.", "trl": 1, "verified_by": [ "werys" ] }, { "asserted_by": "arek", "certainty": "MODERATE", "certainty_reasons": [ { "code": "assumption_unverified", "direction": "downgrade", "evidence_ids": [ "E-0005", "E-0006" ] }, { "code": "exact_analytic_derivation", "direction": "upgrade", "evidence_ids": [ "E-0008" ] } ], "challenged_by": [ "redteam", "straz" ], "contradicts": [], "created_at": "2026-08-06T15:25:44Z", "depends_on": [], "derivation_refs": [], "epistemic_status": "peer_reviewed_contested", "evidence_ids": [ "E-0003", "E-0005", "E-0006", "E-0007", "E-0008" ], "id": "C-0002", "modality": "theorem", "regime": { "assumptions": [ "generic Natario-class warp drive metric: intrinsically flat spatial 3-slices with unit lapse, so all nontrivial physics sits in the extrinsic curvature", "the flow field obeys fall-off conditions at spatial infinity so the warp field stays localizable; the authors note this is certainly true if the ADM mass vanishes", "subsidiary conditions are imposed to exclude trivial cases, so that the metric describes a warp drive rather than, for example, the Painleve-Gullstrand form of Schwarzschild spacetime", "regularity: Christoffel symbols at worst piecewise once differentiable, hence a Riemann tensor at worst piecewise continuous with delta-function contributions", "standard general relativity; for modified gravity the paper claims only that the geometric convergence conditions 'will place very strong constraints', not that no rescue exists" ], "invalid_outside": "configurations that do not satisfy those subsidiary conditions", "metric_family": "general_gr" }, "status": "GREEN", "supports": [], "text": "Generic warp drives violate the null energy condition under plausible subsidiary conditions.", "trl": 1, "verified_by": [ "werys" ] }, { "asserted_by": "klaudiusz", "certainty": "LOW", "certainty_reasons": [ { "code": "contested_in_literature", "direction": "downgrade", "evidence_ids": [ "E-0004" ] }, { "code": "indirectness", "direction": "downgrade" } ], "challenged_by": [ "straz" ], "contradicts": [], "created_at": "2026-08-06T15:25:44Z", "depends_on": [ "C-0001", "C-0002" ], "derivation_refs": [], "epistemic_status": "our_synthesis", "evidence_ids": [ "E-0004" ], "id": "C-0003", "modality": "interpretation", "note": "Re-scoped after X-0004. Search Q-0001 logged the citation sweep that dated the debate to 2026.", "regime": { "assumptions": [ "standard general relativity", "the literature surveyed is not exhaustive" ], "invalid_outside": "modified-gravity settings, which have not been surveyed at all", "metric_family": "general_gr" }, "status": "DRAFT", "supports": [], "text": "Whether warp-drive configurations necessarily violate the energy conditions is an open and actively contested question in the peer-reviewed literature, disputed continuously from 2021 through 2026; it is not settled in either direction.", "trl": 1, "verified_by": [] }, { "asserted_by": "tenzor", "certainty": "MODERATE", "certainty_reasons": [ { "code": "machine_verified_computation", "direction": "upgrade" }, { "code": "exact_analytic_derivation", "direction": "upgrade" }, { "code": "assumption_unverified", "direction": "downgrade" } ], "challenged_by": [ "straz" ], "contradicts": [], "created_at": "2026-08-07T06:27:11Z", "depends_on": [ "C-0001", "C-0006" ], "derivation_refs": [ "compute/warpkit/alcubierre.py", "compute/energy_budget.py", "tests/test_energy_budget.py" ], "epistemic_status": "our_derivation", "evidence_ids": [ "E-0009", "E-0010", "E-0012" ], "id": "C-0004", "modality": "derivation_under_assumptions", "regime": { "assumptions": [ "the tanh shape function of eq. 3, with wall thickness identified as 1/sigma", "r_c = r_s in eq. 16 — no longer an assumption: derived independently in compute/verify_energy_density.py and recorded as C-0006", "classical general relativity, no quantum corrections and no backreaction", "energy density as measured by Eulerian observers", "no quantum inequality constraint is applied, so these are a lower bound on the difficulty rather than an estimate of it" ], "invalid_outside": "any construction that is not the original 1994 metric with this shape function; in particular Van Den Broeck-type volume tricks and Natario-class metrics are not covered", "metric_family": "alcubierre" }, "status": "GREEN", "supports": [], "text": "For the original Alcubierre metric with the tanh shape function, the total negative energy scales as |E| ~ v_s^2 R^2 / d, where R is the bubble radius and d the wall thickness. There is no wall thickness that makes the requirement small.", "trl": 1, "verified_by": [ "werys" ] }, { "asserted_by": "tenzor", "certainty": "MODERATE", "certainty_reasons": [ { "code": "machine_verified_computation", "direction": "upgrade" }, { "code": "assumption_unverified", "direction": "downgrade" }, { "code": "numerical_only_no_analytic", "direction": "downgrade" } ], "challenged_by": [ "straz" ], "contradicts": [], "created_at": "2026-08-07T06:27:11Z", "depends_on": [ "C-0001", "C-0006" ], "derivation_refs": [ "compute/energy_budget.py", "tests/test_energy_budget.py" ], "epistemic_status": "our_derivation", "evidence_ids": [ "E-0009", "E-0010", "E-0012" ], "id": "C-0005", "modality": "numerical_result", "regime": { "assumptions": [ "the tanh shape function of eq. 3, with wall thickness identified as 1/sigma", "r_c = r_s in eq. 16 — no longer an assumption: derived independently in compute/verify_energy_density.py and recorded as C-0006", "classical general relativity, no quantum corrections and no backreaction", "energy density as measured by Eulerian observers", "no quantum inequality constraint is applied, so these are a lower bound on the difficulty rather than an estimate of it" ], "invalid_outside": "any construction that is not the original 1994 metric with this shape function; in particular Van Den Broeck-type volume tricks and Natario-class metrics are not covered", "metric_family": "alcubierre" }, "status": "GREEN", "supports": [], "text": "A 100 m Alcubierre bubble travelling at v_s = c with a 1 mm wall requires about 3.74e32 kg of negative mass-equivalent, that is roughly 188 solar masses. The requirement is astrophysical in scale, not engineering.", "trl": 1, "verified_by": [ "werys" ] }, { "asserted_by": "tenzor", "certainty": "HIGH", "certainty_reasons": [ { "code": "machine_verified_computation", "direction": "upgrade" }, { "code": "exact_analytic_derivation", "direction": "upgrade" } ], "challenged_by": [ "straz" ], "contradicts": [], "created_at": "2026-08-07T06:49:58Z", "depends_on": [], "derivation_refs": [ "compute/verify_energy_density.py", "tests/test_q1_rc.py" ], "epistemic_status": "our_derivation", "evidence_ids": [ "E-0009", "E-0012" ], "id": "C-0006", "modality": "derivation_under_assumptions", "note": "Resolves open question Q1. Three rival readings of r_c (R, rho, x) leave non-zero residuals.", "regime": { "assumptions": [ "the metric of eq. 5 with unit lapse and flat spatial slices", "K_ij as given by the paper's own eq. 7", "a GENERAL shape function f(r_s) — the result does not use the tanh profile" ], "invalid_outside": "metrics whose spatial slices are not intrinsically flat, where the three-Ricci scalar no longer drops out of the Hamiltonian constraint", "metric_family": "alcubierre" }, "status": "GREEN", "supports": [ "C-0004", "C-0005" ], "text": "The symbol r_c in Alcubierre's energy-density equation denotes the spherical radius r_s. Recomputing the density from the metric via the Hamiltonian constraint reproduces the published equation exactly, and only, under that reading.", "trl": 1, "verified_by": [ "werys" ] }, { "asserted_by": "tenzor", "certainty": "HIGH", "certainty_reasons": [ { "code": "assumption_unverified", "direction": "downgrade" }, { "code": "multiple_independent_sources", "direction": "upgrade", "evidence_ids": [ "E-0041" ] } ], "challenged_by": [ "straz" ], "contradicts": [], "created_at": "2026-08-07T07:05:36Z", "depends_on": [], "derivation_refs": [ "compute/quantum_inequality.py" ], "epistemic_status": "peer_reviewed_contested", "evidence_ids": [ "E-0013" ], "id": "C-0007", "modality": "bound", "regime": { "assumptions": [ "the Ford-Roman quantum inequality for a free massless scalar field in four-dimensional Minkowski spacetime, applied on a scale where the region can be treated as locally flat", "a single quantised free scalar field; the bound is not established for arbitrary matter content", "the piecewise-linear shape function S-0007 uses, whose slope is 1/Delta across the whole wall", "the sampling-time choice t_0 = alpha * 2 Delta / (sqrt(3) v_b) with alpha << 1" ], "invalid_outside": "matter content or field states to which the Ford-Roman inequality has not been extended, and regimes where the local-flatness approximation used to import the flat-space inequality fails", "metric_family": "alcubierre" }, "status": "GREEN", "supports": [], "text": "The quantum inequality constrains the Alcubierre bubble wall to at most about 10^2 v_b Planck lengths, roughly 1.6e-33 m at light speed — about 10^-18 of a proton radius.", "trl": 1, "verified_by": [ "werys" ] }, { "asserted_by": "tenzor", "certainty": "MODERATE", "certainty_reasons": [ { "code": "machine_verified_computation", "direction": "upgrade" }, { "code": "independently_reproduced", "direction": "upgrade" }, { "code": "single_source", "direction": "downgrade" } ], "challenged_by": [ "straz" ], "contradicts": [], "created_at": "2026-08-07T07:05:36Z", "depends_on": [], "derivation_refs": [ "compute/quantum_inequality.py", "tests/test_quantum_inequality.py" ], "epistemic_status": "our_derivation", "evidence_ids": [ "E-0013", "E-0014", "E-0016" ], "id": "C-0008", "modality": "order_of_magnitude", "regime": { "assumptions": [ "the Ford-Roman quantum inequality for a free massless scalar field in four-dimensional Minkowski spacetime, applied on a scale where the region can be treated as locally flat", "a single quantised free scalar field; the bound is not established for arbitrary matter content", "the piecewise-linear shape function S-0007 uses, whose slope is 1/Delta across the whole wall", "the sampling-time choice t_0 = alpha * 2 Delta / (sqrt(3) v_b) with alpha << 1" ], "invalid_outside": "matter content or field states to which the Ford-Roman inequality has not been extended, and regimes where the local-flatness approximation used to import the flat-space inequality fails", "metric_family": "alcubierre" }, "status": "GREEN", "supports": [], "text": "Under that constraint a 100 m warp bubble at light speed requires of order 10^20 galaxy masses of negative energy. Recomputing it independently from the paper's own eq. 22 and eq. 26 gives 3.47e20 galaxy masses against the 3e20 the paper states.", "trl": 1, "verified_by": [ "werys" ] }, { "asserted_by": "tenzor", "certainty": "MODERATE", "certainty_reasons": [ { "code": "machine_verified_computation", "direction": "upgrade" }, { "code": "indirectness", "direction": "downgrade" } ], "challenged_by": [ "straz" ], "contradicts": [], "created_at": "2026-08-07T07:05:36Z", "depends_on": [ "C-0004", "C-0006" ], "derivation_refs": [ "compute/quantum_inequality.py" ], "epistemic_status": "our_synthesis", "evidence_ids": [ "E-0012", "E-0013", "E-0014" ], "id": "C-0009", "modality": "interpretation", "regime": { "assumptions": [ "the Ford-Roman quantum inequality for a free massless scalar field in four-dimensional Minkowski spacetime, applied on a scale where the region can be treated as locally flat", "a single quantised free scalar field; the bound is not established for arbitrary matter content", "the piecewise-linear shape function S-0007 uses, whose slope is 1/Delta across the whole wall", "the sampling-time choice t_0 = alpha * 2 Delta / (sqrt(3) v_b) with alpha << 1" ], "invalid_outside": "matter content or field states to which the Ford-Roman inequality has not been extended, and regimes where the local-flatness approximation used to import the flat-space inequality fails", "metric_family": "alcubierre" }, "status": "GREEN", "supports": [], "text": "No energy source addresses the warp-drive requirement, because the requirement is for negative energy density and every source of energy produces positive energy. Even with the quantum inequality set aside entirely and a full 1-metre wall allowed, a 100 m bubble at light speed still needs of order a solar mass of NEGATIVE energy.", "trl": 1, "verified_by": [ "werys" ] }, { "asserted_by": "arek", "certainty": "MODERATE", "certainty_reasons": [ { "code": "single_source", "direction": "downgrade" }, { "code": "not_independently_reproduced", "direction": "downgrade" }, { "code": "large_effect", "direction": "upgrade" } ], "challenged_by": [], "contradicts": [], "created_at": "2026-08-07T07:56:19Z", "depends_on": [], "derivation_refs": [], "epistemic_status": "peer_reviewed_contested", "evidence_ids": [ "E-0017", "E-0018", "E-0019" ], "id": "C-0010", "modality": "numerical_result", "note": "The reduction is GEOMETRIC, not energetic: it changes how much is needed, not where energy comes from. The requirement is still for negative energy, and the author's own follow-up lists high energy densities, Planck-scale curvature radii and naked singularities as unresolved.", "regime": { "assumptions": [ "the modified metric ds^2 = -dt^2 + B^2(r_s)[(dx - v_s f dt)^2 + dy^2 + dz^2], which is NOT the Alcubierre metric", "a bubble whose exterior surface area is microscopic while the interior spatial volume is macroscopic", "classical general relativity plus the Ford-Roman quantum inequality as the author applies it" ], "invalid_outside": "the original Alcubierre construction, to which none of this transfers; and any regime where curvature radii of order the Planck length invalidate the semiclassical treatment", "metric_family": "van_den_broeck" }, "status": "GREEN", "supports": [ "C-0011" ], "text": "Van Den Broeck's modification reduces the total negative mass for a macroscopic warp bubble from of order 1e62 kg to of order a few solar masses (~1e30 kg) — about 32 orders of magnitude — by keeping the bubble's exterior surface microscopically small while expanding the spatial volume inside it. The author states it satisfies the Ford-Roman quantum inequality.", "trl": 1, "verified_by": [ "werys" ] }, { "asserted_by": "arek", "certainty": "HIGH", "certainty_reasons": [ { "code": "exact_analytic_derivation", "direction": "upgrade" } ], "challenged_by": [ "redteam", "straz" ], "contradicts": [], "created_at": "2026-08-07T07:56:19Z", "depends_on": [], "derivation_refs": [], "epistemic_status": "peer_reviewed_consensus", "evidence_ids": [ "E-0022" ], "id": "C-0011", "modality": "interpretation", "note": "Was 'the single most load-bearing opening in the corpus'. CLOSED by X-0009: independent recomputation (compute/hawking_ellis_scan.py) confirms the VdB warp wall carries Type IV stress-energy — no rest frame, no invariant energy density — for 87-99 percent of the wall. The theorem-coverage gap in the claim text remains true and remains irrelevant. Auditor addition (X-0019): SSV's adjacent caveat reads 'There are other problematic issues with both of these models' — the concession was never an endorsement.", "regime": { "assumptions": [ "the modified metric ds^2 = -dt^2 + B^2(r_s)[(dx - v_s f dt)^2 + dy^2 + dz^2], which is NOT the Alcubierre metric", "a bubble whose exterior surface area is microscopic while the interior spatial volume is macroscopic", "classical general relativity plus the Ford-Roman quantum inequality as the author applies it" ], "invalid_outside": "the original Alcubierre construction, to which none of this transfers; and any regime where curvature radii of order the Planck length invalidate the semiclassical