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Current state (2026-07-30, post-Session 57): the radial exact-symbolic evaluator (warp_factory_py/solvers/axisymmetric_ec.py) is the certified EC oracle for sharp shell profiles (Session 30; Cartesian FD demoted to smooth-only cross-check), Phase 3.3+ is fully closed NEGATIVE (Sessions 28–31), and Session 32's Task 3.10 quantified the one positive residue: the canonical Fuchs mass is over-provisioned 1.75× (certified floor M_min = 2.568e27 kg nominal / 2.650e27 ADM; certified-radial κ = 4.64 ± 0.57 over the 14 located thresholds of the 18-cell grid, where ±0.57 is the 1σ cross-cell spread — dominated by a systematic rise with R₂, not a random error bar; four v=0.05c null-configuration cells). Session 33 closed Task 2D.11 NEGATIVE across all three vortical families (the irrotational restriction is not the driver of the "all wall, no interior" pathology within the static smooth-N slice at the canonical anchor), and Session 34's Task 2B.8 assessment closed Path 2B as a physical mechanism — no gravitational conductor exists in known physics, and even a perfect one falls 63.5–69.6 orders of magnitude short of the certified density targets (QUANTUM_CLASSICAL_BRIDGE.md §8). Within 4D semiclassical GR the project now has no known candidate for a vacuum+DEC+dynamical warp realisation; the next active lead is Task 2D.5e (Z-axis-symmetry symbolic fallback), then the Garattini–Zatrimaylov reproduction and the Phase 2E relaxations. Session 35 ran a pre-Phase-2E deep audit + remediation: no closure verdicts flip, but a one-cell mask bug in the Cartesian-path harnesses was found and fixed (the corrected Cartesian-vs-ground-truth error is 9.1%→94.0%, not the recorded 24%→94% — demotion verdict unchanged), two latent search-logic bugs in mmin_map were fixed (behavior-preserving, GATE-2 regression passes), three negatives were flagged as weakened (Slice-1 0/140, hybrid-wall 0/480, the 2D.11 anchor) and queued for kill-tests, and the never-explored process-closures (Lentz pentagonal scan, anisotropic-Π exponent, G–Z reproduction) are recorded in ROADMAP's Session-35 audit queue pending the next checkpoint. Session 36 ran the first queued kill-test (Slice-1) and it escalated: the Slice-1 evaluator had a frame-projection transpose bug (its recorded observable was coordinate −T_tt, not ρ_E — the "0.94 free-form ridge" never existed), fixed in the sweep module and adjudicated 20/20 (verification/test_shift_families_frame_adjudication.py); the Slice-1 negative is now analytic (all four shift families closed by profile-independent identities; corrected 0/140 preview + first-ever 0/2496 full dispatch concur — see SHIFT_FAMILIES_NOTES.md §Session-36 correction). Sessions 37–41 (2026-07-05/06) completed the queue's Block 2 — all six kill-tests: the GW-recoil SXS anchor is NR-verified conservative (TRUST_AUDIT #5 closed C→B), the 2D.11 closure is re-based on genuinely strict-pass anchors and upheld, kill-test (d) produced the audit programme's first verdict flip — the Session-26 nested-shell result is REVERSED (certified radial: small mass-splits improve the NEC margin ~8×; sign flip at $f^* \approx 0.63$ not 0.1–0.2), yielding a new unranked candidate lead (nested-variant minimal-mass map — ROADMAP) — the hybrid-wall negative strengthened 72× on its first full dispatch (0/34,560 WEC for η ≥ 0.1; 0/82,944 DEC), and the Session-18/19 Δ-ladder is certified radially (12 genuine crossings κ = 4.93 ± 0.44, anchor κ ∈ (4.479, 4.583], 3 nulls confirmed, cross-direction consistent with 3.10). Block 3 (Lentz pentagonal scan, anisotropic-Π exponent, G–Z reproduction) remains queued. Session 42 closed Task 2D.5e with the arc's biggest re-scoping: exploiting the FH ansatz's exact axisymmetry gives closed-form principal pressures everywhere (the Session-14c det() wall was an artifact of ignoring the symmetry), and following the exact slack fields beyond the evaluation box shows the FH "strict-pass" classification was an L=12 truncation artifact — every tested $a > 0$ configuration violates WEC+DEC beyond a finite equatorial radius $R^$ (FD cross-check at L=45: A1's wec margin +0.037 → −0.848). Within the adopted $m,n$ concretization, no swept FH configuration satisfies the energy conditions globally; the load-bearing-assumptions table row 1 is re-scoped accordingly (FELL_HEISENBERG_SWEEP_NOTES.md §18). Session 44 closed the first Phase-2E axis NEGATIVE in ~50 s of compute (the anisotropic-Π exponent is irrelevant: passenger-zone