Dashboard Roadmap Fuchs Shell Six Slices Fell–Heisenberg Warp Factory Figures Notebooks About
Alcubierre · Boundary-Mode
At a glance
Phase status

Click any row to expand its detailed status, task list, and reopening criteria.

Phase 0Foundation — seed documents, literature atlas✓ Closed

Assemble the theoretical context and formulate the boundary-mode hypothesis. All three foundational tasks closed during the project's seed conversations (March 30 / April 4).

Closed

  • [✓] 0.1 Literature review and atlas of the surrounding field
  • [✓] 0.2 Image-method hypothesis formulation (April 4 seed document)
  • [✓] 0.3 Integration of both into ALCUBIERRE_MARCH30_INTEGRATION.md
Phase 1Linearization & feasibility — ADM constraint structure, gauge cleanup✓ Closed

Extract the mathematical structure of the Alcubierre metric in the subluminal regime and decide whether boundary-value methods apply. Disposition (Session 15): partial yes — ADM constraint equations are well-posed and gauge-clean (Tasks 1.7, 1.10) and admit a multi-mode positive-energy WEC+DEC-passing solution at the static smooth-N level (Phase 2D Sessions 11-15), but no useful classical warp-drive interior is recovered within the static slice. Phase 1 exits with content — the framework is the right tool — but the practical Phase 2 work has been running in parallel since Session 5.

Closed (11/11)

  • [✓] 1.1 Extract hμν + verify subluminal regime
  • [✓] 1.2 Compute exact ADM ρ, ji
  • [✓] 1.3 Order structure: gravitomagnetic vs energy
  • [✓] 1.4 Poisson equation for shift vector
  • [✓] 1.5 Thin-wall limit: monopole + dipole surface layers
  • [✓] 1.6 Test point-image decomposition — does not work
  • [✓] 1.7 Identify boundary-mode framework as the right tool
  • [✓] 1.8 Lobo & Visser 2004 read (Session 15 closeout) — opened Task 2D.12
  • [✓] 1.9 Fuchs et al. 2024 read (subsumed by Phase 2A)
  • [✓] 1.10 Gauge analysis — confirmed ADM is the natural framework
  • [✓] 1.11 Spin-2 vs spin-1 differences (Costa-Natário catalog)
Phase 2AClassical matter-shell realization (primary track)✓ Closed (slice)

Closed within the static + Alcubierre-shift + asymptotically-flat-vacuum slice. All 14 listed tasks (2A.0-2A.15, with 2A.9 split into 2A.9a/9b in Session 15c) are closed. Headline disposition: within the slice, no useful classical warp drive exists with classical matter alone. Analytic and numerical bracket on the minimum shell thickness: Δmin/R = κβ/C with κnum ∈ (4.17, 5.83] (Session 18 Warp Factory cross-check, ~6× tighter than the analytic [0.05, 0.875] from Session 15c). Adjacent slices delegated to Phase 2C and 2D.

Detailed plan: MATTER_SHELL_PATH.md; landscape synthesis: LANDSCAPE_SYNTHESIS.md. Full prose summary: Fuchs Shell page.

Closed (15/15)

  • [✓] 2A.0 Path doc + verification notebook scaffolding
  • [✓] 2A.1-2A.5 Fuchs reproduction, dipole structure, OOM bound
  • [✓] 2A.6 Full Israel junction (static + boosted), λ* ≈ 0.55
  • [✓] 2A.7 Δmin/R = κβ/C, analytic κ ∈ [0.05, 0.875]; certified-radial κ = 4.93 ± 0.44 (Session 41)
  • [✓] 2A.8 VSH decomposition — Fuchs is a 98.65% two-mode doublet
  • [✓] 2A.9a Anisotropic-tangential analytic refinement
  • [✓] 2A.9b Warp Factory cross-check — κnum ∈ (4.17, 5.83]
  • [✓] 2A.10 Acceleration — ADM 4-momentum forbids self-acc.; GW recoil ≲0.25%
  • [✓] 2A.11 Lentz 2020 comparison — different mechanisms, not interpolable; closed negative at class level Sessions 43–45 (every compact ℓ¹ soliton violates full WEC/DEC on its outermost wavefront, at every amplitude)
  • [✓] 2A.12 Natário 2002 — special case of Slice 1, dismissed
  • [✓] 2A.13 Krasnikov tube — universal scaling, WEC pass = 0.0000
  • [✓] 2A.14 Toroidal Fuchs — strictly worse than spherical (≥2π thicker)
  • [✓] 2A.15 Slab-patch (k=0) — codimension-counting hierarchy (3 data points)
Reopening criteria: (i) any new analytic upper bound on κ that closes the ~6× analytic-vs-numerical gap; (ii) any non-spherical / non-static / non-asymptotically-flat construction inside this slice that beats Fuchs (none currently in the literature).
Phase 2BCasimir / boundary-mode QFT (parallel track)✓ Closed (no-go, Session 34)