treatment", "metric_family": "van_den_broeck" }, "status": "GREEN", "supports": [], "text": "The strongest recent no-go result for warp drives does not cover the Van Den Broeck construction. Santiago, Schuster and Visser (2022) state that the van den Broeck spacetime 'cannot simply be dismissed out of hand' and must be addressed with different techniques, because it lies outside the Natario class their theorem treats.", "trl": 1, "verified_by": [ "werys" ] }, { "asserted_by": "arek", "certainty": "MODERATE", "certainty_reasons": [ { "code": "single_source", "direction": "downgrade" }, { "code": "multiple_independent_sources", "direction": "upgrade" } ], "challenged_by": [ "redteam" ], "contradicts": [], "created_at": "2026-08-07T07:56:19Z", "depends_on": [], "derivation_refs": [], "epistemic_status": "peer_reviewed_contested", "evidence_ids": [ "E-0020", "E-0021" ], "id": "C-0012", "modality": "interpretation", "note": "Notable because it is the author of the largest energy reduction saying where he thinks the remaining possibility lies, in the same year.", "regime": { "assumptions": [ "the modified metric ds^2 = -dt^2 + B^2(r_s)[(dx - v_s f dt)^2 + dy^2 + dz^2], which is NOT the Alcubierre metric", "a bubble whose exterior surface area is microscopic while the interior spatial volume is macroscopic", "classical general relativity plus the Ford-Roman quantum inequality as the author applies it" ], "invalid_outside": "the constructions S-0011 actually reviews: the original Alcubierre geometry and its immediate modifications; the follow-up's verdict is about superluminal bubbles in GR+QFT generally, but its computations are Alcubierre-based", "metric_family": "alcubierre" }, "status": "GREEN", "supports": [], "text": "Van Den Broeck's own follow-up concludes that superluminal warp bubbles are unlikely within general relativity plus quantum field theory, while stating that SUBLUMINAL bubbles remain an open possibility and that microscopic ones might even occur naturally.", "trl": 1, "verified_by": [ "werys" ] }, { "asserted_by": "tenzor", "certainty": "MODERATE", "certainty_reasons": [ { "code": "machine_verified_computation", "direction": "upgrade" }, { "code": "independently_reproduced", "direction": "upgrade" }, { "code": "assumption_unverified", "direction": "downgrade" } ], "challenged_by": [ "straz" ], "contradicts": [], "created_at": "2026-08-07T08:03:30Z", "depends_on": [ "C-0010" ], "derivation_refs": [ "compute/vdb_pricing.py", "tests/test_vdb_pricing.py" ], "epistemic_status": "our_derivation", "evidence_ids": [ "E-0017", "E-0018" ], "id": "C-0013", "modality": "numerical_result", "note": "Also found: the equation extractor missed VDB's equations because he wraps eqnarray in \\newcommand macros (\\bear/\\eear). Extractor gap, logged in Plane.", "regime": { "assumptions": [ "his stated parameters alpha=1e17, R~=D~=1e-15 m, R=3e-15 m", "region II treated as static via x' = x - v_s t at constant velocity, so rho = R3/16pi with K_ij = 0", "the three-Ricci derived symbolically from Christoffel symbols for B^2(dr^2+r^2 dOmega^2)", "two unrelated C2 interpolating profiles standing in for his unstated one" ], "invalid_outside": "non-constant v_s, where the region II slice is no longer static and the extrinsic curvature terms return", "metric_family": "van_den_broeck" }, "status": "RED", "supports": [ "C-0010" ], "text": "Independent recomputation confirms the headline of the Van Den Broeck reduction: region IV reproduces to 1% with our existing closed form, the total requirement at his parameters is solar-mass scale (~1e30 kg), and the reduction versus the unmodified 100 m bubble is ~32 orders of magnitude. His +/- sign split within region II does NOT reproduce: it depends on the unstated interpolating profile, and a half-cosine profile yields no negative transition energy at all. The profile-independent negative energy is region IV's -6.2e29 kg, which no choice of B removes.", "trl": 1, "verified_by": [] }, { "asserted_by": "arek", "certainty": "MODERATE", "certainty_reasons": [ { "code": "machine_verified_computation", "direction": "upgrade" }, { "code": "independently_reproduced", "direction": "upgrade" }, { "code": "assumption_unverified", "direction": "downgrade" } ], "challenged_by": [ "straz" ], "contradicts": [], "created_at": "2026-08-07T08:53:48Z", "depends_on": [], "derivation_refs": [ "compute/mission_budget.py" ], "epistemic_status": "our_derivation", "evidence_ids": [], "id": "C-0014", "modality": "derivation_under_assumptions", "note": "Numbers computed twice independently: workflow track A (wf_3e70bff5-044) and this repo artifact; they agree. D-T kinematics from CODATA-2022 masses, byte-checked against physics.nist.gov in the workflow record.", "regime": { "assumptions": [ "textbook special relativity, no exotic physics", "one-way distance 4.394928 ly from the SIMBAD parallax of alpha Cen A fetched at run time (742.12 +/- 1.4 mas, Hipparcos bibcode)", "1000 t dry ship, stated as an assumption and cross-checked against open-loop consumables", "ideal conversion: all released energy becomes directed exhaust kinetic energy — every fuel number is therefore a floor" ], "invalid_outside": "beamed or staged architectures, which remove the exponential and are costed separately in the same artifact", "metric_family": "minkowski" }, "status": "GREEN", "supports": [], "text": "For a 4-person Sol to alpha Centauri round trip, special relativity is not the obstacle — the rocket equation is. Round-trip coordinate time is 175.8/87.9/43.9 years at 0.05c/0.1c/0.2c, with crew time shorter by only 0.13/0.50/2.02 percent. At 0.2c a 1000 t ship needs, as floors, 1.25e6 kg of annihilation fuel, 1.17e10 kg of D-T at the full mass defect, or 1.08e15 kg of D-T if only charged products are steerable — the spread is driven by two-body kinematics putting 79.76 percent of the Q-value into the neutral neutron. Stopping at the target multiplies the flyby fuel by 11.4, not 2, because rapidity adds and mass ratios multiply. At 0.05c open-loop consumables alone exceed the dry mass.", "trl": 1, "verified_by": [ "werys" ] }, { "asserted_by": "arek", "certainty": "HIGH", "certainty_reasons": [ { "code": "multiple_independent_sources", "direction": "upgrade" } ], "challenged_by": [], "contradicts": [], "created_at": "2026-08-07T08:53:48Z", "depends_on": [], "derivation_refs": [ "compute/fh_ssv_identity.py" ], "epistemic_status": "peer_reviewed_contested", "evidence_ids": [ "E-0023", "E-0024", "E-0025" ], "id": "C-0015", "modality": "interpretation", "note": "compute/fh_ssv_identity.py proves symbolically, for a fully general phi: the FH 'hidden geometric structure' (sum of second-order principal minors of the Hessian) is identically (1/2)[(tr H)^2 - tr(H^2)] = 8*pi*rho of the Hamiltonian constraint — the exact quantity SSV analyse. The papers disagree interpretively, not computationally.", "regime": { "assumptions": [ "the Fell-Heisenberg ansatz: unit lapse, flat induced 3-metric, time-independent purely irrotational shift", "'positive energy' means the energy density measured by co-moving Eulerian observers, and only that" ], "invalid_outside": "any statement about the full WEC over all observers, which the paper itself concedes fails", "metric_family": "other", "metric_family_note": "Fell-Heisenberg irrotational-shift solitons; neither Alcubierre nor Natario class" }, "status": "RED", "supports": [], "text": "The Fell-Heisenberg positive-energy warp result is narrower than its abstract: positivity is proven for the Eulerian energy density only, within a restricted ansatz, and the published text itself concedes that the full weak energy condition is violated in compact regions and that no modification of the configuration removes those regions. It therefore does not lift the negative-energy requirement for a superluminal jump.", "trl": 1, "verified_by": [] }, { "asserted_by": "arek", "certainty": "LOW", "certainty_reasons": [ { "code": "single_source", "direction": "downgrade" }, { "code": "preprint_not_refereed", "direction": "downgrade" } ], "challenged_by": [], "contradicts": [], "created_at": "2026-08-07T08:53:48Z", "depends_on": [], "derivation_refs": [], "epistemic_status": "preprint_only", "evidence_ids": [ "E-0026", "E-0027", "E-0028" ], "id": "C-0016", "modality": "interpretation", "regime": { "assumptions": [ "the three 2026 papers S-0003/S-0004/S-0005 as posted on arXiv", "citation counts as returned by OpenAlex on 2026-08-07, URLs in the workflow record" ], "invalid_outside": "any weight these findings would carry after independent peer review, which none has yet", "metric_family": "general_gr" }, "status": "RED", "supports": [], "text": "The three 2026 warp papers in the corpus are one correlated source, not three: the same single author, all arXiv preprints without journal DOIs, each with zero citations on OpenAlex as of 2026-08-07. Within that caveat, S-0003 certifies the Van Den Broeck walls as Hawking-Ellis Type IV — no rest frame, no invariant energy density — and energy-condition violating for all observers; and S-0005's 'warp without exotic matter' is, in its own words, a causal SUBLUMINAL reaction drive with steep but positive cost.", "trl": 1, "verified_by": [] }, { "asserted_by": "arek", "certainty": "MODERATE", "certainty_reasons": [ { "code": "machine_verified_computation", "direction": "upgrade" }, { "code": "independently_reproduced", "direction": "upgrade" }, { "code": "assumption_unverified", "direction": "downgrade" } ], "challenged_by": [ "straz" ], "contradicts": [], "created_at": "2026-08-07T08:53:48Z", "depends_on": [], "derivation_refs": [ "compute/navigation_budget.py" ], "epistemic_status": "our_derivation", "evidence_ids": [], "id": "C-0017", "modality": "numerical_result", "note": "Numbers and fetch URLs in the workflow record (wf_3e70bff5-044, track D). The proper-motion/orbit component is now orbit-solved in compute/ab_orbit.py (C-0019): 24-35 au over 22-88 yr, bounded by the orbit's size — superseding track D's rough 27-83 au.", "regime": { "assumptions": [ "the SIMBAD parallax fetched at run time plus two further catalogued parallaxes for the same star (VizieR I/131A and I/311), embedded with provenance", "arrival ambiguity compared at 0.1c cruise" ], "invalid_outside": "targeting done from a single adopted Gaia-grade parallax, which is the fix this claim calls for", "metric_family": "minkowski" }, "status": "GREEN", "supports": [], "text": "Navigation to alpha Centauri A is dominated by catalogue disagreement, not by relativity: three published parallaxes for the same star imply distances spanning 4673 au, which at 0.1c is 270 days of arrival-time ambiguity — 1.7 times the 161-day relativistic clock divergence accumulated over the entire 88-year round trip. The image aimed at is also 4.4 years old on arrival. A jump-targeting computation therefore needs, in order: one adopted Gaia-grade parallax, an AB-barycentre orbit solution, and only then relativistic corrections.", "trl": 1, "verified_by": [ "werys" ] }, { "asserted_by": "tenzor", "certainty": "HIGH", "certainty_reasons": [ { "code": "machine_verified_computation", "direction": "upgrade" }, { "code": "independently_reproduced", "direction": "upgrade" } ], "challenged_by": [ "straz" ], "contradicts": [], "created_at": "2026-08-07T09:58:41Z", "depends_on": [ "C-0006" ], "derivation_refs": [ "compute/numgr.py", "compute/hawking_ellis_scan.py", "tests/test_hawking_ellis.py" ], "epistemic_status": "our_derivation", "evidence_ids": [ "E-0028" ], "id": "C-0018", "modality": "numerical_result", "note": "The negative-control test was written expecting Type I on the motion axis 'by symmetry' and the computation refuted the expectation: zero density with irremovable flux is still Type IV. The test now records that correction.", "regime": { "assumptions": [ "fourth-order finite-difference Einstein tensor, validated: Minkowski to 1e-27, Alcubierre Eulerian density against the C-0006 analytic formula to 5e-9, Schwarzschild vacuum to 1e-6 of curvature scale", "comoving coordinates at constant v_s, where the metric is static", "Type IV detected as a complex eigenvalue pair of the mixed stress-energy at relative tolerance 1e-6", "transfer to the microscopic VdB wall argued from scale invariance of the dimensionless metric functions and verified as stability across sigma*R = 5 and 50" ], "invalid_outside": "non-constant v_s, and any wall so thin that semiclassical gravity itself fails (Planck-scale curvature radii, which VdB's own follow-up lists as unresolved)", "metric_family": "alcubierre" }, "status": "GREEN", "supports": [], "text": "Independent recomputation confirms the Type IV certification of warp-bubble walls: at v_s = 0.5 the Alcubierre wall's stress-energy carries a complex-conjugate eigenvalue pair — no rest frame, no observer-invariant energy density — over 90.6 to 99.7 percent of the wall across two sigma*R scales, bracketing S-0003's stated 87-99 percent. On the motion axis the density vanishes but an irremovable flux keeps the point Type IV. The classification is scale-stable and the Van Den Broeck f-wall is metric-identical to the Alcubierre wall, so it transfers; the VdB B-transition is Type I, as a static region must be. The energy-condition escape recorded in C-0011 is therefore closed in practice: the construction the 2022 theorem missed fails the same physical requirement by direct computation.", "trl": 1, "verified_by": [ "werys" ] }, { "asserted_by": "tenzor", "certainty": "MODERATE", "certainty_reasons": [ { "code": "machine_verified_computation", "direction": "upgrade" }, { "code": "single_source", "direction": "downgrade" } ], "challenged_by": [ "straz" ], "contradicts": [], "created_at": "2026-08-07T10:35:42Z", "depends_on": [ "C-0017" ], "derivation_refs": [ "compute/ab_orbit.py", "tests/test_ab_orbit.py" ], "epistemic_status": "our_derivation", "evidence_ids": [], "id": "C-0019", "modality": "numerical_result", "note": "Replaces Track D's rough 27-83 au estimate with orbit-solved 24-35 au: the error is BOUNDED by the orbit's size rather than growing without limit, which the rough estimate missed. Solver validated: closure after one period 2.4e-13 au.", "regime": { "assumptions": [ "orbital elements from Pourbaix & Boffin 2016 (S-0012), HARPS+ESO column, transcribed from the paper's Table 1 — a LaTeX table the canonicaliser strips, so the values cannot be quoted through the evidence pipeline (extractor gap PDB-26)", "sky-plane error metric; the radial component is folded into the distance-uncertainty budget of C-0017", "departure epoch 2026.6; the scale of the error is epoch-robust, its digits are not" ], "invalid_outside": "epochs where the Pourbaix-Boffin solution itself is superseded", "metric_family": "minkowski" }, "status": "GREEN", "supports": [ "C-0017" ], "text": "Targeting alpha Centauri A with the catalogue state vector extrapolated linearly misses by 24 to 35 au over coasts of 22 to 88 years from a 2026.6 departure — a planetary system's width, from geometry alone — because component A orbits the AB barycentre with a 79.91-year period and eccentricity 0.524. The full Kepler solution that removes the error costs one Newton iteration per epoch.", "trl": 1, "verified_by": [ "werys" ] }, { "asserted_by": "tenzor", "certainty": "HIGH", "certainty_reasons": [ { "code": "machine_verified_computation", "direction": "upgrade" }, { "code": "independently_reproduced", "direction": "upgrade" }, { "code": "survived_red_team_challenge", "direction": "upgrade" } ], "challenged_by": [ "redteam" ], "contradicts": [], "created_at": "2026-08-07T12:19:36Z", "depends_on": [ "C-0010" ], "derivation_refs": [ "compute/vdb_pricing.py", "tests/test_vdb_pricing.py" ], "epistemic_status": "our_derivation", "evidence_ids": [ "E-0017", "E-0018", "E-0032" ], "id": "C-0020", "modality": "numerical_result", "note": "Root-cause chain worth remembering: canonicaliser strips '$n=80$' from prose AND the extractor (pre-PDB-26) missed the macro-wrapped equation, so the profile was invisible to every tool — and 'invisible' was misread as 'unstated'. Two silent gaps compounded into a false published finding.", "regime": { "assumptions": [ "his stated parameters alpha=1e17, R~=D~=1e-15 m, R=3e-15 m", "region II treated as static via x' = x - v_s t at constant velocity, so rho = R3/16pi with K_ij = 0", "the three-Ricci derived symbolically from Christoffel symbols for B^2(dr^2+r^2 dOmega^2)", "two unrelated C2 interpolating profiles standing in for his unstated one" ], "invalid_outside": "non-constant v_s, where the region II slice is no longer static and the extrinsic curvature terms return", "metric_family": "van_den_broeck" }, "status": "DRAFT", "supersedes": "C-0013", "supports": [ "C-0010" ], "text": "Independent recomputation confirms the Van Den Broeck construction IN FULL, correcting C-0013: region IV reproduces to 1% with our closed form, and — under the profile the paper does state (B = alpha(-(n-1)w^n + n w^(n-1)) + 1 with n = 80, E-0032) — the region II sign split also reproduces to 1%: -1.380e30 vs the printed -1.4e30 and +4.865e30 vs +4.9e30 kg, sign boundary w = 0.9815 vs the printed 0.981. C-0013's 'profile-dependence' finding rested on a false premise (the profile was invisible because the canonicaliser strips inline math and, at the time, the extractor missed macro-wrapped equations) and on a C^1 counterexample outside the paper's stated twice-differentiable class. Residual anomaly, unresolved: VDB's printed POINTWISE peak values appear inconsistent with his own stated profile under recomputation, even though his integrated totals reproduce.", "trl": 1, "verified_by": [] }, { "asserted_by": "arek", "certainty": "HIGH", "certainty_reasons": [ { "code": "multiple_independent_sources", "direction": "upgrade" }, { "code": "survived_red_team_challenge", "direction": "upgrade" } ], "challenged_by": [ "redteam" ], "contradicts": [], "created_at": "2026-08-07T12:19:36Z", "depends_on": [], "derivation_refs": [ "compute/fh_ssv_identity.py" ], "epistemic_status": "peer_reviewed_contested", "evidence_ids": [ "E-0023", "E-0024", "E-0025", "E-0030" ], "id": "C-0021", "modality": "interpretation", "regime": { "assumptions": [ "the Fell-Heisenberg ansatz: unit lapse, flat induced 3-metric, time-independent purely irrotational shift", "'positive energy' means the energy density measured by co-moving Eulerian observers, and only that" ], "invalid_outside": "any statement about the full WEC over all observers, which the paper itself concedes fails", "metric_family": "other", "metric_family_note": "Fell-Heisenberg irrotational-shift solitons; neither Alcubierre nor Natario class" }, "status": "DRAFT", "supersedes": "C-0015", "supports": [], "text": "The Fell-Heisenberg positive-energy result is narrower than its abstract: positivity is proven for the Eulerian energy density only, within a restricted ansatz. On the full WEC their text states both halves in consecutive sentences, and both must be carried together: 'No amount of modification to the configuration could get rid of these WEC-violating regions' — immediately followed by — 'it may still be possible to satisfy the WEC in the presented configurations too, given sufficient modifications', conditional on another cited configuration's claimed WEC compliance. The paper concedes present WEC violation while leaving a conditional door open; it does not lift the negative-energy requirement for a superluminal jump today, and it does not close it forever.", "trl": 1, "verified_by": [] }, { "asserted_by": "arek", "certainty": "LOW", "certainty_reasons": [ { "code": "single_source", "direction": "downgrade" }, { "code": "preprint_not_refereed", "direction": "downgrade" }, { "code": "survived_red_team_challenge", "direction": "upgrade" } ], "challenged_by": [ "redteam" ], "contradicts": [], "created_at": "2026-08-07T12:19:36Z", "depends_on": [], "derivation_refs": [], "epistemic_status": "preprint_only", "evidence_ids": [ "E-0026", "E-0027", "E-0028", "E-0031" ], "id": "C-0022", "modality": "interpretation", "regime": { "assumptions": [ "the three 2026 papers S-0003/S-0004/S-0005 as posted on arXiv", "citation counts as returned by OpenAlex on 2026-08-07, URLs in the workflow record" ], "invalid_outside": "any weight these findings would carry after independent peer review, which none has yet", "metric_family": "general_gr" }, "status": "DRAFT", "supersedes": "C-0016", "supports": [], "text": "The three 2026 warp papers are one correlated source: same single author, arXiv preprints without journal DOIs, zero citations each on OpenAlex (reproduced live with a positive control: S-0001 shows 45). Within that caveat, S-0003 certifies the Van Den Broeck walls as Hawking-Ellis Type IV — no rest frame — ABOVE a Type-I to Type-IV transition at v_s ~ 0.36 (the value lives in a source macro; the canonical text loses it), with Alcubierre and Natario walls Type-IV dominated at all speeds; and S-0005's 'no exotic matter' drive is, in its own words, causal, subluminal, and steeply but positively costly.", "trl": 1, "verified_by": [] }, { "asserted_by": "arek", "certainty": "MODERATE", "certainty_reasons": [ { "code": "multiple_independent_sources", "direction": "upgrade" }, { "code": "contested_in_literature", "direction": "downgrade" } ], "challenged_by": [], "contradicts": [], "created_at": "2026-08-07T12:28:42Z", "depends_on": [ "C-0021" ], "derivation_refs": [], "epistemic_status": "peer_reviewed_contested", "evidence_ids": [ "E-0033", "E-0034", "E-0035", "E-0036", "E-0037", "E-0031" ], "id": "C-0023", "modality": "interpretation", "note": "Closes PDB-21 and the FH/Lentz/B-M leg of PDB-24. The VDB leg was priced in C-0010/C-0020.", "regime": { "assumptions": [ "the corpus as of 2026-08-07: S-0013/S-0014/S-0015 for the proposals, S-0001 for the rebuttal, S-0003 for the Type classification", "'unrebutted in the corpus' means exactly that — an absence in twelve-plus-three sources, not in the literature at large" ], "invalid_outside": "any future peer-reviewed WEC-for-all-observers demonstration for a superluminal configuration, which is precisely what the corpus lacks", "metric_family": "general_gr" }, "status": "DRAFT", "supports": [], "text": "The positive-energy warp programme, priced on its own terms: Lentz (2020) asserts superluminal solitons from purely positive energy densities; Santiago-Schuster-Visser (2022) rebut Lentz, Bobrick-Martire and Fell-Heisenberg collectively — each 'merely asserts the existence of one sub-class of timelike observers for which the energy density is positive', which does not establish the WEC — and exhibit boosted observers who see negative density. What survives unrebutted in the corpus is explicitly SUBLUMINAL: Bobrick-Martire's positive-energy class ('any warp drive requires propulsion') and the 2024 constant-velocity solution, which satisfies the energy conditions by adding a positive-ADM matter shell. Consistently, the 2026 certifier finds the irrotational Lentz/Fell-Heisenberg-class geometry globally Type I while vortical walls are Type IV. The surviving programme is subluminal shells with shift — rockets in geometric dress — and superluminal positive energy remains asserted, contested, and unpriced.", "trl": 1, "verified_by": [] }, { "asserted_by": "arek", "certainty": "MODERATE", "certainty_reasons": [ { "code": "textbook_corroborated", "direction": "upgrade" }, { "code": "indirectness", "direction": "downgrade" } ], "challenged_by": [], "contradicts": [], "created_at": "2026-08-07T12:33:35Z", "depends_on": [], "derivation_refs": [], "epistemic_status": "peer_reviewed_consensus", "evidence_ids": [ "E-0038", "E-0039", "E-0040" ], "id": "C-0024", "modality": "interpretation", "regime": { "assumptions": [ "Fewster 2012 lecture notes (S-0016) as a review of the QEI field", "the distinction between minimal and non-minimal scalar coupling, and the non-existence of spacelike-averaged QEIs, as stated there" ], "invalid_outside": "claims that a non-minimal coupling actually DELIVERS a physical warp drive — that is unproven and unpriced; this claim only locates where the bound's assumptions are soft", "metric_family": "qft_curved_spacetime" }, "status": "DRAFT", "supports": [], "text": "The quantum-inequality wall bound rests on assumptions a real configuration could target, and the corpus names them: the Ford-Roman inequality is derived for a free, minimally-coupled, massless scalar field on a locally-flat patch. Fewster's lectures show the bound is not universal — a NON-minimally coupled scalar has stress-energy whose extra terms are 'not of the sum of squares form', so 'even NEC can be violated', and no quantum energy inequality exists at all for smearings over spacelike surfaces. So the honest statement is not 'the QI forbids warp drive' but 'the QI as applied by Pfenning-Ford forbids it for a minimally-coupled scalar sampled along a timelike worldline'; a non-minimal coupling or a genuinely different field content is the specific, named place an escape would have to live.", "trl": 1, "verified_by": [] }, { "asserted_by": "arek", "certainty": "MODERATE", "certainty_reasons": [ { "code": "multiple_independent_sources", "direction": "upgrade" }, { "code": "textbook_corroborated", "direction": "upgrade" } ], "challenged_by": [], "contradicts": [], "created_at": "2026-08-07T12:33:35Z", "depends_on": [], "derivation_refs": [], "epistemic_status": "peer_reviewed_consensus", "evidence_ids": [ "E-0041" ], "id": "C-0025", "modality": "interpretation", "regime": { "assumptions": [ "Everett-Roman 1997 (S-0017) and Fewster 2012 (S-0016) as the corroborating sources", "'the same class of conclusion' means QI-type magnitude/duration limits on negative energy, not the identical numeric bound" ], "invalid_outside": "the specific 10^2 v_b L_Planck coefficient, which remains from Pfenning-Ford alone and is not independently reproduced here", "metric_family": "qft_curved_spacetime" }, "status": "DRAFT", "supports": [ "C-0007" ], "text": "The quantum-inequality obstruction to warp drive has independent corroboration in the corpus beyond the single Pfenning-Ford paper. Everett & Roman (1997), analysing the Krasnikov tube — a different superluminal geometry — apply the same Ford-Roman inequalities and reach the same class of conclusion, explicitly noting the parallel Pfenning-Ford warp result; and Fewster's lectures derive quantum energy inequalities from first principles as 'remnants of the classical energy conditions' that quantum field theory does satisfy. The wall bound C-0007 therefore no longer rests on one paper: the inequality it uses is a reviewed, independently-applied result, which lifts the single-source downgrade even as the specific 10^2 coefficient remains Pfenning-Ford's.", "trl": 1, "verified_by": [] }, { "asserted_by": "arek", "certainty": "MODERATE", "certainty_reasons": [ { "code": "multiple_independent_sources", "direction": "upgrade" }, { "code": "extrapolation_beyond_regime", "direction": "downgrade" }, { "code": "contested_in_literature", "direction": "downgrade" } ], "challenged_by": [], "contradicts": [], "created_at": "2026-08-07T13:08:48Z", "depends_on": [ "C-0009" ], "derivation_refs": [], "epistemic_status": "peer_reviewed_contested", "evidence_ids": [ "E-0042", "E-0043", "E-0044" ], "id": "C-0026", "modality": "interpretation", "note": "The wall chart's 'open door' now has two named routes, both beyond standard GR+QFT: (1) non-minimal scalar coupling softening the QI (C-0024); (2) modified gravity redefining the classical energy conditions (this claim). Independent recomputation would require a Bach-tensor implementation in numgr — schedulable, filed as a new issue.", "regime": { "assumptions": [ "Conformal (Weyl) Gravity, a fourth-order theory based on the conformal action, NOT standard general relativity", "the Hartle shaping function rather than Alcubierre's original", "'no exotic matter' is a statement about the Eulerian T^00 being non-negative; all-observer WEC is not demonstrated and DEC is conceded to be violated" ], "invalid_outside": "standard general relativity, under which C-0001/C-0006 show the density is non-positive; and any test of the full WEC over boosted observers, which the paper does not perform", "metric_family": "other", "metric_family_note": "Alcubierre metric evaluated under Conformal Gravity field equations (Bach tensor source)" }, "status": "DRAFT", "supports": [], "text": "A concrete escape from the negative-energy requirement exists in the corpus, but only by leaving standard general relativity. Varieschi & Burstein (2012) recompute the Alcubierre metric in Conformal Gravity — a fourth-order theory whose field equations replace Einstein's — and find that with the Hartle shaping function the Eulerian energy density T^00 is non-negative, so no exotic matter is needed. The result is stated by its authors as strictly conditional: 'if CG is the correct extension of GR'. Two limitations the corpus makes visible: conformal gravity is a speculative alternative to GR, not the accepted theory; and the positivity demonstrated is of the Eulerian T^00, the same one-observer quantity Santiago-Schuster-Visser showed is necessary but not sufficient for the full weak energy condition, while the paper itself concedes the dominant energy condition is violated.", "trl": 1, "verified_by": [] } ], "sources": [ { "added_at": "2026-08-06T15:22:23Z", "added_by": "klaudiusz", "authors": [ "Jessica Santiago", "Sebastian Schuster", "Matt Visser" ], "fulltext": { "acquired": true, "canonical_sha256": "8964eabea56ff77a513c73a93ddae1064432728df213c87a9c39f0d712d0bca4", "canonicalizer": "pdb-canon/1.1", "chars": 60483, "route": "arxiv-eprint-latex" }, "id": "S-0001", "ids": { "arxiv": "2105.03079", "arxiv_version": 2, "doi": "10.1103/PhysRevD.105.064038" }, "refereed": true, "retraction": { "checked_at": "2026-08-07T10:30:18Z", "checked_by": [ "crossref.update-to", "crossref.updated-by", "arxiv.withdrawal" ], "status": "clean" }, "source_tier": "primary", "title": "Generic warp drives violate the null energy condition", "type": "journal-article", "venue_class": "peer_reviewed_indexed", "year": 2022 }, { "added_at": "2026-08-06T15:22:23Z", "added_by": "klaudiusz", "authors": [ "Miguel Alcubierre" ], "fulltext": { "acquired": true, "canonical_sha256": "f487c5a4082114b7e22821442347ffbaa7b56c96307724328bd45d3792b315e5", "canonicalizer": "pdb-canon/1.1", "chars": 12007, "route": "arxiv-eprint-latex" }, "id": "S-0002", "ids": { "arxiv": "gr-qc/0009013", "arxiv_version": 1, "doi": "10.1088/0264-9381/11/5/001" }, "refereed": true, "retraction": { "checked_at": "2026-08-07T10:30:18Z", "checked_by": [ "crossref.update-to", "crossref.updated-by", "arxiv.withdrawal" ], "status": "clean" }, "source_tier": "primary", "title": "The warp drive: hyper-fast travel within general relativity", "type": "journal-article", "venue_class": "peer_reviewed_indexed", "year": 1994 }, { "added_at": "2026-08-07T06:30:11Z", "added_by": "klaudiusz", "authors": [ "An T. Le" ], "fulltext": { "acquired": true, "canonical_sha256": "2d8763bfe07a1f7e2279a4a6ff75dc6d0d896fef998024ce64b4c28b6771fd1d", "canonicalizer": "pdb-canon/1.1", "chars": 89536, "route": "arxiv-eprint-latex" }, "id": "S-0003", "ids": { "arxiv": "2602.18023", "arxiv_version": 4 }, "refereed": false, "retraction": { "checked_at": "2026-08-07T10:30:18Z", "checked_by": [ "arxiv.withdrawal" ], "status": "clean" }, "source_tier": "primary", "title": "Observer-robust energy condition verification for warp drive spacetimes", "type": "preprint", "venue_class": "preprint", "year": 2026 }, { "added_at": "2026-08-07T06:30:14Z", "added_by": "klaudiusz", "authors": [ "An T. Le" ], "fulltext": { "acquired": true, "canonical_sha256": "08d7340db08f49d25b757a6c81c911543638ea6e17ed6e9d3715edc8d1ca0256", "canonicalizer": "pdb-canon/1.1", "chars": 60840, "route": "arxiv-eprint-latex" }, "id": "S-0004", "ids": { "arxiv": "2605.25417", "arxiv_version": 2 }, "refereed": false, "retraction": { "checked_at": "2026-08-07T10:30:21Z", "checked_by": [ "arxiv.withdrawal" ], "status": "clean" }, "source_tier": "primary", "title": "On the boundary cost of source-consistent warp shells", "type": "preprint", "venue_class": "preprint", "year": 2026 }, { "added_at": "2026-08-07T06:30:18Z", "added_by": "klaudiusz", "authors": [ "An T. Le" ], "fulltext": { "acquired": true, "canonical_sha256": "c5c38eb634a690e5d631e9462dc2e4388170c762293d2a9b60f0e86468ba5fb8", "canonicalizer": "pdb-canon/1.1", "chars": 218034, "route": "arxiv-eprint-latex" }, "id": "S-0005", "ids": { "arxiv": "2606.22531", "arxiv_version": 3 }, "refereed": false, "retraction": { "checked_at": "2026-08-07T10:30:24Z", "checked_by": [ "arxiv.withdrawal" ], "status": "clean" }, "source_tier": "primary", "title": "Steering a warp drive without exotic matter", "type": "preprint", "venue_class": "preprint", "year": 2026 }, { "added_at": "2026-08-07T07:02:47Z", "added_by": "klaudiusz", "authors": [ "L. H. Ford", "Thomas A. 