slacks are Π-independent to machine precision and the far-field WEC failure is common to all 24 swept exponent pairs — FELL_HEISENBERG_SWEEP_NOTES.md §19). Sessions 43+45 executed the last Block-3 never-explored closure with teeth: Lentz 2020 is closed NEGATIVE at class level (verification/test_lentz_full_wec.py, 5/5) — the published construction is the ℓ¹ ansatz under 1+1 propagation, its quadrants block-diagonalise into closed-form principal pressures, and every compact member strictly violates the full WEC and DEC on its outermost unidirectional wavefront, at every amplitude (ρ_E ≡ 0 marginal exactly there; Eulerian positivity — the paper's only checked condition — is achieved precisely where the pressures bite); the digitised Fig.-1 member additionally shows the paper's Eulerian positivity is not reproducible from the paper (~37% ρ_E < 0; the fine structure is not in the figure), and 46% of its Eulerian-positive set violates full WEC (LENTZ2020_EVALUATION.md). Session 46 executed the final Block-3 item and completed the Session-35 audit queue: the Garattini–Zatrimaylov 2025 de Sitter bubble is REPRODUCED EXACTLY (verification/test_gz_desitter_reproduction.py, 9/9) — the first external construction in the programme to survive reproduction (every checked equation at machine precision, incl. against the full 4D Einstein tensor of the exact time-dependent moving-bubble metric) — and sharpened against usefulness: the Hubble-matched bubble is exactly comoving (a vacuum void riding the expansion; zero transport content), its "averaged" WEC/NEC are fixed-time volume averages inherited from the background, ANEC along every wall-crossing null geodesic tested is strictly violated, and the local violations are a wall-shape-set multiple of the background vacuum density; assumption 5b is re-graded B→A within slice with these caveats — no useful-warp loophole (GARATTINI_ZATRIMAYLOV2025_EVALUATION.md). Session 47 resolved the Session-39 unranked candidate POSITIVE: the nested-shell margin reversal is a real mass-reduction lever — a 100-point certified map (first science run on jaga; f=0 baselines exact vs the S32 map) shows the canonical-cell floor drops to 2.2256e27 kg nominal (−13.3%, RES_CONF-certified; κ 4.77→4.13; over-provisioning now 2.02×) and the R₂=15 cell −17.8%, with the certified optimum at f ≈ 0.10 and the inner component adjacent to the outer wall, while the thin-wall Δ/R₂=0.25 cell shows monotone degradation (no improvement at any split) (verification/test_mmin_nested_map.py, SESSION_LOG Session 47). Session 48 closed the graded-wall follow-on NEGATIVE and corrected S47's mechanism: the continuous graded-wall family has 0/80 members below the single-shell floor (best +1.2%, RES_CONF-certified), and a cross-builder discriminator at identical nominal ρ (per-shell-TOV floor 0.8824× the S32 floor vs single-TOV 1.1409×) shows the S47 lever is the two-body pressure ansatz — the inner component's own P=0 surface shaping the lapse — not density grading; the S47 winner's mask kill-test passes (worst EC point sits mid-wall), so its −13.3% stands as reattributed (verification/test_mmin_graded_map.py, SESSION_LOG Session 48). Session 49 opened Phase 2E (owner decision) and closed 2E.1's first leg POSITIVE-within-slice: rigid-profile spin-up $v \to v(t)$ is an exact time-dependent spacetime (TOV parts exactly v-independent) whose Einstein tensor carries no $\ddot v$, so the whole inflate-coast-deflate lifecycle reduces to a margin surface min-EC(v, $\dot v$) — the quasi-static corridor is clean for all three certified configurations and the fastest EC-clean spin-up is $\tau^ \approx 0.4$–$0.8,R_2/c$ (25–50 ns): EC bookkeeping does not obstruct inflate-then-coast in this family; DEC binds first near the floor, and small-rate deflation gains margin (verification/test_spinup_margin.py, SESSION_LOG Session 49; dynamical-restructuring and superluminal legs stay deferred). Session 50 closed 2E.4 in full: the exact far-field saturation (Π symbolic, certified 6.3e-15) shows the R-linear coefficient −V√(σπ) is independent of every family parameter, so compact quotients admit no member of the adopted FH family and interior-only topology surgeries cannot rescue global EC (analytic), while the joint vortical+Π space with independently varied A-exponents is negative at 180/180 dual-box cells (far-field gate everywhere; passenger zone single-voxel everywhere) — verification/test_2e4_residual_axes.py, FELL_HEISENBERG_SWEEP_NOTES §20, SESSION_LOG Session 50. Session 