C-0018 Verified HIGH certainty
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.
Standing our derivation · numerical result · TRL 1 Assumes 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 Stops applying 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) Computed in compute/numgr.py, compute/hawking_ellis_scan.py, tests/test_hawking_ellis.py 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.
What it rests on
E-0028 · S-0003 — Observer-robust energy condition verification for warp drive spacetimes · direct
…dest by one to two orders of magnitude yet still violating. Across the four matched drives 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 ; the one certified positive case, the Fuchs shell (Table), evades the theorem's hypothese…
EXACT · re-found in source
Attacks run against it
X-0013 SURVIVED recomputation · by straz
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.