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Ford" ], "fulltext": { "acquired": true, "canonical_sha256": "713ee65eda5e2c853cc6bb5dff2617c9baa704b3a93e9675006efbc4bc82ad64", "canonicalizer": "pdb-canon/1.1", "chars": 19555, "route": "arxiv-eprint-latex" }, "id": "S-0007", "ids": { "arxiv": "gr-qc/9702026", "arxiv_version": 3, "doi": "10.1088/0264-9381/14/7/011" }, "note": "registries disagree on the title: {\"arxiv.export\": \"The unphysical nature of \\\"Warp Drive\\\"\", \"doi.org\": \"The unphysical nature of `warp drive'\"}", "refereed": true, "retraction": { "checked_at": "2026-08-07T10:30:30Z", "checked_by": [ "crossref.update-to", "crossref.updated-by", "arxiv.withdrawal" ], "status": "clean" }, "source_tier": "primary", "title": "The unphysical nature of \"Warp Drive\"", "type": "journal-article", "venue_class": "peer_reviewed_indexed", "year": 1997 }, { "added_at": "2026-08-07T07:46:17Z", "added_by": "klaudiusz", "authors": [ "Shaun D. B. Fell", "Lavinia Heisenberg" ], "fulltext": { "acquired": true, "canonical_sha256": "7b147718571ffb84c5bfa2049bf1a404daaa59a5eb0966e4aff81cad72ba5833", "canonicalizer": "pdb-canon/1.1", "chars": 34864, "route": "arxiv-eprint-latex" }, "id": "S-0008", "ids": { "arxiv": "2104.06488", "arxiv_version": 4, "doi": "10.1088/1361-6382/ac0e47" }, "refereed": true, "retraction": { "checked_at": "2026-08-07T10:30:33Z", "checked_by": [ "crossref.update-to", "crossref.updated-by", "arxiv.withdrawal" ], "status": "clean" }, "source_tier": "primary", "title": "Positive Energy Warp Drive from Hidden Geometric Structures", "type": "journal-article", "venue_class": "peer_reviewed_indexed", "year": 2021 }, { "added_at": "2026-08-07T07:46:20Z", "added_by": "klaudiusz", "authors": [ "Francisco S. N. 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J. Boffin" ], "fulltext": { "acquired": true, "canonical_sha256": "89bfacb1a6fbb466c9709ad9b644c865731cf2bb0566db0e4d97adbce4c03397", "canonicalizer": "pdb-canon/1.1", "chars": 12004, "route": "arxiv-eprint-latex" }, "id": "S-0012", "ids": { "arxiv": "1601.01636", "arxiv_version": 1, "doi": "10.1051/0004-6361/201527859" }, "note": "registries disagree on the title: {\"arxiv.export\": \"Parallax and masses of alpha Centauri revisited\", \"doi.org\": \"Parallax and masses ofαCentauri revisited\"}", "refereed": true, "retraction": { "checked_at": null, "checked_by": [], "status": "unchecked" }, "source_tier": "primary", "title": "Parallax and masses of alpha Centauri revisited", "type": "journal-article", "venue_class": "peer_reviewed_indexed", "year": 2016 }, { "added_at": "2026-08-07T12:27:33Z", "added_by": "klaudiusz", "authors": [ "Erik W. Lentz" ], "fulltext": { "acquired": true, "canonical_sha256": "c68819660e235df05e939c91b23b8b432102a8b3721f8690bc7695dc8b2d108e", "canonicalizer": "pdb-canon/1.1", "chars": 23651, "route": "arxiv-eprint-latex" }, "id": "S-0013", "ids": { "arxiv": "2006.07125", "arxiv_version": 2 }, "refereed": false, "retraction": { "checked_at": null, "checked_by": [], "status": "unchecked" }, "source_tier": "primary", "title": "Breaking the Warp Barrier: Hyper-Fast Solitons in Einstein-Maxwell-Plasma Theory", "type": "preprint", "venue_class": "preprint", "year": 2020 }, { "added_at": "2026-08-07T12:27:36Z", "added_by": "klaudiusz", "authors": [ "Alexey Bobrick", "Gianni Martire" ], "fulltext": { "acquired": true, "canonical_sha256": "613fd66757ab2586197c91507d770b13c7562905736ad3a227693dd1979e1226", "canonicalizer": "pdb-canon/1.1", "chars": 66175, "route": "arxiv-eprint-latex" }, "id": "S-0014", "ids": { "arxiv": "2102.06824", "arxiv_version": 2, "doi": "10.1088/1361-6382/abdf6e" }, "refereed": true, "retraction": { "checked_at": null, "checked_by": [], "status": "unchecked" }, "source_tier": "primary", "title": "Introducing Physical Warp Drives", "type": "journal-article", "venue_class": "peer_reviewed_indexed", "year": 2021 }, { "added_at": "2026-08-07T12:27:39Z", "added_by": "klaudiusz", "authors": [ "Jared Fuchs", "Christopher Helmerich", "Alexey Bobrick", "Luke Sellers", "Brandon Melcher", "Gianni Martire" ], "fulltext": { "acquired": true, "canonical_sha256": "1cea4e851dc6548dbbb2144012a5d91454ea5cd716c72a53f912b754aac48871", "canonicalizer": "pdb-canon/1.1", "chars": 41970, "route": "arxiv-eprint-latex" }, "id": "S-0015", "ids": { "arxiv": "2405.02709", "arxiv_version": 1, "doi": "10.1088/1361-6382/ad26aa" }, "refereed": true, "retraction": { "checked_at": null, "checked_by": [], "status": "unchecked" }, "source_tier": "primary", "title": "Constant Velocity Physical Warp Drive Solution", "type": "journal-article", "venue_class": "peer_reviewed_indexed", "year": 2024 }, { "added_at": "2026-08-07T12:31:20Z", "added_by": "klaudiusz", "authors": [ "Christopher J. Fewster" ], "fulltext": { "acquired": true, "canonical_sha256": "13bf911f214168b29664ad1a352d92f83fd5c5b89fde57010f7b5e9fc2c864c5", "canonicalizer": "pdb-canon/1.1", "chars": 73634, "route": "arxiv-eprint-latex" }, "id": "S-0016", "ids": { "arxiv": "1208.5399", "arxiv_version": 1 }, "refereed": false, "retraction": { "checked_at": null, "checked_by": [], "status": "unchecked" }, "source_tier": "primary", "title": "Lectures on quantum energy inequalities", "type": "preprint", "venue_class": "preprint", "year": 2012 }, { "added_at": "2026-08-07T12:31:24Z", "added_by": "klaudiusz", "authors": [ "Allen E. Everett", "Thomas A. Roman" ], "fulltext": { "acquired": true, "canonical_sha256": "e8908276ad41c854bde9c6d226bb2a06ef3771e3beaf4ac3d166a7f40a2f70a4", "canonicalizer": "pdb-canon/1.1", "chars": 37518, "route": "arxiv-eprint-latex" }, "id": "S-0017", "ids": { "arxiv": "gr-qc/9702049", "arxiv_version": 1, "doi": "10.1103/PhysRevD.56.2100" }, "note": "registries disagree on the title: {\"arxiv.export\": \"A Superluminal Subway: The Krasnikov Tube\", \"doi.org\": \"Superluminal subway: The Krasnikov tube\"}", "refereed": true, "retraction": { "checked_at": null, "checked_by": [], "status": "unchecked" }, "source_tier": "primary", "title": "A Superluminal Subway: The Krasnikov Tube", "type": "journal-article", "venue_class": "peer_reviewed_indexed", "year": 1997 }, { "added_at": "2026-08-07T13:07:41Z", "added_by": "klaudiusz", "authors": [ "Gabriele U. Varieschi", "Zily Burstein" ], "fulltext": { "acquired": true, "canonical_sha256": "3c2273b201b168ebb53e9bc251bc55c815bd8831fd88f13d0b997bba22376f5e", "canonicalizer": "pdb-canon/1.1", "chars": 28968, "route": "arxiv-eprint-latex" }, "id": "S-0018", "ids": { "arxiv": "1208.3706", "arxiv_version": 1, "doi": "10.1155/2013/482734" }, "refereed": true, "retraction": { "checked_at": null, "checked_by": [], "status": "unchecked" }, "source_tier": "primary", "title": "Conformal Gravity and the Alcubierre Warp Drive Metric", "type": "journal-article", "venue_class": "peer_reviewed_indexed", "year": 2013 } ], "challenges": [ { "artifacts": [], "at": "2026-08-06T19:25:18Z", "attack_type": "A3_span_overreach", "attempt": "Tried to show the claim says more than its spans do. The claim attributes the negative energy density to Eulerian observers, and the quote itself does not name them — it says only 'this expression is everywhere negative'. Checked the extracted context_before: it reads 'uses the fact that the four-velocity of the Eulerian observers is given by: then one can show that these observers will see an energy density given by:', so the attribution is present in the source immediately before the span and is not imported by the claim. Also checked 'everywhere negative' against the quote verbatim rather than paraphrased. No overreach found.", "by": "straz", "claim_id": "C-0001", "evidence_ids": [ "E-0001", "E-0002" ], "id": "X-0001", "outcome": "SURVIVED", "resulting_claim_ids": [], "search_ids": [] }, { "artifacts": [ "compute/eq_energy_density_sign.py" ], "at": "2026-08-06T19:26:53Z", "attack_type": "A2_recomputation", "attempt": "Recomputed the sign claim from the equation instead of from prose about the equation. pdb-canon strips mathematics, so the corpus copy reads 'these observers will see an energy density given by:' followed by nothing; the expression was lifted from corpus/S-0002/body.tex and checked symbolically. It is -(1/8pi)(v_s^2 rho^2)/(4 r_c^2)(df/dr_s)^2: every varying factor appears squared, so the density is NON-POSITIVE everywhere, and it is exactly ZERO at rho = 0 (the axis of motion) and wherever df/dr_s = 0, which is both inside and outside the bubble wall for any shape function flat there. The claim said 'everywhere-negative'. That is the paper's own wording and the equation does not support it. The energy-condition violation itself stands, because a strictly negative density anywhere is enough to violate WEC and DEC.", "by": "straz", "claim_id": "C-0001", "evidence_ids": [ "E-0001" ], "id": "X-0002", "note": "Refutes the wording, not the physics. Corrected claim text recorded via update_field.", "outcome": "REFUTED", "resulting_claim_ids": [ "C-0001" ], "search_ids": [] }, { "artifacts": [], "at": "2026-08-06T19:27:09Z", "attack_type": "A1_counter_source", "attempt": "Attacked the epistemic standing rather than the content. C-0002 was recorded as peer_reviewed_consensus. Its own source contradicts the label: the extracted context of E-0004 reads 'Three recent articles have argued for the existence of physically reasonable positive-energy warp drive configurations, either satisfying the weak energy condition (WEC), or minimizing violations thereof', and S-0001 exists precisely as a rebuttal to them. A position that a 2022 Physical Review D paper had to be written to defend is contested, not consensus. The NEC result itself survives on E-0003 and E-0008; the label overstates how settled the question is, and epistemic_status is exactly the field a reader uses to decide how hard to look for the other side.", "by": "straz", "claim_id": "C-0002", "evidence_ids": [ "E-0003", "E-0004" ], "id": "X-0003", "note": "Refutes the label, not the theorem.", "outcome": "REFUTED", "resulting_claim_ids": [ "C-0002" ], "search_ids": [] }, { "artifacts": [], "at": "2026-08-06T19:27:09Z", "attack_type": "A4_unstated_assumption", "attempt": "Attacked the time index. C-0003 asserts what the peer-reviewed literature holds 'as of 2022' and rests entirely on one 2022 paper's characterisation of its own field. Two problems, neither resolvable from the corpus. First, a paper describing the consensus it argues against is an interested witness. Second, and worse for a claim written in 2026: nothing here covers 2022 to 2026, no search of the intervening literature has been run, so the claim's date is the date of its evidence rather than the date of the field. INSUFFICIENT_EVIDENCE. The queries that would resolve it: INSPIRE-HEP citations of S-0001 restricted to 2022 onward, plus an arXiv gr-qc search for warp drive AND (energy condition OR NEC) over the same window, both logged to searches.ndjson including a null result if it is null.", "by": "straz", "claim_id": "C-0003", "evidence_ids": [ "E-0004" ], "id": "X-0004", "outcome": "REFUTED", "resulting_claim_ids": [ "C-0003" ], "search_ids": [ "Q-0001" ] }, { "artifacts": [ "compute/verify_energy_density.py" ], "at": "2026-08-07T06:49:58Z", "attack_type": "A2_recomputation", "attempt": "Attacked the reading by trying to make a different one work. Built the extrinsic curvature from the paper's eq. 7 with a general shape function, contracted it through the Hamiltonian constraint with R^(3) = 0 (valid because eq. 1 gives flat spatial slices), and compared the result against the published expression under four candidate readings of r_c: the spherical radius r_s, the bubble radius R, the perpendicular distance rho, and the axial distance x. Only r_s gives a zero residual; the other three leave residuals that are explicitly printed rather than summarised. The derivation never uses the tanh profile, so the identification is not an artefact of the shape function.", "by": "straz", "claim_id": "C-0006", "evidence_ids": [ "E-0012" ], "id": "X-0005", "outcome": "SURVIVED", "resulting_claim_ids": [], "search_ids": [] }, { "artifacts": [ "compute/quantum_inequality.py" ], "at": "2026-08-07T07:05:36Z", "attack_type": "A2_recomputation", "attempt": "Tried to break the published figure by recomputing it from the paper's own inputs rather than quoting it. Took the wall bound from eq. 22 and the energy expression from eq. 26, evaluated the integral exactly rather than in the thin-wall approximation, and compared. Got 3.47e20 galaxy masses against the stated 3e20 — a ratio of 1.157, which is inside the order of magnitude the paper quotes it at. Also checked the prefactor: eq. 26 uses -1/12, which is the constant this programme derived independently from the Hamiltonian constraint before this paper was in the corpus, and the paper never says where its own constant comes from, so the agreement is not circular. The remaining difference between the two calculations is a factor of exactly 3/2 traced to the shape function: a linear ramp carries constant maximal slope across the wall, the tanh profile does not. Verified numerically as 1.5000, so it is a property of the profiles and not an error.", "by": "straz", "claim_id": "C-0008", "evidence_ids": [ "E-0013", "E-0014", "E-0016" ], "id": "X-0006", "outcome": "SURVIVED", "resulting_claim_ids": [], "search_ids": [] }, { "artifacts": [ "compute/vdb_pricing.py" ], "at": "2026-08-07T08:03:30Z", "attack_type": "A2_recomputation", "attempt": "Recomputed the construction region by region rather than trusting the paper. Region IV is pure Alcubierre at R=3e-15 m, so the existing closed form applies with no VDB-specific code: -6.25e29 kg against his -6.3e29, ratio 0.992. Region II was derived from scratch: the three-Ricci of the conformally flat static slice via explicit Christoffel summation, rho = R3/16pi, integrated with the proper volume element B^3 r^2 dr under two unrelated C2 profiles at his stated parameters. Total comes out ~1e30 kg for both profiles — solar-mass scale, confirming the ~32-order reduction. What failed to reproduce is his -1.4e30/+4.9e30 sign split: it is profile-dependent, and the half-cosine gives zero negative