51 opened 2E.2/6b with the deliberate target f(R) = R + αR² (Jordan-frame matter ECs + pointwise viability gates; designer-f excluded as near-tautological): the required-stress evaluator is built and certified (T = G_certified + αC with the correction exact-cancelled and code-generated; battery 6/6 — α→0 ≡ GR exactly, Schwarzschild/de Sitter anchors at machine precision), and the first physics is strongly negative — bare Alcubierre's WEC violation is improved at best 0.036% over eight decades of α (then amplified ~linearly; large α non-viable), and the certified Fuchs floor's viable direction strictly degrades (EC window αR ≲ 10⁻³): within the quadratic-f Jordan-frame slice, the ∇∇f′ terms at a warp wall add EC obligations rather than absorbing them (verification/test_fr_matter.py, MODIFIED_GRAVITY_LIT.md §6b, SESSION_LOG Session 51). Session 52 closed 2E.2 NEGATIVE, completing Phase 2E's disposition: the 161-point α × geometry map is uniformly negative (no EC-violating configuration rescued at any α; every EC-passing configuration's best viable α is exactly 0; floor window αR < 1.4e-5), and the designer-f LP theorem kills the reconstruction mode outright — Jordan-frame NEC is linear in (f′, f″, f‴) per R value, and on the Alcubierre wall 24/24 level-set bins are infeasible with 23.4% of wall points individually infeasible: no f(R) with a ghost-free graviton, of any shape, yields NEC-respecting Jordan matter on that class (verification/test_fr_designer_lp.py, SESSION_LOG Session 52; the Slice-6 "4D Einstein gravity" assumption is thereby narrowed — the f(R) corner closed, Horndeski/f(R,T)/EGB untested). Phase 2E stands fully dispositioned (S49–52): 2E.1 first leg positive-within-slice, 2E.2 and 2E.4 closed negative, 2E.3/2E.5 externally gated — none of the computationally accessible relaxations opens a useful-warp loophole.Sessions 53–55 (2026-07-12/13) retired all three optional residues: the two-body standoff gap is a plateau, not a knob (bisections bit-identical for gaps ≲ 0.5 m, monotone degradation beyond; the S48 standoff hint was a wall-thickness confound — the certified two-body floor stands at 2.2256e27 kg); the Session-27 oblate +3.09% is REVERSED as a sign error in a lost gitignored scratch driver (four driver reconstructions — one matching the recorded 70,724 mask cells exactly — all give ≈ −3.1%, and the full-3D re-test confirms oblate deformation degrades monotonically on both axes: W5 fully discharged, spherical optimality holds — verification/test_oblate_full3d_retest.py); and the Lentz ℓ¹ kink sheets are adjudicated as admissible Israel-type surface layers carrying finite, strictly EC-violating surface density (ε-independent ≈ 1.06 in A² units; the a-priori dipole-layer hypothesis was refuted by the measured ε⁻¹ scaling and recorded — verification/test_lentz_kink_sheets.py), the class's third independent EC failure. Session 56 (2026-07-29) closed Task 3.8: Natário 2002 is REPRODUCED EXACTLY (verification/test_natario2002_reproduction.py, 10/10) — the second external construction to survive reproduction, and its verified content is itself a no-go (Theorem 1.7 is the class-level ancestor of the S36 Slice-1 identities); sharpened far beyond the paper: WEC violated at 100% of wall points including the axis, Hawking–Ellis Type IV dominance growing as $v \to 0$, a wall ergo-band at $v^* \approx 0.18$, and Rodal 2025's comparison table independently confirmed (NATARIO2002_EVALUATION.md). Session 57 (2026-07-30, overnight) executed Phase 4 — all four named no-gos (SSV 2021, Pfenning–Ford 1997, Everett 1996 via Everett–Roman 1997, Hiscock 1997) confronted through our own machinery (verification/test_nogo_confrontation.py, 12/12; record NOGO_CONFRONTATION.md): no certified result contradicts any of them; our identities and adjudications instantiate and strengthen them (including upgrading the Alcubierre–Lobo NEC identity $G_{zz}=3G_{nn}$ to an exact class identity for any z-directed flow); and the EC-clean shell corridor sits precisely in SSV's declared open flank (their Appendix B). v0.2.0 is archived on Zenodo (concept DOI 10.5281/zenodo.19689587); the board holds externally-gated items (2E.3, 2E.5, watch-list triggers), the deferred deep-dynamical legs (2E.1 remainder, 5.3 stability), and unscheduled minor 3.6. The ranked open leads, the closed-leads ledger with reopening criteria, and outstanding admin live in ROADMAP.md; the session-by-session chronology is in SESSION_LOG.md; derivation-trust grades are in TRUST_AUDIT.md.