Closed as a physical mechanism for warp-relevant negative energy (Task 2B.8, Session 34). Three legs, recorded in QUANTUM_CLASSICAL_BRIDGE.md §8: (1) no material gravitational conductor exists in known physics (impedance ZG ~ 2.8 × 10⁻¹⁸ SI + Dyson absorption bounds); (2) the sole claimed loophole (Heisenberg–Coulomb superconductor effect) is speculative, experimentally unsupported, and contradicted in the literature; (3) the loophole-independent even-if bound: a perfect graviton mirror at favourable sign yields |ρC| ≤ ħc/d⁴ — 63.5–69.6 orders of magnitude short of every radially-certified density target (harness verification/test_2b8_casimir_gap.py).

Disposition

  • [✓] 2B.8 Spin-2 obstruction assessment — executed Session 34; closes the phase
  • [—] 2B.1–2B.7 mode-decomposition tasks — mooted as physics; the math survives as a possible classification tool only
Reopening triggers: (i) experimental demonstration of anomalous GW reflection/absorption by any material (reopens Leg 2 only — Leg 3 still stands); (ii) a demonstrated vacuum state with |⟨T₀₀⟩| ≫ ħc/d⁴ at macroscopic d consistent with quantum inequalities; (iii) a horizon-class boundary compatible with a subluminal shell.
Phase 2CAdjacent slices exploration (6 slices)✓ Closed

Each slice relaxes one explicit assumption from Path 2A's static-slice analysis. All six slices return null; slice 1 produces the most interesting partial loophole (multi-mode Fell-Heisenberg follow-up promoted to Phase 2D).

Closed (6/6)

  • [✓] 2C.1 Alternate shifts — closed analytically (Session 36): no single-mode axisymmetric family member satisfies WEC everywhere; corrected sweeps 0/140 + 0/2496 concur
  • [✓] 2C.2 Hybrid Fuchs+Krasnikov wall — 0/34,560 WEC for η ≥ 0.1 and 0/82,944 DEC anywhere (Session-40 full dispatch, ε/n unfrozen); matter perturbation shifts but does not remove the negative region
  • [✓] 2C.3 Time-dependent v(t) — Δρ peaks at 0.3% of static ρp; antisymmetric in x ⇒ no quadrupole-order momentum injection
  • [✓] 2C.4 Krasnikov 2003 QI loosening — three substantive loopholes; our 2A.13 no-go is QI-independent
  • [✓] 2C.5 Cosmological exterior — McVittie momentum-exchange ceiling Δv ≤ 5.7×10-36 m/s
  • [✓] 2C.6 Modified gravity — Jordan-frame loophole exists; "DEC-respecting matter" is interpretation-dependent
Outcome: mixed; Slice 1's multi-mode follow-up (Fell-Heisenberg 2021, 1.3% of cells violate full WEC at the canonical anchor) became the seed for Phase 2D.
Phase 2DFell–Heisenberg multi-mode follow-up✓ Closed (Session 42 re-scope)

Strict-pass FH existence is mathematically real as a statement about the L = 12 evaluation box, pipeline-verified at A-grade, triple-anchored against external no-go literatures, and — at every structural test applied — degraded as a warp-drive interpretation; never restored. The Session-42 closed-form far-field analysis completes the arc: every tested a > 0 configuration violates WEC + DEC beyond a finite equatorial radius R* outside the box, so no swept FH configuration satisfies the energy conditions globally within the adopted concretization. Kept honest along the way by Sessions 14-17's structural tests (single-cell passenger, CTC sea, 76× mass overhead, no asymptotic decay envelope).

Closed (13/13)

  • [✓] 2D.1-2D.4 Pull, evaluate, reproduce, and sweep the FH 2021 ansatz — 1404/15000 strict-pass at Npts=65
  • [✓] 2D.5 Connectivity & topology — single connected 5-D manifold, smooth boundary
  • [✓] 2D.5b Polynomial implicit boundary — degree-4 dense, no clean sparse form
  • [✓] 2D.5c-d Resolution convergence (Npts=65→97→129) — boundary region 47% pass→fail flips
  • [✓] 2D.6 Horizon test — every strict-pass row is "all wall, no interior" (single-cell passenger)
  • [✓] 2D.7 Full horizon & CTC analysis — 6624/6738 (98.3%) host CTCs
  • [✓] 2D.8 xAct independent re-implementation — 9-anchor sweep, A-grade cross-check
  • [✓] 2D.9 Bobrick-Martire matter classification — Class III geometric, anisotropic
  • [✓] 2D.10 Asymptotic matching residual + double-bubble destruction
  • [✓] 2D.12 VIQ post-processing — 76× mass overhead at the passenger zone
  • [✓] 2D.5e Symbolic boundary extraction — closed Session 42, beyond plan: the ansatz is exactly axisymmetric about z, giving closed-form principal pressures everywhere (the earlier SymPy det() wall was symmetry-blindness) and the far-field certificate that re-scoped the whole phase
  • [✓] 2D.5f Full Npts=129 sweep — closed Session 22: 6240/10080 strict-pass (box-scoped), +5.8% above extrapolation, no reopening trigger
  • [✓] 2D.11 Vorticity-augmented FH — all three phases negative (Sessions 15, 33); kill-tested at four certified strict-pass anchors and upheld (Session 38): vorticity never improves either slack and never opens the passenger zone
Phase 2EDeliberately-deferred relaxations (5 items)✓ Fully dispositioned (Sessions 49–52)