transition energy. The headline survives; the decomposition is an artefact of an unstated choice.", "by": "straz", "claim_id": "C-0010", "evidence_ids": [ "E-0017" ], "id": "X-0007", "outcome": "SURVIVED", "resulting_claim_ids": [ "C-0013" ], "search_ids": [] }, { "artifacts": [], "at": "2026-08-07T08:53:48Z", "attack_type": "A1_counter_source", "attempt": "Attacked the significance of the opening rather than its text. C-0011 correctly states that the Santiago-Schuster-Visser theorem does not cover the Van Den Broeck spacetime. Searched the 2026 corpus for a direct check that fills the gap and found one: S-0003 certifies the Van Den Broeck walls as Hawking-Ellis Type IV and energy-condition violating for all observers — an explicit all-observer realization of the SSV conclusion on the very construction the theorem missed. The counter-source is a zero-citation arXiv preprint by a single author, unrefereed, so it cannot refute the claim on its own. INCONCLUSIVE pending an independent recomputation of S-0003's Type analysis on the VdB wall, which our machinery can run and which is now scheduled.", "by": "straz", "claim_id": "C-0011", "evidence_ids": [ "E-0028" ], "id": "X-0008", "outcome": "INCONCLUSIVE", "resulting_claim_ids": [ "C-0016" ], "search_ids": [] }, { "artifacts": [ "compute/numgr.py", "compute/hawking_ellis_scan.py" ], "at": "2026-08-07T09:58:41Z", "attack_type": "A2_recomputation", "attempt": "Recomputed the certification that X-0008 could only mark INCONCLUSIVE. Built a numerical Einstein tensor from scratch (fourth-order stencils, comoving static form) and REFUSED to use it until it passed three gates: Minkowski flat to 1e-27, the Alcubierre Eulerian density against the analytic formula independently derived in C-0006 to 5e-9 relative, and Schwarzschild vacuum to noise. Then classified the mixed stress-energy across the wall at v_s = 0.5 on a cos-theta-uniform grid at two sigma*R scales: 99.7 and 90.6 percent Type IV, bracketing S-0003's 87-99. Checked velocity dependence (100/90.6/86.1 percent at v = 0.1/0.5/0.9) and the VdB B-transition (10/10 Type I, as a static diagonal region must be). What this refutes is not C-0011's text — the SSV theorem still does not cover Van Den Broeck — but its recorded significance as 'the most load-bearing opening in the corpus': the VdB f-wall is metric-identical to the Alcubierre wall, its stress-energy has no rest frame for 87-99 percent of the wall, and no observer exists for whom its energy density is even defined, let alone positive. The opening closes by direct computation rather than by theorem coverage.", "by": "straz", "claim_id": "C-0011", "evidence_ids": [ "E-0028" ], "id": "X-0009", "outcome": "REFUTED", "resulting_claim_ids": [ "C-0018" ], "search_ids": [] }, { "artifacts": [ "compute/thrust_profile.py", "tests/test_mission_sims.py" ], "at": "2026-08-07T10:49:27Z", "attack_type": "A2_recomputation", "attempt": "Attacked the impulsive-burn assumption by recomputing the mission under continuous constant-proper-acceleration profiles (accelerate-flip-brake), with the trajectory integrated two independent ways — closed form and a blind RK4 that knows no hyperbolic functions — agreeing to ~1e-4. If finite thrust had beaten the impulsive numbers, C-0014's 'floors' framing would be refuted. It did not: at comparable trip time (0.03 g profile, 48.5 yr Earth) the annihilation bill is 3.34e6 kg against the impulsive 0.2c cruise's 1.25e6 kg at 43.9 yr, and every finite-thrust profile is costlier than the impulsive bound at its own duration. The frontier also confirms the D-T exclusion brutally: at 1 g the D-T mass ratio reaches 1e43 kg. The claim's numbers are floors, exactly as stated.", "by": "straz", "claim_id": "C-0014", "evidence_ids": [], "id": "X-0010", "outcome": "SURVIVED", "resulting_claim_ids": [], "search_ids": [] }, { "artifacts": [ "compute/targeting_sim.py", "tests/test_mission_sims.py" ], "at": "2026-08-07T10:49:27Z", "attack_type": "A2_recomputation", "attempt": "Attacked the ordering ('catalogue first, orbit second, relativity third') by building the full targeting computer and measuring what actually moves the aim point. With astrometry fetched live, the barycentre velocity mass-weighted to cancel the orbital wobble exactly, and the 3D Keplerian offset added, the total aim-vs-image correction is 188 au at 0.2c and 328 au at 0.1c — fully computable, hence not an error at all once modelled. The residual uncertainty is then the catalogue disagreement (4673 au of distance, C-0017's headline), which exceeds the entire computable correction by an order of magnitude and the relativistic clock terms by more. The claimed ordering survives with its margins quantified.", "by": "straz", "claim_id": "C-0017", "evidence_ids": [], "id": "X-0011", "outcome": "SURVIVED", "resulting_claim_ids": [], "search_ids": [] }, { "artifacts": [ "compute/ab_orbit.py", "compute/targeting_sim.py", "tests/test_ab_orbit.py" ], "at": "2026-08-07T10:49:27Z", "attack_type": "A2_recomputation", "attempt": "Attacked the 24-35 au figure from two directions. Robustness: the finite-difference velocity stencil in linear_extrapolation_error_au was varied across two orders of magnitude of step with no change in the reported errors, and the orbit solver's closure after one period is 2.4e-13 au, so the numbers are not integration artefacts. Consistency: the independent targeting simulator, which embeds the same orbit in full 3D with the barycentre moving, attributes 32.8 au to orbital motion over the 26.3-year image-age-plus-travel span of the 0.2c mission — inside the claim's 24-35 au band for comparable spans. Two artifacts, one number.", "by": "straz", "claim_id": "C-0019", "evidence_ids": [], "id": "X-0012", "outcome": "SURVIVED", "resulting_claim_ids": [], "search_ids": [] }, { "artifacts": [ "compute/hawking_ellis_scan.py", "tests/test_hawking_ellis.py" ], "at": "2026-08-07T10:49:27Z", "attack_type": "A2_recomputation", "attempt": "Attacked the Type IV certification as a possible numerical artefact. The classification fraction at v_s = 0.5, sigma*R = 50 is 91.1 percent and IDENTICAL across finite-difference steps of 5e-4, 1e-3 and 2e-3 — three settings, same 82/90 points — and the off-axis wall classification is stable across detector tolerances 1e-5 to 1e-7, with the imaginary pair at 6-8 percent of the eigenvalue scale, four orders above the noise floor the Minkowski and Schwarzschild gates established. A stencil artefact would move with the stencil; this does not.", "by": "straz", "claim_id": "C-0018", "evidence_ids": [], "id": "X-0013", "outcome": "SURVIVED", "resulting_claim_ids": [], "search_ids": [] }, { "artifacts": [ "compute/attack_energy_axis.py", "tests/test_energy_budget.py" ], "at": "2026-08-07T11:12:57Z", "attack_type": "A3_span_overreach", "attempt": "Attacked the scope: if the exponents in |E| ~ v^2 R^2 / d were properties of the tanh profile the claim is scoped to, the law would be decoration. Recomputed the radial integral under an unrelated C2 quintic smoothstep by blind midpoint summation: the fitted exponents are 2.00000 in R and -1.00000 in d — profile-generic to five decimals — while the constant is profile-dependent (the smoothstep wall costs 4.29x the tanh wall at equal width). The claim's self-restriction to tanh is therefore honest and conservative: no smooth profile tested is cheaper. No overreach found.", "by": "straz", "claim_id": "C-0004", "evidence_ids": [], "id": "X-0014", "outcome": "SURVIVED", "resulting_claim_ids": [], "search_ids": [] }, { "artifacts": [ "compute/attack_energy_axis.py", "tests/test_energy_budget.py" ], "at": "2026-08-07T11:12:57Z", "attack_type": "A4_unstated_assumption", "attempt": "Hunted for a convention smuggled under 'wall thickness'. A reader who takes d to mean the 10-90 transition width — the laboratory convention — rather than 1/sigma gets a wall 2.1972x thinner at the same words (factor found by bisection on the exact shape function) and a figure of 8.22e32 kg instead of 3.74e32: the third digit of the claim lives in the convention. The claim survives because the regime of C-0004, which it depends on, states 'wall thickness identified as 1/sigma' explicitly. Without that line this attack would have been a refutation.", "by": "straz", "claim_id": "C-0005", "evidence_ids": [], "id": "X-0015", "outcome": "SURVIVED", "resulting_claim_ids": [], "search_ids": [] }, { "artifacts": [ "compute/attack_energy_axis.py", "tests/test_energy_budget.py" ], "at": "2026-08-07T11:12:57Z", "attack_type": "A4_unstated_assumption", "attempt": "Attacked the coefficient: the 10^2 in Delta <= 10^2 v_b L_Planck is not a constant of nature. S-0007's own eq. 19 introduces the sampling-time parameter alpha with 0 < alpha << 1, and eq. 21 (E-0029, cited by hash) gives Delta <= (3/4)sqrt(3/pi) v_b/alpha^2 = 0.733/alpha^2 — the published 10^2 is alpha = 0.1. Swept alpha: at 0.01, a hundred-fold weaker sampling assumption, the bound loosens to ~7300 L_P and the 100 m bubble still requires 4.7e18 galaxy masses. The coefficient moves by two orders; the verdict moves by two orders and remains eighteen orders beyond absurd. The claim's wording ('at most about 10^2') plus its regime, which carries the sampling-time choice as an assumption, survive.", "by": "straz", "claim_id": "C-0007", "evidence_ids": [ "E-0029" ], "id": "X-0016", "outcome": "SURVIVED", "resulting_claim_ids": [], "search_ids": [] }, { "artifacts": [ "compute/attack_energy_axis.py", "compute/quantum_inequality.py" ], "at": "2026-08-07T11:12:57Z", "attack_type": "A3_span_overreach", "attempt": "Attacked the synthesis for overreach beyond its parents. Its strongest sentence — even with the quantum inequality set aside and a 1 m wall allowed, the requirement is of order a solar mass of negative energy — was stress-tested against both sensitivities found on this axis: under the 10-90 wall convention (2.20x) it becomes 1.2 solar masses, and under the costlier quintic profile 2.4 — 'of order a solar mass' holds across every tested reading. The sign argument (no energy source produces negative energy density) rests on C-0006's derived expression, which is GREEN. No overreach found.", "by": "straz", "claim_id": "C-0009", "evidence_ids": [], "id": "X-0017", "outcome": "SURVIVED", "resulting_claim_ids": [], "search_ids": [] }, { "artifacts": [], "at": "2026-08-07T12:18:53Z", "attack_type": "A3_span_overreach", "attempt": "Independent auditor (wf_1946b5d7-102) attacked the scope word 'generic' and the proof's completeness. Verified against S-0001 offsets 8600-41524: 'generic' means the generic Natario class exactly as the regime lists; the paper's own 'delicate point' hedge at offset 39078 is resolved via the cited Pfenning-Ford analysis and the proof concluded at 41366 needing only localization, not zero ADM mass — so the regime is conservative. Cross-check: S-0003 (2026) treats the result as established. Residual accepted and applied: the regime's 'modified gravity does not rescue' was stronger than the source's 'very strong constraints' wording — softened by update_field.", "by": "redteam", "claim_id": "C-0002", "evidence_ids": [], "id": "X-0018", "outcome": "SURVIVED", "resulting_claim_ids": [], "search_ids": [] }, { "artifacts": [], "at": "2026-08-07T12:18:53Z", "attack_type": "A3_span_overreach", "attempt": "Independent auditor attacked whether the claim overstates the SSV concession. Adjacency verified at offset 49737: the concession is SSV's own conclusion, not a strawman; the following sentence supports both remaining components. Suppression check: exactly one 'Broeck' occurrence in S-0001, so no contrary passage is hidden. The superlative 'the strongest recent no-go' is editorial but unopposed in the corpus. Residual applied to the note: SSV's adjacent caveat 'there are other problematic issues with both of these models' now quoted there.", "by": "redteam", "claim_id": "C-0011", "evidence_ids": [], "id": "X-0019", "outcome": "SURVIVED", "resulting_claim_ids": [], "search_ids": [] }, { "artifacts": [], "at": "2026-08-07T12:18:53Z", "attack_type": "A3_span_overreach", "attempt": "Independent auditor read S-0011 in full, re-found E-0020/E-0021 at their offsets, and audited for hedge cherry-picking: the intro independently states the negative verdict without 'seem' (offset 986), local hedges are subsidiary, and the authorship/date premise checks mechanically (gr-qc/9905084 May 1999, gr-qc/9906050 June 1999, same author). Residual accepted and applied: the regime mis-scoped the source — S-0011's central analysis is performed on the ORIGINAL Alcubierre metric, not the B^2-modified one — fixed by update_field.", "by": "redteam", "claim_id": "C-0012", "evidence_ids": [], "id": "X-0020", "outcome": "SURVIVED", "resulting_claim_ids": [], "search_ids": [] }, { "artifacts": [ "compute/vdb_pricing.py", "tests/test_vdb_pricing.py" ], "at": "2026-08-07T12:19:36Z", "attack_type": "A2_recomputation", "attempt": "Independent auditor found the premise false and the computation wrong. The interpolating profile IS stated in S-0010 (body.tex offset 12042, equation labelled B, 'let us choose n=80' at 12199); it was invisible to the tooling because the canonicaliser strips inline math and the pre-PDB-26 extractor missed macro-wrapped equations. Plugging the stated profile into the module's own unmodified integrator reproduces the published split to 1% (-1.380e30 / +4.865e30 vs -1.4e30 / +4.9e30; boundary w = 0.9815 vs 0.981) — verified by the lead before this record was written. The 'half-cosine counterexample' is C^1 only, outside the paper's stated twice-differentiable class, so it could not witness in-class profile dependence. The headline half of C-0013 (region IV to 1%, solar-mass totals, ~32-order reduction) survives and is carried by the superseding claim.", "by": "redteam", "claim_id": "C-0013", "evidence_ids": [ "E-0032" ], "id": "X-0021", "outcome": "REFUTED", "resulting_claim_ids": [ "C-0020" ], "search_ids": [] }, { "artifacts": [], "at": "2026-08-07T12:19:36Z", "attack_type": "A3_span_overreach", "attempt": "Independent auditor re-found E-0023/24/25 at their offsets, then read one sentence further: S-0008 offset 26615 reads 'it may still be possible to satisfy the WEC in the presented configurations too, given sufficient modifications' — the claim's conjunct 'concedes that no modification removes those regions' quoted a concession out of the frame that immediately reopens it, the mirror image of the strawman failure the hedge scan catches. The scan only looked at context_before; the reopening lived in context_after, on the record all along. Control extended (reopening-frame scan), claim superseded with both sentences carried verbatim.", "by": "redteam", "claim_id": "C-0015", "evidence_ids": [ "E-0030" ], "id": "X-0022", "outcome": "REFUTED", "resulting_claim_ids": [ "C-0021" ], "search_ids": [] }, { "artifacts": [], "at": "2026-08-07T12:19:36Z", "attack_type": "A3_span_overreach", "attempt": "Independent auditor reproduced the zero-citation check live (OpenAlex title.search per paper, all cited_by_count = 0, positive control S-0001 = 45) — that prong stands. The Type-IV conjunct was quoted without the source's own qualifier: S-0003 certifies Van Den Broeck Type IV only ABOVE a Type-I to Type-IV transition at v_s ~ 0.36 (E-0031; the numeric value survives only in main.tex as a macro — another instance of the inline-math-stripping hazard). Blanket 'for all observers' phrasing without the velocity qualifier overreached the source. Superseded with the qualifier carried.", "by": "redteam", "claim_id": "C-0016", "evidence_ids": [ "E-0031" ], "id": "X-0023", "outcome": "REFUTED", "resulting_claim_ids": [ "C-0022" ], "search_ids": [] } ], "evidence": [ { "added_at": "2026-08-06T15:25:00Z", "added_by": "arek", "id": "E-0001", "kind": "direct", "locator": { "char_offset": 10852, "context_after": "In a similar way one can show that the strong energy condition is also violated. We see then that, just as it happens with wormholes, one needs exotic matter to travel faster than the speed of light. However, even if one believes that exot", "context_before": "tive for all\\/ observers. If one calculates the Einstein tensor from the metric (), and uses the fact that the four-velocity of the Eulerian observers is given by: then one can show that these observers will see an energy density given by:", "section": "Sec. 4 (energy conditions)" }, "quote": "The fact that this expression is everywhere negative implies that the weak and dominant energy conditions are violated.", "source_id": "S-0002", "verification": { "against_canonical_sha256": "f487c5a4082114b7e22821442347ffbaa7b56c96307724328bd45d3792b315e5", "match_ratio": 1, "status": "EXACT", "verified_at": "2026-08-07T12:45:00Z", "verified_by": "werys" } }, { "added_at": "2026-08-06T15:25:00Z", "added_by": "arek", "id": "E-0002", "kind": "direct", "locator": { "char_offset": 10457, "context_after": ". Both the weak and the dominant energy conditions require the energy density to be positive for all\\/ observers. If one calculates the Einstein tensor from the metric (), and uses the fact that the four-velocity of the Eulerian observers i", "context_before": "ortion of spacetime. A propulsion mechanism based on such a local distortion of spacetime just begs to be given the familiar name of the \"warp drive\" of science fiction. The metric I have just described has one important drawback, however:", "section": "Sec. 4 (energy conditions)" }, "quote": "it violates all three energy conditions (weak, dominant and strong)", "source_id": "S-0002", "verification": { "against_canonical_sha256": "f487c5a4082114b7e22821442347ffbaa7b56c96307724328bd45d3792b315e5", "match_ratio": 1, "status": "EXACT", "verified_at": "2026-08-07T12:45:00Z", "verified_by": "werys" } }, { "added_at": "2026-08-06T15:25:00Z", "added_by": "arek", "id": "E-0003", "kind": "direct", "locator": { "char_offset": 1400, "context_after": "While warp drives are certainly interesting examples of speculative physics, the violation of the energy conditions, at least within the framework of standard general relativity, is unavoidable. Even in modified gravity, physically reasona", "context_before": "hows that the situation is actually much grimmer than advertised - within the framework adopted by those three papers all physically reasonable warp drives will certainly violate the WEC, and both the strong and dominant energy conditions.", "section": "Abstract" }, "quote": "Under plausible subsidiary conditions the null energy condition is also violated.", "source_id": "S-0001", "verification": { "against_canonical_sha256": "8964eabea56ff77a513c73a93ddae1064432728df213c87a9c39f0d712d0bca4", "match_ratio": 1, "status": "EXACT", "verified_at": "2026-08-07T12:45:00Z", "verified_by": "werys" } }, { "added_at": "2026-08-06T15:25:00Z", "added_by": "arek", "id": "E-0004", "kind": "contextual", "locator": { "char_offset": 2513, "context_after": "Specifically, known results already include: -3pt Alcubierre warp drives have long been known to violate the WEC, and have more recently been shown to also violate the null energy condition (NEC). Nat\\'ario zero-expansion warp drives have", "context_before": "ree recent articles have argued for the existence of \"physically reasonable\" positive-energy warp drive configurations, either satisfying the weak energy condition (WEC), or minimizing violations thereof. (See also the series of articles.)", "section": "Sec. 1 (Introduction)" }, "quote": "These claims are in sharp contrast to the 25-year-old consensus opinion that at least some energy condition violations are necessary for the generation of warp fields.", "source_id": "S-0001", "verification": { "against_canonical_sha256": "8964eabea56ff77a513c73a93ddae1064432728df213c87a9c39f0d712d0bca4", "match_ratio": 1, "status": "EXACT", "verified_at": "2026-08-07T12:45:00Z", "verified_by": "werys" } }, { "added_at": "2026-08-06T19:21:52Z", "added_by": "arek", "id": "E-0005", "kind": "definition", "locator": { "char_offset": 31795, "context_after": ". It is certainly more than sufficient if for large distances, which is in turn certainly true if, which is in turn certainly true if the ADM mass is zero. Vanishing of the ADM mass is certainly the case for Alcubierre's warp drive, and als", "context_before": "y anything more precise about the energy conditions.) Fortunately, the average pressure is reasonably tractable. From equation (), Now, given that we want our warp field to be localizable, to not spread over and affect the whole spacetime,", "section": "Sec. 4 (generic Natario warp drives)" }, "quote": "it is natural to make the assumption that the flow field obeys some sort of fall-off conditions at spatial infinity", "source_id": "S-0001", "verification": { "against_canonical_sha256": "8964eabea56ff77a513c73a93ddae1064432728df213c87a9c39f0d712d0bca4", "match_ratio": 1, "status": "EXACT", "verified_at": "2026-08-07T12:45:00Z", "verified_by": "werys" } }, { "added_at": "2026-08-06T19:21:53Z", "added_by": "arek", "id": "E-0006", "kind": "definition", "locator": { "char_offset": 32009, "context_after": ". Vanishing of the ADM mass is certainly the case for Alcubierre's warp drive, and also for Natario's zero-expansion warp drive, and is a first crude approximation for well-localized warp fields. (We will subsequently significantly weaken t", "context_before": "fect the whole spacetime, it is natural to make the assumption that the flow field obeys some sort of fall-off conditions at spatial infinity. It is certainly more than sufficient if for large distances, which is in turn certainly true if,", "section": "Sec. 4 (generic Natario warp drives)" }, "quote": "which is in turn certainly true if the ADM mass is zero", "source_id": "S-0001", "verification": { "against_canonical_sha256": "8964eabea56ff77a513c73a93ddae1064432728df213c87a9c39f0d712d0bca4", "match_ratio": 1, "status": "EXACT", "verified_at": "2026-08-07T12:45:00Z", "verified_by": "werys" } }, { "added_at": "2026-08-06T19:21:53Z", "added_by": "arek", "id": "E-0007", "kind": "definition", "locator": { "char_offset": 9533, "context_after": "Nat\\'ario metric () in order to distinguish a warp drive from, for instance, the Painlev\\'e-Gullstrand version of Schwarzschild spacetime. The line element () is sufficiently general and explicit to be physically interesting as a warp driv", "context_before": "e Christoffel symbols are C^1- at worst, that is, piecewise once differentiable with at worst step-function discontinuities. Then the Riemann tensor is C^0 at worst, piecewise continuous with at worst delta-function contributions. Finally,", "section": "Sec. 4 (generic Natario warp drives)" }, "quote": "we emphasize the need for at least some subsidiary conditions to be applied to the generic", "source_id": "S-0001", "verification": { "against_canonical_sha256": "8964eabea56ff77a513c73a93ddae1064432728df213c87a9c39f0d712d0bca4", "match_ratio": 1, "status": "EXACT", "verified_at": "2026-08-07T12:45:00Z", "verified_by": "werys" } }, { "added_at": "2026-08-06T19:22:23Z", "added_by": "arek", "hedge_review": { "reason": "the preceding 'assume that' is the authors stating their own localization assumption, which the theorem depends on; it is not a position the paper goes on to reject", "reviewed_at": "2026-08-06T19:23:40Z", "reviewed_by": "werys" }, "id": "E-0008", "kind": "direct", "locator": { "char_offset": 40201, "context_after": "\"restore its asymptotics\" after a warp drive passes through a particular point. A delicate point must be discussed before this proof is called closed and complete: The question regarding what happens to such a geodesic Eulerian observer wh", "context_before": "K increases as it returns to its original value.Since we still have to assume that any contribution to K_ij from the warp drive is sufficiently localized. This, however, is not allowed if the NEC is always satisfied, as given by equation.", "section": "Sec. 6 (asymptotics)" }, "note": "Hedge scan fired on 'assume that'; see hedge_review.", "quote": "This proves that the violation of the NEC is a necessary condition for the spacetime to", "source_id": "S-0001", "verification": { "against_canonical_sha256": "8964eabea56ff77a513c73a93ddae1064432728df213c87a9c39f0d712d0bca4", "match_ratio": 1, "status": "EXACT", "verified_at": "2026-08-07T12:45:00Z", "verified_by": "werys" } }, { "added_at": "2026-08-07T06:23:03Z", "added_by": "arek", "id": "E-0009", "kind": "equation", "locator": { "char_offset": null, "context_after": "It is easy to understand the geometry of our spacetime from the previous expressions. First, from equation () we see that the 3-geometry of the hypersurfaces is always flat. Moreover, the fact that the lapse is given by", "context_before": "1 f R > 0 and > 0 the function f(r)$ approaches very rapidly a \"top hat\" function: With the above definitions, the metric () can be rewritten as:", "equation_index": 5, "section": "Sec. 3 (the metric)" }, "note": "Display equation 5 (\\label{final_metric}), equation environment.", "quote": "d s^2 = - d t^2 + ( d x - v_s f ( r_s ) d t )^2 + d y^2 + d z^2 .", "source_id": "S-0002", "verification": { "against_canonical_sha256": "f487c5a4082114b7e22821442347ffbaa7b56c96307724328bd45d3792b315e5", "match_ratio": 1, "status": "EXACT", "verified_at": "2026-08-07T12:45:00Z", "verified_by": "werys" } }, { "added_at": "2026-08-07T06:23:03Z", "added_by": "arek", "id": "E-0010", "kind": "equation", "locator": { "char_offset": null, "context_after": "with R>0 and sigma>0 arbitrary parameters. Notice that for large sigma the function f(r) approaches very rapidly a \"top hat\" function: With the above definitions, the metric () can be rewritten as: It is easy to understa", "context_before": "We want to find a metric that will \"push\" the spaceship along a trajectory described by an arbitrary function of time x_s (t). A metric that has this property is given by (G = c = 1): where: and where f is the function:", "equation_index": 3, "section": "Sec. 3 (shape function)" }, "note": "Display equation 3, equation environment.", "quote": "f ( r_s ) = \\frac{\\tanh ( \\sigma ( r_s + R ) ) - \\tanh ( \\sigma ( r_s - R ) ) }{ 2 \\tanh ( \\sigma R )} ,", "source_id": "S-0002", "verification": { "against_canonical_sha256": "f487c5a4082114b7e22821442347ffbaa7b56c96307724328bd45d3792b315e5", "match_ratio": 1, "status": "EXACT", "verified_at": "2026-08-07T12:45:00Z", "verified_by": "werys" } }, { "added_at": "2026-08-07T06:23:04Z", "added_by": "arek", "id": "E-0011", "kind": "equation", "locator": { "char_offset": null, "context_after": "Figure shows a graph of theta as a function of x and, in the particular case when sigma = 8 and R =v_s = 1. The center of the perturbation corresponds to the spaceship's position. We clearly see how the volume elements a", "context_before": "not difficult to see that this expression reduces to: The expansion theta of the volume elements associated with the Eulerian observers is given in terms of K_ij as: From this expression it is not difficult to show that:", "equation_index": 9, "section": "Sec. 3 (expansion)" }, "note": "Display equation 9 (\\label{expansion}), equation environment.", "quote": "\\theta = v_s \\frac{x_s}{r_s} \\frac{d f}{d r_s} .", "source_id": "S-0002", "verification": { "against_canonical_sha256": "f487c5a4082114b7e22821442347ffbaa7b56c96307724328bd45d3792b315e5", "match_ratio": 1, "status": "EXACT", "verified_at": "2026-08-07T12:45:00Z", "verified_by": "werys" } }, { "added_at": "2026-08-07T06:23:04Z", "added_by": "arek", "id": "E-0012", "kind": "equation", "locator": { "char_offset": null, "context_after": "The fact that this expression is everywhere negative implies that the weak and dominant energy conditions are violated. In a similar way one can show that the strong energy condition is also violated. We see then that, j", "context_before": "rvers. If one calculates the Einstein tensor from the metric (), and uses the fact that the four-velocity of the Eulerian observers is given by: then one can show that these observers will see an energy density given by:", "equation_index": 16, "section": "Sec. 4 (energy conditions)" }, "note": "Display equation 16, equation environment.", "quote": "T^{\\alpha \\beta} n_{\\alpha} n_{\\beta} = \\alpha^2 T^{ 0 0} = \\frac{1}{8 \\pi} G^{ 0 0} = - \\frac{1}{8 \\pi} \\frac{v_s^2 \\rho^2}{4 {r_c}^2} ( \\frac{d f}{d r_s} )^2 .", "source_id": "S-0002", "verification": { "against_canonical_sha256": "f487c5a4082114b7e22821442347ffbaa7b56c96307724328bd45d3792b315e5", "match_ratio": 1, "status": "EXACT", "verified_at": "2026-08-07T12:45:00Z", "verified_by": "werys" } }, { "added_at": "2026-08-07T07:05:08Z", "added_by": "arek", "id": "E-0013", "kind": "equation", "locator": { "char_offset": null, "context_after": "where is the Planck length. Thus, unless v_b is extremely large, the wall thickness cannot be much above the Planck scale. Typically, the walls of the warp bubble are so thin that the shape function could be considered a", "context_before": "r the sampling time is compared to the minimal radius of curvature. If we insert this into the quantum inequality and use we may neglect the term involving 1-f(rho) to find Now as an example, if we let alpha = 1/10, then", "equation_index": 22, "section": "Sec. 3 (QI restrictions)" }, "note": "Display equation 22 (\\label{eq:wall_thickness}), equation environment.", "quote": "\\Delta \\leq 10^2 v_b L_{Planck} ,", "source_id": "S-0007", "verification": { "against_canonical_sha256": "713ee65eda5e2c853cc6bb5dff2617c9baa704b3a93e9675006efbc4bc82ad64", "match_ratio": 1, "status": "EXACT", "verified_at": "2026-08-07T12:45:00Z", "verified_by": "werys" } }, { "added_at": "2026-08-07T07:05:09Z", "added_by": "arek", "id": "E-0014", "kind": "equation", "locator": { "char_offset": null, "context_after": "For a macroscopically useful warp drive, we want the radius of the bubble to be at least in the range of 100 meters so that we may fit a ship inside. It has been shown in the previous section that the wall thickness is c", "context_before": "approximation to the shape function given by Equation (). When one takes the derivative of this shape function, we find that the contributions to the energy come only from the bubble wall region, and we end up evaluating", "equation_index": 26, "section": "Sec. 4 (total energy)" }, "note": "Display equation 26 (\\label{eq:energy}), eqnarray environment.", "quote": "E &=&- {1\\over 12} v_b^2 \\int_{R-{\\Delta\\over 2}}^{R+{\\Delta\\over 2}} r^2 (- 1 \\over \\Delta )^2 dr\\\\ &=&- {1\\over 12} v_b^2 ( {R^2 \\over\\Delta}+{\\Delta\\over 12} ).", "source_id": "S-0007", "verification": { "against_canonical_sha256": "713ee65eda5e2c853cc6bb5dff2617c9baa704b3a93e9675006efbc4bc82ad64", "match_ratio": 1, "status": "EXACT", "verified_at": "2026-08-07T12:45:00Z", "verified_by": "werys" } }, { "added_at": "2026-08-07T07:05:09Z", "added_by": "arek", "id": "E-0015", "kind": "equation", "locator": { "char_offset": null, "context_after": "Because a typical galaxy has a mass of approximately the energy required for a warp bubble is on the order of This is a fantastic amount of negative energy, roughly ten orders of magnitude greater than the total mass of", "context_before": "section that the wall thickness is constrained by (). If we use this constraint and let the bubble radius be equal to 100 meters, then we