This is the front-door map for the Alcubierre boundary-mode reformulation project: what the project is, the headline result, the load-bearing-assumptions table, and the document index. If you're returning to the project after a break, read the paragraph above, then go to ROADMAP.md for the plan and SESSION_LOG.md for recent history. If you want the long-form story, see LANDSCAPE_SYNTHESIS.md.
What this project is
A personal landscape exploration of the Alcubierre warp drive in general relativity, asking whether the standard "exotic-matter requirement" can be reformulated as a boundary effect rather than a substance to be manufactured. Project mode is "surfing", not "paper-writing" — there are no concrete deliverables; the goal is to understand the structure of the obstructions to a working classical warp drive.
After 57 sessions, the project has produced (i) a static-slice classical no-go for useful warp drives, (ii) a six-slice exploration of which assumptions in the no-go are load-bearing, (iii) a documented set of published candidate constructions outside the slice — four adversarially adjudicated (Fell–Heisenberg, Lentz, Garattini–Zatrimaylov, Natário), (iv) certified minimal-mass floors for the Fuchs shell family, (v) the full disposition of the Phase-2E relaxations (time-dependence, topology, modified gravity), and (vi) an instrument-verified confrontation of the four canonical no-go works (Phase 4, NOGO_CONFRONTATION.md).
The *_EVALUATION.md files (Rodal 2025, Krasnikov 2003, Fell-Heisenberg 2021 when present)
The wider program this project is one branch of
..\exotic-transport\00-fence\ — the exotic-transport program umbrella (no-go lattice, branch index, methodology/epistemology). Private sister repo (bshepp/the-fence on GitHub); this project is its continuum-GR branch (lattice row G5).
Headline
Within the slice of parameter space defined by:
Alcubierre $\beta^x \hat x$ shift (or other single-mode axisymmetric shifts);
Spherical Fuchs-class matter shell or static cylindrical Krasnikov tube;
Asymptotically flat vacuum exterior;
Steady-state metric or its Lorentz boost;
4D Einstein gravity;
…no useful classical positive-matter warp drive exists that is simultaneously DEC-compatible, accelerable to warp-relevant velocities, and transport-relevant.
Outside that slice, several published candidate constructions exist:
Fell & Heisenberg 2021 (multi-mode "hidden geometric structures" in standard GR — outside Slice 1). Sessions 11-14 in FELL_HEISENBERG_SWEEP_NOTES.md: a connected smooth-boundaried 5-D manifold of strict WEC+DEC-passing configurations exists, with $E_{\rm neg} = 0$ (no negative energy density anywhere). The Npts=97 sweep originally reported 6818/10080 strict-pass; Session 14b §11 Npts=129 convergence test revises this down to ~5900/10080 because boundary points (47% of which flip pass→fail at higher resolution) were over-counted at Npts=97. The boundary surface is approximately a degree-4 polynomial implicit surface (99.98% in-sample classifier accuracy) but dense (no sparse closed-form per Session 14 §10). Critical caveat from Session 14a §9: every passing configuration is "all wall, no interior" — the connected $|\vec{N}| < 1$ region containing the origin (the would-be passenger zone) is a single grid cell with apparent radius $h/2$ that scales to zero physical volume in the continuum limit. The bubble geometry is "calm point at origin surrounded immediately by uniform $\sim 15c$ shift throughout the box." This degrades the warp-drive interpretation substantially: the existence claim holds mathematically, but no observer can occupy an extended interior. The acceleration / source-matter / asymptotic-matching questions are partially moot at this finding — there's nothing to propel. See FELL_HEISENBERG2021_EVALUATION.md and FELL_HEISENBERG_SWEEP_NOTES.md;
Garattini & Zatrimaylov 2025 (de Sitter bubble at Hubble velocity — averaged WEC/NEC only; reproduced exactly Session 46: the bubble is a comoving vacuum void with zero transport content, and ANEC is violated — GARATTINI_ZATRIMAYLOV2025_EVALUATION.md);
Rodal 2025 (irrotational Natário-class, 38× peak-deficit reduction in standard GR but still violates NEC/WEC/DEC/SEC).
