Fuchs et al. 2024 (arXiv:2405.02709) show a constant-velocity Alcubierre shift can be embedded in a Tolman-Oppenheimer-Volkoff matter shell that satisfies all four energy conditions (NEC, WEC, DEC, SEC) in the bubble interior and on the wall.
Anchor point: R₁=10 m, R₂=20 m, β=0.02 c, M = R₂c²/(6G). Reproduced independently in Warp Factory v1.0 at all four ECs = 1.0000.
The shell cannot be arbitrarily thin. Across a 27-cell (C, R₂, β) sweep at 6 inner Δ values each, the smallest DEC-respecting thickness obeys
with κ ≈ 5 typical (median 6, mean 5.3, std 1.0; range [4.0, 6.0] for 15 bracketed cells of 27).
Form universal across the surface; numerical κ is a slice-value, not a constant. Decision-gate-B per Session 19.
ADM 4-momentum conservation forbids self-acceleration of the shell in vacuum (Schuster–Santiago–Visser 2023 Theorem 3). Three escape routes catalogued; only ordinary mass ejection is viable.
Quantitative ceiling under the most favourable Fuchs-compatible parameters (HF-Jobs sweep + Varma 2022 NR rescaling): GW recoil ≲ 0.25% of vwarp. Not enough.
Krasnikov-tube networks: symbolic Einstein tensor reproduces Everett–Roman 1997 Eq. 14 to 14 decimals; universal scaling ρpmin ∝ −η/ε². WEC pass-rate 0.0000 across 300 (η, ε, n) points.
Closes the static-infrastructure-network branch independently of QFT loopholes.
Within the canonical static slice — Alcubierre βxx̂ shift × spherical Fuchs-class shell × asymptotically flat vacuum exterior × steady-state metric or its Lorentz boost × 4D General Relativity — the answer is "a positive-energy bubble exists, but no classical mechanism can accelerate it to useful speeds and no static infrastructure walls can be built."
This is not the closure of the classical question. Six adjacent slices (alternate shifts, hybrid walls, time-dependent acceleration, Krasnikov-2003 QI loopholes, cosmological exterior, modified gravity) are mapped in Phase 2C and all return null; the unenumerated landscape is logged with reopening criteria as Phase 2E.
C = 1/3, R₂ = 20 m, β = 0.02 c → κ ∈ (5, 7], overlapping the Session-18 bracket of (4.17, 5.83]. Anchor independently reproduced at sweep resolution.
| Diagnostic | Value |
|---|---|
| Mean κ (15 bracketed cells) | 5.33 |
| Median κ | 6.00 |
| Std / rel-std | 0.98 / 18.3% |
| Range | [4.0, 6.0] |
| Decision gate | B · scaling-law form universal, number not |
At high β + low C, the geometrical cap Δ < R₂ saturates before any DEC-passing shell exists. These are null configurations — no Fuchs shell exists regardless of mass.
Adds a binding constraint to the Path-2A landscape that the analytic 2A.7 / 2A.9a derivations did not surface: high-velocity low-compactness Fuchs shells do not exist as energy-condition-positive constructions, regardless of mass.
See WARP_FACTORY_NOTES.md §3 for the full 27-cell table and dispositions.
Standard Alcubierre at Pfenning–Ford 1997 textbook params (v=c, R=4 m, σ=8 m⁻¹) violates all four energy conditions in 92.6% of in-mask cells (in-mask EC pass = 0.0737; min(NEC) = −9.6 × 10⁴³). Confirms the Warp Factory pipeline returns the textbook negative result on a known violator — the positive Fuchs-shell results are not artefacts.
Closed: 0 (Foundation), 1 (Linearization), 2A (Matter-shell, slice-scoped), 2C (six adjacent slices, all null).
In progress: 2D (Fell–Heisenberg multi-mode static shift) · 3 (Numerical verification: 3.1, 3.2 closed; 3.3 next).
Gated: 2B (Casimir route) on Task 2B.8 spin-2 obstruction. Not started: 4, 5.
10 / 10 trust-audit rows currently A-grade. Row #3 (Fuchs existence) was upgraded B → A by independent Warp Factory reproduction in Session 18.
Row #5 (NR rescaling) carries a documented Colab-rerun caveat. Row #9 (Rodal 2025 numerical comparison) sits at B by explicit choice — formal QFT calculation deferred to Phase 2B.
Full table: TRUST_AUDIT.md.
Session 19 κ-surface: 162 Warp Factory metric builds (27 cells × 6 inner Δ), ~140 min headless MATLAB R2023a on 8 cores.
HF Jobs: 16+ parameter sweeps dispatched to date across fell_heisenberg, shift_families, hybrid_wall, krasnikov_tube, GW recoil. Live: npts=129 Fell–Heisenberg sweep on cpu-xl.
Outputs: bshepp/alcubierre-sweeps.
Phase 2A · the κβ/C scaling, the acceleration obstruction, the Krasnikov no-go. Anchor result of the project.
Phase 2C · six independent assumption-relaxations of the static-slice no-go. All six return null. Side-by-side.
Phase 2D · multi-mode static shift, 1404 strict-pass points, then dismantled by four structural tests.
Phase 3 · independent MATLAB reproduction of the Fuchs anchor and the κ-surface across 162 metric builds.
Phase tracker: 0 through 5, with status, decision gates, and reopening criteria for every closed item.
13 Jupyter notebooks, the MATLAB Warp Factory reproduction kit, and the HF-Jobs sweep dispatcher.