may neglect the second term on the right-hand-side of Equation (). It follows that", "equation_index": 27, "section": "Sec. 4 (total energy)" }, "note": "Display equation 27, equation environment.", "quote": "E \\leq -6.2\\times10^{70} v_b L_{Planck} \\sim -6.2\\times10^{65} v_b {\\rm grams}.", "source_id": "S-0007", "verification": { "against_canonical_sha256": "713ee65eda5e2c853cc6bb5dff2617c9baa704b3a93e9675006efbc4bc82ad64", "match_ratio": 1, "status": "EXACT", "verified_at": "2026-08-07T12:45:00Z", "verified_by": "werys" } }, { "added_at": "2026-08-07T07:05:09Z", "added_by": "arek", "id": "E-0016", "kind": "equation", "locator": { "char_offset": null, "context_after": "This is a fantastic amount of negative energy, roughly ten orders of magnitude greater than the total mass of the entire visible universe. If one can violate the quantum inequality restrictions and make a bubble with a w", "context_before": "qual to 100 meters, then we may neglect the second term on the right-hand-side of Equation (). It follows that Because a typical galaxy has a mass of approximately the energy required for a warp bubble is on the order of", "equation_index": 29, "section": "Sec. 4 (total energy)" }, "note": "Display equation 29, equation environment.", "quote": "E \\leq - 3 \\times 10^{20} M_{galaxy} v_b .", "source_id": "S-0007", "verification": { "against_canonical_sha256": "713ee65eda5e2c853cc6bb5dff2617c9baa704b3a93e9675006efbc4bc82ad64", "match_ratio": 1, "status": "EXACT", "verified_at": "2026-08-07T12:45:00Z", "verified_by": "werys" } }, { "added_at": "2026-08-07T07:55:53Z", "added_by": "arek", "id": "E-0017", "kind": "direct", "locator": { "char_offset": 460, "context_after": ". This puts the warp drive in the mass scale of large traversable wormholes. The new geometry satisfies the quantum inequality concerning WEC violations and has the same advantages as the original Alcubierre spacetime. width 5cm 2mm ^dagger", "context_before": "elgium 4cm Abstract I show how a minor modification of the Alcubierre geometry can dramatically improve the total energy requirements for a 'warp bubble' that can be used to transport macroscopic objects. A spacetime is presented for which", "section": "Abstract" }, "quote": "the total negative mass needed is of the order of a few solar masses, accompanied by a comparable amount of positive energy", "source_id": "S-0010", "verification": { "against_canonical_sha256": "5744e51a6e9ee1437ec6997bd0e44d9d7beed600aa69ebd7ed710e65ccc02113", "match_ratio": 1, "status": "EXACT", "verified_at": "2026-08-07T12:45:00Z", "verified_by": "werys" } }, { "added_at": "2026-08-07T07:55:53Z", "added_by": "arek", "id": "E-0018", "kind": "definition", "locator": { "char_offset": 5478, "context_after": ". The most natural way to do this is the following: ds^2 = - dt^2 + B^2(r_s) [(dx - v_s(t) f(r_s) dt)^2 + dy^2 + dz^2]. For simplicity, the velocity v_s will be taken constant. B(r_s) is a twice differentiable function such that, for some a", "context_before": "me drawbacks of the new geometry are discussed. Throughout this note, we will use units such that c=G=hbar=1, except when stated otherwise. A modification of the Alcubierre geometry We will solve the problem of the large negative energy by", "section": "Sec. 2 (the modification)" }, "quote": "keeping the surface area of the warp bubble itself microscopically small, while at the same time expanding the spatial volume inside the bubble", "source_id": "S-0010", "verification": { "against_canonical_sha256": "5744e51a6e9ee1437ec6997bd0e44d9d7beed600aa69ebd7ed710e65ccc02113", "match_ratio": 1, "status": "EXACT", "verified_at": "2026-08-07T12:45:00Z", "verified_by": "werys" } }, { "added_at": "2026-08-07T07:55:53Z", "added_by": "arek", "id": "E-0019", "kind": "direct", "locator": { "char_offset": 660, "context_after": "and has the same advantages as the original Alcubierre spacetime. width 5cm 2mm ^dagger chris.vandenbroeck@fys.kuleuven.ac.be Introduction In recent years, ways of effective superluminal travel (EST) within general relativity have generate", "context_before": "cts. A spacetime is presented for which the total negative mass needed is of the order of a few solar masses, accompanied by a comparable amount of positive energy. This puts the warp drive in the mass scale of large traversable wormholes.", "section": "Abstract" }, "quote": "The new geometry satisfies the quantum inequality concerning WEC violations", "source_id": "S-0010", "verification": { "against_canonical_sha256": "5744e51a6e9ee1437ec6997bd0e44d9d7beed600aa69ebd7ed710e65ccc02113", "match_ratio": 1, "status": "EXACT", "verified_at": "2026-08-07T12:45:00Z", "verified_by": "werys" } }, { "added_at": "2026-08-07T07:55:54Z", "added_by": "arek", "id": "E-0020", "kind": "direct", "locator": { "char_offset": 280, "context_after": ". width 5cm 2mm ^ast vdbroeck@starlab.net Introduction Since Alcubierre published his 'warp drive' spacetime, the proposal has been criticized from various viewpoints by a number of authors. One of the problems, concerning the amount of exo", "context_before": "n the (im)possibility of warp bubbles 1.5cm Chris Van Den Broeck ^ast Physics Division, Starlab Research Boulevard St.-Michel 47, 1040 Brussels, Belgium 4cm Abstract Various objections against Alcubierre's warp drive geometry are reviewed.", "section": "Abstract" }, "quote": "Superluminal warp bubbles seem an unlikely possibility within the framework of general relativity and quantum field theory, although subluminal bubbles may still be possible", "source_id": "S-0011", "verification": { "against_canonical_sha256": "010b825fc736d328444d0e2c153c00210bc9373af858b903da7af3592332fb40", "match_ratio": 1, "status": "EXACT", "verified_at": "2026-08-07T12:45:00Z", "verified_by": "werys" } }, { "added_at": "2026-08-07T07:55:54Z", "added_by": "arek", "id": "E-0021", "kind": "direct", "locator": { "char_offset": 9641, "context_after": ". Due to the absence of horizons, potential problems due to diverging vacuum fluctuations will not arise, and there will be no tachyonic motion of exotic matter. Possibly the geometry can be chosen in such a way that the necessary negative", "context_before": "ved without retaining some unphysical features or introducing new ones, such as high energy densities, curvature radii of the order of the Planck length, and naked singularities. We have limited the discussion to superluminal warp bubbles.", "section": "Conclusion" }, "quote": "Subluminal bubbles are still an open possibility, and it is not inconceivable that microscopic ones might even occur naturally", "source_id": "S-0011", "verification": { "against_canonical_sha256": "010b825fc736d328444d0e2c153c00210bc9373af858b903da7af3592332fb40", "match_ratio": 1, "status": "EXACT", "verified_at": "2026-08-07T12:45:00Z", "verified_by": "werys" } }, { "added_at": "2026-08-07T07:55:54Z", "added_by": "arek", "id": "E-0022", "kind": "direct", "locator": { "char_offset": 51156, "context_after": ". There are other problematic issues with both of these models, but they are physically different from the Nat\\'ario class, (unit lapse, spatially flat 3-geometry), and must be directly addressed using different techniques. Some defective w", "context_before": "measure zero.) While the transformations made in appendices A.1 and A.2 of reference satisfy the determinant condition, they fail the more basic condition; they are simply not coordinate transformations. For our purposes then it means that", "section": "Sec. 3" }, "quote": "the non-unit-lapse and van den Broeck warp drive spacetimes cannot simply be dismissed out of hand", "source_id": "S-0001", "verification": { "against_canonical_sha256": "8964eabea56ff77a513c73a93ddae1064432728df213c87a9c39f0d712d0bca4", "match_ratio": 1, "status": "EXACT", "verified_at": "2026-08-07T12:45:00Z", "verified_by": "werys" } }, { "added_at": "2026-08-07T08:49:58Z", "added_by": "arek", "id": "E-0023", "kind": "direct", "locator": { "char_offset": 1037, "context_after": ". A modest numerical analysis is carried out on a set of example configurations, finding total energy requirements four orders of magnitude smaller than the solar mass. Extraordinarily, the example configurations are generated by purely pos", "context_before": "tic energy distributions. With this new interpretation, it becomes a relatively simple matter to generate solitonic configurations, within a certain subclass, that respect the positive energy constraint. Using this newfound interpretation,", "section": "Abstract" }, "quote": "a superluminal solitonic spacetime is presented that possesses positive semi-definite energy", "source_id": "S-0008", "verification": { "against_canonical_sha256": "7b147718571ffb84c5bfa2049bf1a404daaa59a5eb0966e4aff81cad72ba5833", "match_ratio": 1, "status": "EXACT", "verified_at": "2026-08-07T12:45:00Z", "verified_by": "werys" } }, { "added_at": "2026-08-07T08:49:58Z", "added_by": "arek", "id": "E-0024", "kind": "direct", "locator": { "char_offset": 26516, "context_after": ". It follows from the Lorentz-invariant eigenvalue equation that the Eulerian energy, Eq., is the first eigenvalue (whose eigenvector is the normal vector) and thus satisfies the first constraint enforced by the WEC for a type-I stress-ener", "context_before": "in hand, the full WEC can now easily be investigated to study the nature of the energy distribution in other frames of reference. By analyzing the Lorentz-invariant eigenvalues of the stress-energy tensor calculated using Eq., it turns out", "section": "Sec. 3.2" }, "quote": "the WEC is violated in compact regions within the energy distribution", "source_id": "S-0008", "verification": { "against_canonical_sha256": "7b147718571ffb84c5bfa2049bf1a404daaa59a5eb0966e4aff81cad72ba5833", "match_ratio": 1, "status": "EXACT", "verified_at": "2026-08-07T12:45:00Z", "verified_by": "werys" } }, { "added_at": "2026-08-07T08:49:58Z", "added_by": "arek", "hedge_review": { "reason": "the reopening sentence that follows (E-0030) is now quoted in full and carried verbatim by the corrected claim C-0021; the span itself remains the paper's own words", "reviewed_at": "2026-08-07T12:18:53Z", "reviewed_by": "werys" }, "id": "E-0025", "kind": "direct", "locator": { "char_offset": 27040, "context_after": "However, the WEC is not violated everywhere and if the configuration in indeed satisfies the WEC, as claimed, then it may still be possible to satisfy the WEC in the presented configurations too, given sufficient modifications. The ansatz", "context_before": "for a type-I stress-energy tensor, which the configuration in Fig. () appears to be. However, the principle momenta constraints is where the violations occur, namely, rho + p_i^p<0 for some i in 123 in compact regions in the distribution.", "section": "Sec. 3.2" }, "quote": "No amount of modification to the configuration could get rid of these WEC-violating regions.", "source_id": "S-0008", "verification": { "against_canonical_sha256": "7b147718571ffb84c5bfa2049bf1a404daaa59a5eb0966e4aff81cad72ba5833", "match_ratio": 1, "status": "EXACT", "verified_at": "2026-08-07T12:45:00Z", "verified_by": "werys" } }, { "added_at": "2026-08-07T08:49:59Z", "added_by": "arek", "id": "E-0026", "kind": "direct", "locator": { "char_offset": 2106, "context_after": ": steering a warp drive is a problem of energy budget, not negative energy. Introduction Alcubierre's warp drive (reviewed in) showed that general relativity permits a compact region (a \"bubble\") to be transported through an ambient spaceti", "context_before": "nt class: the 3 is the collimation penalty of dipole exhaust over a floor of 1. The radiating equilibrium is linearly unstable (flux anti-damps the radial mode), yet growth sim luminosity is bounded over any finite burn by the fuel budget.", "section": "Abstract" }, "quote": "The drive is causal, subluminal, and a reaction drive needing no exotic matter in the thin-shell idealization", "source_id": "S-0005", "verification": { "against_canonical_sha256": "c5c38eb634a690e5d631e9462dc2e4388170c762293d2a9b60f0e86468ba5fb8", "match_ratio": 1, "status": "EXACT", "verified_at": "2026-08-07T12:45:00Z", "verified_by": "werys" } }, { "added_at": "2026-08-07T08:49:59Z", "added_by": "arek", "id": "E-0027", "kind": "direct", "locator": { "char_offset": 120023, "context_after": "The barrier is the size of the budget, the sense in which warp propulsion is here an engineering problem. [Local in retarded time.] The solution is a finite maneuver on a u -slab; global, eternal existence is not claimed, and mass(u)>0 on", "context_before": "light (Deltaetatoinfty) sends mass_f/mass_0to0. A steering history that changes direction has (the integrated rapidity arc exceeds the net rapidity, as boosts do not add as vectors), so a turn costs strictly more than the collinear figure.", "section": "Limitations and scope" }, "quote": "The cost is steep, but positive and finite: no negative energy and no quantum-inequality violation appear at any point.", "source_id": "S-0005", "verification": { "against_canonical_sha256": "c5c38eb634a690e5d631e9462dc2e4388170c762293d2a9b60f0e86468ba5fb8", "match_ratio": 1, "status": "EXACT", "verified_at": "2026-08-07T12:45:00Z", "verified_by": "werys" } }, { "added_at": "2026-08-07T08:49:59Z", "added_by": "arek", "id": "E-0028", "kind": "direct", "locator": { "char_offset": 73200, "context_after": "; the one certified positive case, the Fuchs shell (Table), evades the theorem's hypotheses through its Schwarzschild exterior rather than contradicting it. We offer as an independent verifier for the warp-drive community: given any metric,", "context_before": "ructure-preserving symplectic integrator and reported with an on-cone witness, and a Ford-Roman comparison preserve this ordering, with Rodal the mildest by one to two orders of magnitude yet still violating. Across the four matched drives", "section": "Conclusion" }, "quote": "the invariant NEC margin is negative wherever the wall is Type I, and the wall is Type IV elsewhere, an explicit, all-observer, all-velocity realization of the Santiago-Schuster-Visser theorem", "source_id": "S-0003", "verification": { "against_canonical_sha256": "2d8763bfe07a1f7e2279a4a6ff75dc6d0d896fef998024ce64b4c28b6771fd1d", "match_ratio": 1, "status": "EXACT", "verified_at": "2026-08-07T12:45:00Z", "verified_by": "werys" } }, { "added_at": "2026-08-07T11:11:07Z", "added_by": "arek", "id": "E-0029", "kind": "equation", "locator": { "char_offset": null, "context_after": "Now as an example, if we let alpha = 1/10, then where is the Planck length. Thus, unless v_b is extremely large, the wall thickness cannot be much above the Planck scale. Typically, the walls of the warp bubble are so th", "context_before": "ecified parameter that describes how much smaller the sampling time is compared to the minimal radius of curvature. If we insert this into the quantum inequality and use we may neglect the term involving 1-f(rho) to find", "equation_index": 21, "section": "Sec. 3 (QI restrictions)" }, "note": "Display equation 21, equation environment.", "quote": "\\Delta \\leq {3\\over 4}\\sqrt{3\\over\\pi} {v_b \\over \\alpha^2} .", "source_id": "S-0007", "verification": { "against_canonical_sha256": "713ee65eda5e2c853cc6bb5dff2617c9baa704b3a93e9675006efbc4bc82ad64", "match_ratio": 1, "status": "EXACT", "verified_at": "2026-08-07T12:45:00Z", "verified_by": "werys" } }, { "added_at": "2026-08-07T12:18:23Z", "added_by": "arek", "id": "E-0030", "kind": "contextual", "locator": { "char_offset": 27133, "context_after": "The ansatz Eq. contains an interesting property related to an O(3) operation. The dynamical equations Eq. are not invariant under the total spacial