The honest project summary, post-Session-22: "the no-go is robust for full WEC within its single-mode-axisymmetric slice; the multi-mode Fell-Heisenberg case admits a positive-energy fully-WEC-and-DEC-respecting static metric at all amplitudes — the energy-condition bottleneck is mathematically solved within this static slice. But the foliation-health analysis (Task 2D.6 / §9) shows the geometry is 'all wall, no interior': a passenger zone of zero continuum volume. The Session 17 triad (VIQ + B-M + CTC) anchors the claim against three independent external no-go literatures: (i) the L-V VIQ is trivially satisfied by construction but the passenger volume is outweighed by a 76× positive-energy mass cost (§13); (ii) every strict-pass point is B-M geometric Class III + non-isotropic + static, outside every B-M positive-result pathway (§14, BOBRICK_MARTIRE2021_EVALUATION.md); (iii) 98.3% of strict-pass rows host an everywhere-outside-passenger CTC region, with the CTC-free tail confined to a low-$V$ weak-warp corner (§15). So we have a positive-energy stationary solution that satisfies WEC+DEC pointwise, does not violate the VIQ, but provides only a single-voxel passenger zone surrounded by a CTC sea. Both questions that drove Session 17 — whether an independent pipeline (Task 2D.8) confirms the strict-pass existence, and whether vorticity-augmented ansätze (Task 2D.11) recover an interior — have now been answered: 2D.8 confirmed the Python pipeline is not artefactual at A-grade across 9 anchors; 2D.11 returned negative across all three phases (axisymmetric, Cartesian-constant-amplitude, and FH-form multi-mode $\vec A$ — Sessions 15, 33); only 2D.5e Z-axis-symmetry plan-B remains genuinely open inside the FH story. Session 22 also closed Task 2D.5f at the canonical resolution: the count is real (6240/10080 strict-pass at $N_{\rm pts}=129$), is +5.8% above the §11.6 extrapolation, and does not trigger the 2D.16 reopening criterion."
This is the authoritative version. Slice notes documents that have their own tables now defer to this one.
#
Sub-assumption
Status
Tested where
Notes
1
Shift profile is single-mode axisymmetric
Load-bearing. AND broken (Sessions 11-12) — Session 42 re-scoped the celebrated multi-mode counterexample: FH "strict-pass" was an L=12 evaluation-box artifact (every tested $a>0$ configuration violates WEC+DEC beyond a finite equatorial radius $R^*$, closed-form-computable; FD cross-check at L=45 concurs). Within the explored slices no tested shift family — single- or multi-mode — satisfies WEC+DEC globally. The multi-mode case additionally has the Session-14 passenger-zone bottleneck; vorticity does not lift it (Sessions 15, 33, 38). Triple-anchored against three external no-go literatures + cross-pipeline-verified + asymptotic-matching residual closed (Session 17).