Five deliberately-deferred relaxations that live outside the explicitly-enumerated 2A/2B/2C/2D structure, each recorded with explicit reopening criteria. Opened by owner decision in Session 49 and fully dispositioned by Session 52 — the decision-point question ("what is the next most-likely-fruitful relaxation?") now has a checked answer: none of the computationally accessible relaxations opens a useful-warp loophole.

Status

  • [✓] 2E.1 Genuinely time-dependent inflate-then-coast — first leg closed POSITIVE-within-slice (Session 49): rigid-profile spin-up is an exact spacetime with no v̈ in its Einstein tensor; the quasi-static corridor is clean and the fastest EC-clean spin-up is τ* ≈ 0.4–0.8 R₂/c — causality-scale, i.e. EC bookkeeping does not obstruct the lifecycle. Deep-dynamical legs (ADM evolution, worldline acceleration, superluminal transitions) remain deferred with original criteria.
  • [✕] 2E.2 Modified-gravity computational follow-through (Slice 6b) — closed negative (Sessions 51–52). Target f(R) = R + αR², Jordan-frame matter ECs on the loophole's own terms: the 161-point α × geometry map rescues nothing and strictly degrades every EC-passing configuration (viable direction); the designer-f LP theorem kills the reconstruction mode — NEC is linear in (f′, f″, f‴) per R value, and 23.4% of Alcubierre-wall points individually admit no coefficient triple: no f(R) with f′ > 0, of any shape, works. Horndeski / f(R,T) / EGB untested.
  • [○] 2E.3 Quantum / semiclassical sources beyond classical AECs — externally gated (scalar-field warm-up, then spin-2 follow-up)
  • [✕] 2E.4 Multi-mode vortical A⃗ + anisotropic Π + non-trivial topologyclosed in full (Sessions 44 + 50): Π axis negative; topology fell analytically (the exact far-field coefficient −V√(σπ) is parameter-independent, so compact quotients admit no family member and interior surgeries can't touch the exterior violation); the joint vortical+Π exponent space is negative at 180/180 dual-box cells.
  • [○] 2E.5 Higher-dimensional / active-matter Krasnikov variants — externally gated
Reopening criteria: per-item, unchanged, in ROADMAP.md (external publications, specific quantitative constructions, or a downstream finding that a recorded slice restriction was binding).
Phase 3Numerical verification — Warp Factory → certified Python port✓ Closed through 3.10

Independent numerical confirmation of analytic Path-2A results — first via the public Warp Factory v1.0 MATLAB toolkit, then via the clean-room Python port warp_factory_py whose exact-symbolic radial evaluator is now the project's certified EC oracle for sharp shell profiles (ground-truth adjudicated, Session 30; Cartesian FD demoted to smooth-only cross-check).

