C-0020 Verified HIGH certainty

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 = 0.9812 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.

Standing our derivation · numerical result · TRL 1 Assumes 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 Stops applying non-constant v_s, where the region II slice is no longer static and the extrinsic curvature terms return Computed in compute/vdb_pricing.py, tests/test_vdb_pricing.py 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.

What it rests on

E-0017 · S-0010 — A `warp drive' with more reasonable total energy requirements · direct

…ble' that can be used to transport macroscopic objects. 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. The new geome…

EXACT · re-found in source

E-0018 · S-0010 — A `warp drive' with more reasonable total energy requirements · definition

…ation of the Alcubierre geometry We will solve the problem of the large negative energy by keeping the surface area of the warp bubble itself microscopically small, while at the same time expanding the spatial volume inside the bubble . The most natural way to do this is the following: ds^2 = - dt^2 + B^2(r_s) [(dx - v_s(t)…

EXACT · re-found in source

E-0032 · S-0010 — A `warp drive' with more reasonable total energy requirements · equation

… large number of derivatives vanish at this point. A choice that meets our requirements is

B = \alpha(-(n-1) w^n + n w^{n-1}) + 1,

with and n sufficiently large. As an example, let us choose n=80. Then one can check that …

EXACT · re-found in source

Attacks run against it

X-0027 SURVIVED recomputation · by redteam

I recomputed the entire Van Den Broeck region II sign split independently of compute/vdb_pricing.py: I took T^00 from VDB's PRINTED eq. (density) in corpus/S-0010/body.tex (not the repo's symbolic three-Ricci), used exact analytic derivatives of the stated n=80 polynomial B = alpha(-(n-1)w^n + n w^(n-1)) + 1 with w = (R~+D~-r)/D~ (not finite differences), located the sign boundary by bisection at mpmath dps=40 after a 10000-point sign scan (my first secant-based findroot escaped [0,1] to w=1.386 and had to be replaced), and integrated 4*pi*D~*Int (2-w)^2 B^3 T~ dw with adaptive tanh-sinh quadrature split at the root, cross-checked with an 8000-point midpoint rule and an independent c^2/G conversion. Results: E_II,- = -1.3802e30 kg (claim: -1.380e30, ratio 1.00015; VDB print -1.4e30, ratio 0.986), E_II,+ = +4.86546e30 kg (claim: +4.865e30, ratio 1.00009; VDB +4.9e30, ratio 0.993), sign boundary w0 = 0.98119035 (VDB prints 0.981; the CLAIM says 0.9815, which is slightly wrong — T^00 is already positive, +9.0e-34, at w=0.9815, and the repo's own rho flips at 0.9812 on a 1e-5 grid I ran through their finite-difference pipeline). I verified symbolically by two further independent routes (conformal transformation of the 3d Ricci scalar with phi=ln B, and a from-scratch Christoffel computation) that VDB's printed T^00 formula is exactly R^(3)/16pi for the static conformally flat slice — both differences simplified to 0 — validating the K_ij=0 assumption chain. Region IV: independent Ford-Pfenning closed form gave -6.2487e29 kg, ratio 0.9919 vs VDB's -6.3e29, identical to the repo's closed form, confirming 'to 1%'. The residual-anomaly statement also checks out: under the stated profile the true pointwise negative peak is T~00 = -176 at w = 0.576 (10000-point scan), while VDB prints -4.9e2 at w=0.349, where the true density is -1.58e-14 — a ~16-orders mismatch at his printed location, so the printed pointwise values are indeed inconsistent with the stated profile even though integrals reproduce. A3 checks: E-0032's quote matches body.tex line 277 and equations.ndjson index 12 verbatim; git archaeology confirmed the historical premise — at pre-fix commit 6dcf86a fulltext.md had zero occurrences of 'n=80' ('let us choose .') and an alpha-stripped equation, restored by the PDB-26/PDB-30 fixes at 3ecdc26. A4 checks: f identically 1 in region II (region II at r_s in [1e-15, 2e-15] m lies inside r_s < R = 3e-15 m where f=1), the Eulerian observer e_0 equals the primed-coordinate slice normal, and constant v_s is properly flagged as the regime boundary. No attack changed a truth value; the closest hit was the mis-reported boundary digit (0.9815 vs true 0.98119), whose error direction understates the claim's own agreement with the print. || FINDINGS: Independent E_II,- = -1.3802e30 kg and E_II,+ = +4.86546e30 kg match the claim's -1.380e30/+4.865e30 to 0.02% and VDB's printed -1.4e30/+4.9e30 to 1.4%/0.7%. True sign boundary w0 = 0.98119035 (bisection, dps 40); repo's own rho flips at 0.9812; claim's quoted 0.9815 is wrong in the last digit — at 0.9815 the density is already +9.0e-34. VDB's printed T^00 formula proven symbolically identical to R^(3)/16pi via two independent derivations (conformal route and brute Christoffel; both differences = 0). Region IV: -6.2487e29 kg, ratio 0.9919 vs print. Pointwise-peak anomaly confirmed: true peak T~00 = -176/D~^2 at w=0.576 vs printed -4.9e2/D~^2 at w=0.349, where true density is only -1.58e-14. Historical premise verified in git: 'n=80' absent from fulltext.md at 6dcf86a (pre-fix), present after canon 1.1 (3ecdc26); equations.ndjson index 12 = 'B = \alpha(-(n-1) w^n + n w^{n-1}) + 1, \label{B}' matching E-0032 verbatim. Repo integrator at samples=2000 yields -1.380132e30/+4.864045e30, so the claim quotes its own derivation faithfully.

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