Single-mode axisymmetric: closed analytically (Session 36) — z-shifts ($\rho_E = -b'^2\sin^2\theta/32\pi \le 0$, any profile incl. radial multi-mode), Natário zero-expansion ($\rho_E \le 0$, any profile; the source paper itself reproduced exactly Session 56 — NATARIO2002_EVALUATION.md), irrotational ($\int\rho_E dV = 0$ ⟹ WEC-everywhere is trivial); corrected sweeps 0/140 + 0/2496 concur. (The Session-9 "0/140" and the 0.94 free-form ridge were measured with a defective frame projection — superseded; the Session-35 kill-test queue item that found this is closed. See SHIFT_FAMILIES_NOTES §Session-36 correction.)Multi-mode irrotational (Fell-Heisenberg 2021): Session 11 sweep found ~6800 / 10080 strict-pass at Npts=97 with $E_{\rm neg} = 0$. Session 12 connectivity: single connected smooth-boundaried 5-D manifold. Session 14 §9 horizon test: every passing configuration has zero-volume passenger zone (single-grid-cell continuum-zero). Session 15 vorticity-augmented (Task 2D.11) Phases 1+2 NEGATIVE: at the canonical FH anchor, neither axisymmetric $A_\phi(R, Z)$ (216 preview points) nor Cartesian constant-amplitude $\vec A$ (27 preview points) recovers the passenger zone or improves the dec slack — vorticity strictly degrades or doesn't help. ⚠ Session 42 (Task 2D.5e): all "strict-pass" statements in this cell are L=12-box-scoped — the closed-form far-field analysis (FELL_HEISENBERG_SWEEP_NOTES.md §18) shows every tested $a>0$ FH configuration violates WEC+DEC beyond a finite equatorial $R^*$ (17–200 depending on parameters; the recorded strict-pass cells are those whose violation region lies outside the box). The Sessions 11–17 statistics below remain correct as box-scoped statements. Session 33 Phase 3 (FH-form multi-mode $\vec A$) NEGATIVE — Task 2D.11 closed; Session 38 kill-test re-based the verdict on informative gates and UPHELD it: Session 33's 2912 augmented points at the canonical anchor 100% strictly degrade both slacks, and the Session-38 multi-anchor re-run (four certified strict-pass anchors × the same grid at Npts=65, 7285 points) confirms: 0 slack improvements anywhere, 100% degrade both slacks, passenger zone = h at every point of every anchor. (The Session-33 anchor's "DEC-violating baseline" turned out to be an Npts=49 resolution artifact — its structure is certified strict-pass at Npts=65 for every V, and slack signs are exactly V²-invariant; the old "0 strict passes" gate line is superseded — at genuine anchors augmented points retain strict-pass at preview amplitudes, so vorticity's failure is that it never helps and never opens the passenger zone, not that it destroys passing configurations at these amplitudes; FELL_HEISENBERG_VORTICAL_NOTES.md §3–§5.) Session 17 triad (across 6738 strict-pass rows): (A) L-V VIQ is trivially satisfied ($E_{\rm neg}=0$ universally) but $M_{\rm passenger}/V_{\rm passenger}$ ratio is 44-98× (median 76×); (B) every strict-pass point is B-M geometric Class III + non-isotropic + static, outside every B-M positive-result pathway; (C) 6624/6738 = 98.3% host an everywhere-outside-passenger CTC region; the CTC-free 1.7% tail is all at $V=0.10$ with weak warp effect ($|\vec N|_{\max}\lesssim 1.2$); naive double-bubble destroys both passenger zones due to missing asymptotic decay envelope. Session 17 Phase E (xAct/Mathematica cross-pipeline check, 9 anchors / 9 A-grade, median rel-diff $\sim 2 \times 10^{-6}$): Python pipeline's strict-pass classification + derived statistics are not artefacts of FD truncation or 3+1 decomposition. Session 17 Phase F (FH↔Schwarzschild box-edge L-sensitivity, $L \in {12, 16, 20, 24}$): $\langle
2
Krasnikov-tube wall is bare-vacuum (no matter shell)
Not load-bearing for single-bump matter perturbations
0/34,560 full-config points achieve WEC for any tube with η ≥ 0.1, and 0/82,944 achieve DEC anywhere (Session 40: first hybrid_wall_full.json dispatch, ε and n unfrozen across 6×6 log rungs; preview regression bit-exact; the recorded "0/480" strengthens 72×). The full box's only WEC passes (236) sit at η ≤ 0.004 — the tube-off trivial limit (near-flat space + a small matter bump), not a loophole; positive margins die by η = 0.008. Best wec_fraction for a functional tube (η ≈ 1–2): 0.89–0.94. Adding matter shifts the WEC-violating region but does not eliminate it. Multi-bump and off-wall configurations not tested.
$\dot v$ correction to $\rho_p$ is antisymmetric in axis-of-motion coordinate $x$, scales as $1/\tau$ (linear in $\dot v$), peaks at 0.3% of static value at $\tau = R/c$. Net momentum injection at quadrupole order is zero by symmetry.