inversion. Additionally, the expansion is not invariant either, since under this operation,", "context_before": ", the principle momenta constraints is where the violations occur, namely, rho + p_i^p<0 for some i in 123 in compact regions in the distribution. No amount of modification to the configuration could get rid of these WEC-violating regions.", "section": "Sec. 3.2 (immediately after E-0025)" }, "quote": "However, the WEC is not violated everywhere and if the configuration in indeed satisfies the WEC, as claimed, then it may still be possible to satisfy the WEC in the presented configurations too, given sufficient modifications.", "source_id": "S-0008", "verification": { "against_canonical_sha256": "7b147718571ffb84c5bfa2049bf1a404daaa59a5eb0966e4aff81cad72ba5833", "match_ratio": 1, "status": "EXACT", "verified_at": "2026-08-07T12:45:00Z", "verified_by": "werys" } }, { "added_at": "2026-08-07T12:18:23Z", "added_by": "arek", "id": "E-0031", "kind": "direct", "locator": { "char_offset": 4553, "context_after": "at v_sapproxvdbTransitionVS, with a stress-energy that has no rest frame. The Type-IV labels are certified physical, not numerical, by a three-solver and 50 -digit cross-check. The geometric control of the algebraic type. The vorticity of", "context_before": "the residual non-Type I points. A velocity-resolved Hawking-Ellis type map across the luminal transition. Sweeping v_s through 1, we find a clean dichotomy (Section): the Rodal irrotational geometry is globally Type I at all speeds, while", "section": "Abstract/results (transition value 0.36 stripped by canonicaliser; in main.tex:29 as \\vdbTransitionVS)" }, "quote": "the Alcubierre and Nat\\'ario walls are Type-IV dominated at all speeds, and Van den Broeck above its Type-I to Type-IV transition", "source_id": "S-0003", "verification": { "against_canonical_sha256": "2d8763bfe07a1f7e2279a4a6ff75dc6d0d896fef998024ce64b4c28b6771fd1d", "match_ratio": 1, "status": "EXACT", "verified_at": "2026-08-07T12:45:00Z", "verified_by": "werys" } }, { "added_at": "2026-08-07T12:18:53Z", "added_by": "arek", "id": "E-0032", "kind": "equation", "locator": { "char_offset": null, "context_after": "with and n sufficiently large. As an example, let us choose n=80. Then one can check that will be negative for 0 leq w leq 0.981 and positive for w>0.981. It has a strong negative peak at w=0.349, where it reaches the va", "context_before": "at = (1,0,0,0) t=0 when r_s=r=(x^2+y^2+z^2)^ 1/2 B r= R + B r= R + $. In addition, we will demand that a large number of derivatives vanish at this point. A choice that meets our requirements is", "equation_index": 12, "section": "Sec. 3 (the interpolating profile, labelled B)" }, "note": "Display equation 12 (\\label{B}), equation environment.", "quote": "B = \\alpha(-(n-1) w^n + n w^{n-1}) + 1,", "source_id": "S-0010", "verification": { "against_canonical_sha256": "5744e51a6e9ee1437ec6997bd0e44d9d7beed600aa69ebd7ed710e65ccc02113", "match_ratio": 1, "status": "EXACT", "verified_at": "2026-08-07T12:45:00Z", "verified_by": "werys" } }, { "added_at": "2026-08-07T12:28:41Z", "added_by": "arek", "id": "E-0033", "kind": "direct", "locator": { "char_offset": 21299, "context_after": "To explicitly see a specific example of this behaviour, let us work in an orthonormal basis. Take rho_0>0 and Gamma>1, and consider: Then in the natural rest frame we have. But a moving observer, with 4-velocity, where n^i is any unit spat", "context_before": "nergy conditions is typically the ANEC (averaged null energy condition) where one averages the NEC along timelike geodesics using an affine parameterization. As a cautionary example regarding application of the energy conditions, note that", "section": "Sec. on energy conditions (the collective rebuttal)" }, "quote": "all three of the recent Lentz, Bobrick-Martire, and Fell-Heisenberg articles merely assert the existence of one sub-class of timelike observers for which the energy density is positive. This is not enough to show that the WEC is satisfied.", "source_id": "S-0001", "verification": { "against_canonical_sha256": "8964eabea56ff77a513c73a93ddae1064432728df213c87a9c39f0d712d0bca4", "match_ratio": 1, "status": "EXACT", "verified_at": "2026-08-07T12:45:00Z", "verified_by": "werys" } }, { "added_at": "2026-08-07T12:28:41Z", "added_by": "arek", "id": "E-0034", "kind": "direct", "locator": { "char_offset": 643, "context_after": ". The solitons are also shown to be capable of being sourced from the stress-energy of a conducting plasma and classical electromagnetic fields. This is the first example of hyper-fast solitons resulting from known and familiar sources, reo", "context_before": "ral relativity. The negative-energy sources required for these solitons must be created through energy-intensive uncertainty principle processes as no such classical source is known in particle physics. This paper overcomes this barrier by", "section": "Abstract" }, "quote": "constructing a class of soliton solutions that are capable of superluminal motion and sourced by purely positive energy densities", "source_id": "S-0013", "verification": { "against_canonical_sha256": "c68819660e235df05e939c91b23b8b432102a8b3721f8690bc7695dc8b2d108e", "match_ratio": 1, "status": "EXACT", "verified_at": "2026-08-07T12:45:00Z", "verified_by": "werys" } }, { "added_at": "2026-08-07T12:28:41Z", "added_by": "arek", "id": "E-0035", "kind": "direct", "locator": { "char_offset": 1304, "context_after": ". We show that a class of subluminal, spherically symmetric warp drive spacetimes, at least in principle, can be constructed based on the physical principles known to humanity today. Introduction The classical-relativistic Alcubierre drive", "context_before": "ity and the rate of time can be chosen in a controlled manner. Conceptually, we demonstrate that any warp drive, including the Alcubierre drive, is a shell of regular or exotic material moving inertially with a certain velocity. Therefore,", "section": "Abstract/Introduction" }, "quote": "any warp drive requires propulsion", "source_id": "S-0014", "verification": { "against_canonical_sha256": "613fd66757ab2586197c91507d770b13c7562905736ad3a227693dd1979e1226", "match_ratio": 1, "status": "EXACT", "verified_at": "2026-08-07T12:45:00Z", "verified_by": "werys" } }, { "added_at": "2026-08-07T12:28:42Z", "added_by": "arek", "id": "E-0036", "kind": "direct", "locator": { "char_offset": 702, "context_after": "; construct superluminal warp-drive solutions which satisfy quantum inequalities; provide optimizations for the Alcubierre metric that decrease the negative energy requirements by two orders of magnitude; and introduce a warp drive spacetim", "context_before": "l. In this study, we develop a model of a general warp drive spacetime in classical relativity that encloses all existing warp drive definitions and allows for new metrics without the most serious issues present in the Alcubierre solution.", "section": "Abstract" }, "quote": "We present the first general model for subluminal positive-energy, spherically symmetric warp drives", "source_id": "S-0014", "verification": { "against_canonical_sha256": "613fd66757ab2586197c91507d770b13c7562905736ad3a227693dd1979e1226", "match_ratio": 1, "status": "EXACT", "verified_at": "2026-08-07T12:45:00Z", "verified_by": "werys" } }, { "added_at": "2026-08-07T12:28:42Z", "added_by": "arek", "id": "E-0037", "kind": "direct", "locator": { "char_offset": 1158, "context_after": ". Introduction Warp drive spacetimes, first introduced by Alcubierre and later by others, offer several unique transportation properties for timelike observers. These properties include the possibility of accelerating through geodesic motio", "context_before": "s well-known warp drive solutions such as the Alcubierre metric. We generate the spacetime metric numerically, evaluate the energy conditions, and confirm that the shift vector distribution cannot be reduced to a coordinate transformation.", "section": "Abstract" }, "quote": "This study demonstrates that classic warp drive spacetimes can be made to satisfy the energy conditions by adding a regular matter shell with a positive ADM mass", "source_id": "S-0015", "verification": { "against_canonical_sha256": "1cea4e851dc6548dbbb2144012a5d91454ea5cd716c72a53f912b754aac48871", "match_ratio": 1, "status": "EXACT", "verified_at": "2026-08-07T12:45:00Z", "verified_by": "werys" } }, { "added_at": "2026-08-07T12:32:51Z", "added_by": "arek", "id": "E-0038", "kind": "direct", "locator": { "char_offset": 8572, "context_after": ": at points where, for example, this happens when the second derivative terms outweigh contributions proportional to phi^2. Violation of Energy Conditions in QFT Quantization and positivity do not mix well. For instance, the prototypical ex", "context_before": "ewise, DEC also holds for this reason, and the same is true for the electromagnetic field. However, we also see that so the SEC can fail even for this model if m>0. The nonminimally coupled field, with coupling xi, has stress-energy tensor", "section": "Sec. on non-minimal coupling" }, "quote": "As the additional terms are not of the sum of squares form, even NEC can be violated", "source_id": "S-0016", "verification": { "against_canonical_sha256": "13bf911f214168b29664ad1a352d92f83fd5c5b89fde57010f7b5e9fc2c864c5", "match_ratio": 1, "status": "EXACT", "verified_at": "2026-08-07T12:45:00Z", "verified_by": "werys" } }, { "added_at": "2026-08-07T12:32:51Z", "added_by": "arek", "id": "E-0039", "kind": "direct", "locator": { "char_offset": 43019, "context_after": "(certainly above 2 -dimensions) or, as already mentioned, along null curves. The argument above, and the analogous argument for the energy density, relies on 'classical positivity' of the quantity in question. This permits a number of rela", "context_before": "curve, e.g., contracted against a null vector or possibly differing future-pointing causal vector fields, to obtain QNEI, QDEI etc. Variants exist for averages over suitable Lorentzian submanifolds, instead of timelike curves (see, e.g.).", "section": "Sec. on QEI variants" }, "quote": "One may show that no such bounds exist for smearings over spacelike surfaces", "source_id": "S-0016", "verification": { "against_canonical_sha256": "13bf911f214168b29664ad1a352d92f83fd5c5b89fde57010f7b5e9fc2c864c5", "match_ratio": 1, "status": "EXACT", "verified_at": "2026-08-07T12:45:00Z", "verified_by": "werys" } }, { "added_at": "2026-08-07T12:32:51Z", "added_by": "arek", "id": "E-0040", "kind": "direct", "locator": { "char_offset": 8497, "context_after": "As the additional terms are not of the sum of squares form, even NEC can be violated: at points where, for example, this happens when the second derivative terms outweigh contributions proportional to phi^2. Violation of Energy Conditions", "context_before": "_0 = u. Then so this theory obeys WEC due to the 'sum of squares' form. Likewise, DEC also holds for this reason, and the same is true for the electromagnetic field. However, we also see that so the SEC can fail even for this model if m>0.", "section": "Sec. on non-minimal coupling" }, "quote": "The nonminimally coupled field, with coupling xi, has stress-energy tensor", "source_id": "S-0016", "verification": { "against_canonical_sha256": "13bf911f214168b29664ad1a352d92f83fd5c5b89fde57010f7b5e9fc2c864c5", "match_ratio": 1, "status": "EXACT", "verified_at": "2026-08-07T12:45:00Z", "verified_by": "werys" } }, { "added_at": "2026-08-07T12:32:52Z", "added_by": "arek", "id": "E-0041", "kind": "direct", "locator": { "char_offset": 4357, "context_after": "\"warp drive\" spacetime of Ref.. It is the goal of this paper to analyze a spacetime recently proposed by Krasnikov which, although differing from that of Ref. in several key respects, shares with it the property of allowing superluminal tr", "context_before": "ry. However, Ford and Roman have proven inequalities which limit the magnitude and duration of negative energy density. These \"quantum inequalities\" (QIs) strongly suggest that it is unlikely that stable Lorentzian wormholes can exist, and", "section": "Introduction" }, "quote": "similar conclusions have been drawn by Pfenning and Ford with regard to the", "source_id": "S-0017", "verification": { "against_canonical_sha256": "e8908276ad41c854bde9c6d226bb2a06ef3771e3beaf4ac3d166a7f40a2f70a4", "match_ratio": 1, "status": "EXACT", "verified_at": "2026-08-07T12:45:00Z", "verified_by": "werys" } }, { "added_at": "2026-08-07T13:08:48Z", "added_by": "arek", "id": "E-0042", "kind": "direct", "locator": { "char_offset": 13979, "context_after": "(mass), thus overcoming the main difficulty of the warp drive mechanism. The explicit expression of T^00 in CG, computed with our Mathematica program, is rather cumbersome and is reproduced in Eq. () of the Appendix. Here we present just t", "context_before": "pletely non-negative, showing that the WEC is verified and no exotic matter is needed to establish the warp drive. This non-negative energy density plot in the bottom right panel of Fig. 1 is the main result of our paper as it shows that -", "section": "Sec. 3 (main result)" }, "quote": "if CG is the correct extension of GR - it might be possible to establish a warp drive without having to use negative energy", "source_id": "S-0018", "verification": { "against_canonical_sha256": "3c2273b201b168ebb53e9bc251bc55c815bd8831fd88f13d0b997bba22376f5e", "match_ratio": 1, "status": "EXACT", "verified_at": "2026-08-07T13:08:48Z", "verified_by": "werys" } }, { "added_at": "2026-08-07T13:08:48Z", "added_by": "arek", "id": "E-0043", "kind": "direct", "locator": { "char_offset": 637, "context_after": ", as was the case of the original solution. In particular, the resulting warp drive does not require the use of exotic matter. Therefore, if conformal gravity is a correct extension of general relativity, super-luminal motion via an Alcubie", "context_before": "ather than standard general relativity. The main characteristics of the resulting warp drive remain the same as in the original study by Alcubierre, namely that effective super-luminal motion is a viable outcome of the metric. We show that", "section": "Abstract" }, "quote": "for particular choices of the shaping function, the Alcubierre metric in the context of conformal gravity does not violate the weak energy condition", "source_id": "S-0018", "verification": { "against_canonical_sha256": "3c2273b201b168ebb53e9bc251bc55c815bd8831fd88f13d0b997bba22376f5e", "match_ratio": 1, "status": "EXACT", "verified_at": "2026-08-07T13:08:48Z", "verified_by": "werys" } }, { "added_at": "2026-08-07T13:08:48Z", "added_by": "arek", "id": "E-0044", "kind": "direct", "locator": { "char_offset": 3135, "context_after": ". Similar issues also exist in other well-known GR solutions for super-luminal motion, such as space-time wormholes. Einstein's General Relativity and the related Standard Model of Cosmology have been highly successful in describing our Uni", "context_before": "Following Alcubierre's seminal paper, many other studies appeared in the literature, either proposing alternatives to the original warp drive mechanism (,) or refining and analyzing in more detail the original idea (,,,,,,,,,,,,). However,", "section": "Introduction" }, "quote": "all these studies were conducted using standard GR and could not avoid the violation of the WEC, meaning that some exotic matter would always be required for faster-than-light travel", "source_id": "S-0018", "verification": { "against_canonical_sha256": "3c2273b201b168ebb53e9bc251bc55c815bd8831fd88f13d0b997bba22376f5e", "match_ratio": 1, "status": "EXACT", "verified_at": "2026-08-07T13:08:48Z", "verified_by": "werys" } } ] }