Warp Factory — Phase 3 · independent numerical verification

Warp Factory v1.0 (Helmerich et al. 2024, arXiv:2404.03095) is a public MATLAB toolkit for evaluating energy conditions on warp-drive metrics. It shares no code with this project's SymPy/NumPy pipeline and is maintained by an independent group. Phase 3 uses it to (i) reproduce the Fuchs et al. 2024 existence anchor independently, (ii) sweep the κ-scaling-law surface across $(M, R_2, \beta)$, and (iii) confirm the textbook Alcubierre violation as a tooling sanity check.

Environment: MATLAB R2023a Update 8 with Parallel Computing Toolbox + default toolboxes; Warp Factory cloned to F:\science-projects\WarpFactory\ (out-of-tree). All scripts and outputs in the project's warp_factory_repro/ directory.

Run the standard Alcubierre metric at $(v=c, R=4\,{\rm m}, \sigma=8\,{\rm m^{-1}})$ — the Pfenning–Ford 1997 textbook configuration — and evaluate NEC, WEC, DEC, SEC pointwise on the in-mask grid:

Reproduce Fuchs et al. 2024 Fig. 10 at canonical parameters $(R_1=10\,{\rm m}, R_2=20\,{\rm m}, M=4.49\times10^{27}\,{\rm kg}, \beta=0.02c)$ and bracket $\Delta_{\min}$ by holding $(M, R_2, \beta)$ fixed and sweeping the shell thickness $\Delta = R_2 - R_1$.

At the canonical point, in-shell pass fractions for all four energy conditions are identically 1.0000 — the existence claim is independently confirmed. The κ bracket:

Numerical bracket: κ^num ∈ (4.17, 5.83], vs the analytic 2A.9a bracket of $\kappa \in [0.05, 0.875]$. The numerical bound is ~6× tighter than the analytic upper. This is not a refutation but a refinement: the analytic 2A.7 calculation is a thin-shell Israel-junction pole-only argument; the numerical 2A.9b calculation is the full thick-TOV-fluid + bump-function pointwise-DEC evaluation. The dominant failure mode at small $\Delta$ is distributed warp-gradient stress through the shell interior, not the pole jump. The matter-shell route is therefore ~6× harder than 2A.7 alone advertises.

This closes TRUST_AUDIT row #3 (Fuchs existence anchor) at A-grade — the only B-row at the start of Session 18, now A.

Hold the scaling-law form $\Delta_{\min}/R_2 = \kappa\beta/C$ and ask: is κ a universal number, or does it vary with $(M, R_2, \beta)$? Outer grid: $C \in \{1/6, 1/3, 1/2\}$, $R_2 \in \{15, 20, 30\}$ m, $\beta \in \{0.005, 0.02, 0.05\}$ — 27 cells. Inner sweep per cell: 6 candidate Δ's spanning a fixed κ-grid $\{1.5, 3, 5, 7, 10, 15\}$, capped at $\Delta \le R_2 - 0.5$ m. 162 Warp Factory metric builds, 140 minutes headless on R2023a.

Bracketed κ midpoint table (cells with grid floor / cap saturation flagged):

Statistics over the 15 bracketed (non-floor, non-cap, non-anomaly) cells:

At $\beta = 0.05$ and $C = 1/6$ the geometrical cap $\Delta < R_2$ saturates before any DEC-passing shell exists. These cells are null configurations — the shell would have to be thicker than the bubble, which is geometrically impossible. This adds a binding constraint to the matter-shell landscape that the analytic 2A.7 / 2A.9a derivations did not surface.

The honest replacement statement for the Path-2A scaling law is:

This rules out the high-velocity low-compactness branch of the Path-2A landscape categorically — a non-trivial tightening of Phase 2A's slice scope that would not have been visible without the full numerical surface sweep.

• Resolution-doubling check is not done. The R₂-dependence trend in κ (cells with $R_2 = 30$ consistently bracket at (5, 7] where $R_2 = 15$ cells bracket at (3, 5]) could partially be a discretisation effect. Closing this would require re-running 1-2 representative cells at spaceScale = 2 × current.
• Below-grid-floor κ is not constrained. Cells flagged $(\text{NaN}, \kappa_0]$ have $\kappa^{\rm true} < \kappa_0$ but no lower bound. Reaching down to where the analytic 2A.9a upper $\kappa = 0.875$ might live would need a finer Δ grid.
• The geometrical-cap null is for finite bubble interiors. Whether the obstruction persists as $R_2 \to \infty$ at fixed $(C, \beta)$ is not tested.
• The β-axis is not explored independently. The κ-sweep here sits at the published Fuchs amplitude $\beta = 0.02$ for the anchor; the broader surface samples three β values but not enough to fit the linear-in-β scaling-law slope independently.

These are reopening criteria. Phase 3 closes 3.1 and 3.2 with full disposition; 3.3 (nested concentric Fuchs shells + non-spherical oblate/prolate Fuchs constructions) is the natural next step and 3.4+ remain gated on Phase 2B and on Phase 2D convergence.