4
Pfenning-Ford-style tight QI bounds on negative energy
Substantively weakened by Krasnikov 2003 (but our classical no-go is QI-independent; the mg-scale Krasnikov budget is too small to repair the classical Krasnikov-tube wall by ≥31 OoM, Session 23)
Krasnikov gives three loopholes (Weyl/Ricci ratio, $E_{\rm tot}^-$ meaningless, dihedral-portal construction with $10^{-3}$ g exotic matter). Our Task 2A.13 classical no-go is independent of QI. Slice 4b (Session 23) asked whether the mg-scale Krasnikov budget could serve as a quantum supplement to repair pointwise DEC failures of the classical Krasnikov-tube wall: across the full ($\eta\in[10^{-2},1)$, $\epsilon\in[10^{-2},1],\mathrm{m}$, $n=\rho_{\max}/\epsilon\in[2,100]$) grid the required supplement exceeds the budget by $\ge 10^{31}$ at $D=1,\mathrm{m}$. Three gates pass: Everett-Roman saturation match, universal $\epsilon^2$ collapse confirming Phase 2A.13 scaling, Everett-Roman $\alpha$-band recovery. The mg budget cannot serve as a quantum patch in this slice.
Cosmological-exterior reaction-mass channel: $\Delta v \le 5.7 \times 10^{-36}$ m/s at $R_{\rm BY} = 100,R_{\rm shell}$, scaling as $R_{\rm BY}^3$. 42+ orders of magnitude below the GW-recoil channel.
Modified for the special case $v = v_{\rm Hubble}$ in de Sitter — reproduced and certified A-within-slice (Session 46), with sharp caveats; no useful-warp loophole
Reproduced exactly (every checked equation at machine precision, incl. vs the full 4D Einstein tensor of the exact time-dependent metric): the Hubble-matched bubble has $\rho_E \ge 0$, zero Eulerian flux, and is an exact mass-conserving vacuum rearrangement whose fixed-$t$ volume-averaged WEC/NEC hold. Sharpened (Session 46): the matching makes the bubble exactly comoving — the interior is a Minkowski patch riding the expansion, so the construction has zero transport content; the "averaged" conditions are fixed-slicing volume averages inherited from the background, and ANEC along every wall-crossing null geodesic tested is strictly violated (wall-grazing rays ~1.3× the background density scale); local NEC/WEC/DEC violations are a wall-shape-set multiple of $\hat\rho$ ($\propto 1/L^2$; dark-energy-scale absolute). The qualifier on Slice 5 is real but applies only to a comoving void.
Lobo & Oliveira 2009 demonstrate $f(R)$ wormholes where matter satisfies WEC and curvature absorbs the violation in Jordan frame. Einstein-frame transformation moves the violation to a scalar field. Whether this counts as "DEC-respecting matter" depends on which frame you take as physical. Phase 6b (computational $f(R)$ analysis) deferred.
7
Shell topology is $S^2$ (spherical)
Not load-bearing — toroidal $T^2$ topology is strictly worse, not a loophole
Linearized Levi-Civita exterior + Israel junction on a cylindrical surface gives $\Delta_{\min}^\text{cyl} = (3/8)\beta L/M$, independent of the shell radius$R$ (one trapped angular dimension instead of two). Torus penalty $\Delta_\text{cyl}/\Delta_\text{sph} = L/R_\text{min} = 2\pi R_\text{maj}/R_\text{min} \geq 2\pi$ for any non-self-intersecting torus. Combined with the Krasnikov-tube no-causal-advantage result, the toroidal-Fuchs path in speculation/RING_NETWORK_CONCEPT.md §4 is closed twice over. Scope (b) fat-torus refinement deferred (would only strengthen the dismissal).
Package 1 (Task 2A.6) — full Israel junction, Part A static + Part B boosted, $\lambda_*$ acceleration obstruction. Includes Cell 4b Schwarzschild $K_{ab}$ regression (TRUST_AUDIT #4)
Critical evaluation + exact reproduction of Natário 2002 (zero-expansion drive). Session 56, Task 3.8. 10/10 gates: second external construction to survive reproduction exactly; its verified content is itself a no-go (Theorem 1.7). Sharpened: 100%-of-wall WEC violation incl. axis; Hawking–Ellis Type IV dominance at small $v$; wall ergo-band $v^* \approx 0.18$; Rodal Table-2 ratios confirmed.