Closed

  • [✓] 3.1 Standard-Alcubierre EC sanity (Pfenning-Ford 1997 params) — 92.6% in-mask EC violation. Tooling confirmed (Session 19).
  • [✓] 3.2 κ-surface sweep — re-based on the certified radial evaluator (Session 41): 12 genuine crossings, κ = 4.93 ± 0.44; spurious MATLAB thin-wall failures identified.
  • [✓] 3.3 Nested + non-spherical Fuchs shells (Session 27) — both halves since adjudicated: the nested half REVERSED by the Session-39 certified kill-test (small mass-splits improve the NEC margin ~8× → the Sessions 47–48 floor re-base); the oblate half's recorded "+3.09% improvement" REVERSED in Session 54 as a sign error in the lost scratch driver (four reconstructions incl. an exact mask-count match give −3.1%; full-3D re-test concurs) — spherical local optimality under shape deformation now holds in both axes.
  • [✓] 3.3+ Fuchs §6 radial-profile optimization, both steps — closed negative (Sessions 28–31); Fuchs's "orders of magnitude" claim unsupported in both slices.
  • [✓] 3.10 Certified minimal-mass map (Session 32) — canonical single-shell floor Mmin = 2.568 × 10²⁷ kg; the canonical Fuchs mass is over-provisioned 1.75×.
  • [✓] 3.10+ Two-body re-base (Sessions 47–48) — the Session-39 reversal converts to a real lever: canonical floor drops 13.3% to 2.226 × 10²⁷ kg (RES_CONF-certified; −17.8% at the R₂=15 cell; over-provisioning now 2.02×). Mechanism corrected in Session 48: the two-body pressure ansatz (per-component P=0 surfaces shaping the lapse), not density grading — the continuous graded-wall family is closed negative (0/80 members below the single-shell floor), and the thin-wall cell degrades under any split.
  • [✓] 3.7 Lentz 2020 kill-test (Sessions 43–45) — closed negative at class level; see Phase 2A.11 line. Session 55 characterized the remaining ℓ¹ kink-sheet residue: the coordinate-plane sheets are finite Israel-type surface layers, strictly EC-violating at every regularization scale — a third independent failure of the class (the a-priori dipole-layer hypothesis was refuted by the measured scaling and recorded).

Residue / candidate

  • [✓ resolved] Nested-variant minimal-mass map — executed as Sessions 47–48 (see 3.10+ above). The standoff-size residue was retired in Session 53: the gap is a plateau (g ≲ 0.5 m bit-identical to the winner; monotone degradation beyond) — the floor stands.
Phase 4No-go theorem confrontation○ Not started

Systematic confrontation against published warp-drive no-go theorems. Informal cross-checks already happened in Tasks 2D.7 (Everett-Roman 1997 / SSV 2023 CTC line), 2D.9 (Bobrick-Martire 2021 matter classification), and 2D.10 (asymptotic matching).

Open

  • [ ] 4.1 SSV 2105.03079 — assumption table + per-row dispute strength
  • [ ] 4.2 Everett-Roman 1997 §4 (CTCs) — formal placement of FH single-cell-passenger result
  • [ ] 4.3 Olum 1998 (averaged null energy condition) — shell-thickness implications
  • [ ] 4.4 Hawking 1992 chronology protection — relevant to 2D.7 CTC-sea finding
Activation: Phase 2D has closed, so the formal gate is lifted. Informal coverage now includes 2A.10 (SSV-2023 acceleration theorem), 2D.7 (Everett-Roman / CTC), 2D.9 (Bobrick-Martire), and the Session-46 ANEC probe of the Garattini-Zatrimaylov bubble (4.3-adjacent). The Phase-4.1 formal SSV-2021 assumption-table enumeration remains the open item (audit-noted).
Phase 5Physical mechanism & realizability○ Not started

"Granted that a Path-2A or Path-2B construction exists on paper, what physical mechanism would build one and what energy budget does it cost?" Task 5.4 (engineering trade-offs for the matter shell) was absorbed into 2A.0-2A.13.

Open

  • [ ] 5.1 SSV-style physical-realizability assumption table for the static-slice matter-shell construction
  • [ ] 5.2 Mass / energy budget for the canonical Fuchs anchor (M = R2c²/(6G) ≈ 4.5×1027 kg ≈ 0.75 MJupiter)
  • [ ] 5.3 Active feedback / stabilization requirements for the wall (perturbation analysis)
  • [—] 5.4 Engineering trade-offs (absorbed into Phase 2A)
Activation: requires a positive Path-2A or Path-2B candidate to exist within an experimentally-relevant slice. Currently dormant.
Trust audit
Honest accounting

The project distinguishes results we derived ourselves (A) from results accepted from a specific paper (B) and heuristics (C), and maintains the grades as dated addenda — including downgrades, corrections, and withdrawals. Recent movements: the Lentz 2020 closure was upgraded from analogy to class-level A-within-slice certification (Session 45); the Garattini–Zatrimaylov 2025 equations were upgraded B → A-within-slice by exact reproduction (Session 46) — headline sharpened to "comoving vacuum void; ANEC violated; no useful-warp loophole"; the Session-47 mass-floor re-base's "graded wall" reading was corrected in place one session later (numbers unchanged; mechanism reattributed to the two-body pressure ansatz, Session 48); the Sessions 49–52 Phase-2E dispositions (spin-up margin surface, far-field topology closure, f(R) map + designer-f LP theorem) all entered at A-within-slice with their batteries; and Session 54 reversed the last thin-slab-provenance number (the Session-27 oblate +3.09% — a sign error in its lost scratch driver, established by four driver reconstructions and a calibrated full-3D re-test) while Session 55's own a-priori hypothesis (dipole-layer kink sheets) was refuted by its instrument and recorded as such.

Full table in TRUST_AUDIT.md.