Phase 4 record (Session 57). The four canonical no-gos — SSV 2021, Pfenning–Ford 1997, Everett 1996 (via Everett–Roman 1997), Hiscock 1997 — premise-mapped and verified through our machinery (battery 12/12). No contradictions; Alcubierre–Lobo NEC identity upgraded to class-level; the shell corridor = SSV's declared open flank; subluminal slice Hiscock-safe with the off-axis Natário ergo-band flagged for 2E.3.
Critical evaluation of Lentz 2020 (hyperbolic-shift Einstein-Maxwell-plasma soliton) + Bobrick-Martire 2021 critique. Session 15c. Closes the citation hole in FELL_HEISENBERG2021_EVALUATION.md: Lentz checks Eulerian energy density only, not full WEC; explicitly admits DEC failure for the superluminal case; the "plasma source" is a target, not a construction. Logically a special case of Slice 5 (Fell-Heisenberg irrotational shifts).
Sessions 11-13 sweep + topology: §1-§6 the strict-WEC+DEC sweep (1404/15000 strict-pass at Npts=65, falsifies FH §3.3 irreducibility claim), §7 the connectivity/topology analysis (single connected smooth-boundaried 5-D manifold; §7.7 polynomial-fit at Npts=65 found degree-3 ~98% accurate boundary; §7.8 Npts=97 resolution-convergence test found the boundary is degree 4-5, not 3, and Npts=65 was systematically biased at low sigma), §8 deferred Hard Fix path (symbolic boundary extraction).
Session 17 Phase B. Critical evaluation of Bobrick-Martire 2021 four-class warp-drive taxonomy (§2.1) + spherically-symmetric isotropic-fluid construction (§3). Places FH strict-pass in the taxonomy: Class III geometric signature but static ($v_s=0$) ⇒ kinematic Class III does not apply; non-isotropic ⇒ B-M §3 positive-energy pathway does not apply. A/B/C honest-accounting table.
Session 17 Phase B (Task 2D.9) outputs: 8 representative strict-pass points at $N_{\rm pts}=65$, per-point eigenvalues.npz + slice_plots.png, summary.json, leaderboard.csv. All 8 tag as B-M Class III geometric + non-isotropic + static. Module: hf_jobs/analysis/fell_heisenberg_matter.py.
Session 17 Phase E (Task 2D.8). Independent symbolic Mathematica pipeline (Wolfram 14.3 + xAct 1.3.0 + xCoba 0.8.6) cross-checks adm_stress_energy (4th-order FD) against D[] symbolic differentiation of the closed-form $\phi_{\rm FH}^{\rm smooth}$. A-grade at the canonical anchor (124/125 points, median rel-diff $2 \times 10^{-6}$) and across a 9-anchor sweep over $(V, \sigma, r)$. Single outlier at $\vec x = (0,0,0)$ traced to the $\Pi=1/4$ fractional-power non-smooth point of the FH ansatz, consistent with Session 14 §9. Sessions 11-17 results not pipeline-artefacts. Wolfram scripts: agent-tools/fh_rho_at_points.wls, agent-tools/fh_rho_at_points_multi.wls; Python harnesses: agent-tools/cross_check_xact.py, agent-tools/cross_check_xact_sweep.py.
Standalone PNG renders of the quantitatively-strongest results (one subdirectory per topic). All produced by figures/plot_figures.py; each subcommand reads a parquet/csv from sweeps/, sweeps_remote/, or warp_factory_repro/ and emits PNGs into the matching figures/<topic>/ folder, mirroring into webpage/assets/figures/<topic>/ for website deploys. Subcommands: fh-corner, kappa-surface-3d, thickness-heatmap, krasnikov-collapse, gw-recoil-cliff, hybrid-wall-heatmap, shift-families-bars, plus all. Slice scopes are recorded in each PNG's suptitle and on the website galleries (webpage/{warp-factory,fell-heisenberg,six-slices}.html).
Permanent figure-generation script (lives under figures/ rather than agent-tools/ because the latter is gitignored throwaway). Argparse dispatch via SUBCOMMANDS dict; _save() mirrors each PNG to webpage/assets/figures/.
Historical (pre-pivot)
These are preserved as record of the project's earlier hypotheses; their symbolic content remains valid where reused, but their strategic recommendations have been superseded.