Roadmap — phase tracker

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

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 h_μν + 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)

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 κ^num ∈ (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 Δ_min/R = κβ/C, κ ∈ [0.05, 0.75]
• [✓] 2A.8 VSH decomposition — Fuchs is a 98.65% two-mode doublet
• [✓] 2A.9a Anisotropic-tangential analytic refinement
• [✓] 2A.9b Warp Factory cross-check — κ^num ∈ (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
• [✓] 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)

The QFT / boundary-mode-decomposition path remains scientifically interesting independent of Phase 2A's outcome and becomes necessary if Path 2A cannot reach useful velocities with classical matter alone. Conceptual foundation: QUANTUM_CLASSICAL_BRIDGE.md.

Gated on Task 2B.8: the spin-2 obstruction. EM has well-defined "conducting plate" boundaries; spin-2 has no analog of a gravitational conductor. Until that gap is closed, Phase 2B does not have a well-posed entry point.

Open (0/8)

• [ ] 2B.1 Vector-Laplacian eigenmode setup on spherical domain
• [ ] 2B.2 Spherical Bessel × VSH expansion of β^x
• [ ] 2B.3 Identify dominant radial mode
• [ ] 2B.4 Mode-by-mode contribution to energy density
• [ ] 2B.5 Compare to Boyer 1968 concentric-spheres Casimir
• [ ] 2B.6 Express ρ as Casimir-like mode sum
• [ ] 2B.7 Semiclassical scalar T_μν on Alcubierre background
• [ ] 2B.8 Spin-2 obstruction assessment (blocking)

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 — 0/140 sweep points achieve WEC ≥ 0.999 (single-mode axisymmetric)
• [✓] 2C.2 Hybrid Fuchs+Krasnikov wall — 0/480 strict-pass; matter perturbation shifts but does not remove the negative region
• [✓] 2C.3 Time-dependent v(t) — Δρ peaks at 0.3% of static ρ_p; 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

Strict-pass FH existence is mathematically real, 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 single largest source of new positive-leaning physics in the project, kept honest by Sessions 14-17's structural tests (single-cell passenger, CTC sea, 76× mass overhead, no asymptotic decay envelope).

Closed (10/13)

• [✓] 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

Open / partial (3)

• [~] 2D.5e Symbolic boundary extraction — definitive SymPy wall hit; Z-axis fallback unattempted
• [~] 2D.5f Full Npts=129 sweep — dispatched 2026-04-21 on cpu-xl (~$3.50, ~3.5h)
• [~] 2D.11 Vorticity-augmented FH — Phases 1 & 2 negative; multi-mode A⃗ Phase 3 not started

Five categories of slices that live outside the explicitly-enumerated 2A/2B/2C/2D structure and are recorded with reopening criteria so the project's "no useful warp drive in the slice" claim is honest about what it does and does not cover.

Mapped (not active)

• [○] 2E.1 Higher-dimensional extensions — Kaluza-Klein, brane-world, RS warp factors
• [○] 2E.2 Quantum-gravity corrections beyond semiclassical — LQG, asymptotic safety
• [○] 2E.3 Non-minimal matter couplings — disformal, scalar-tensor, vector-tensor
• [○] 2E.4 Truly novel shift functionals — beyond Alcubierre/Natário/FH/Lentz family
• [○] 2E.5 Engineering-side simplifications — passive structures, repeating cycles

Independent numerical confirmation of analytic Path-2A results using the public Warp Factory v1.0 MATLAB toolkit. Pipeline tested on a known EC-violator (textbook Alcubierre) before being trusted on the positive Fuchs result.

Closed (2)

• [✓] 3.1 Standard-Alcubierre EC sanity (Pfenning-Ford 1997 params) — 92.6% in-mask EC violation, min(NEC) = −9.6×10⁴³. Tooling confirmed (Session 19).
• [✓] 3.2 κ-surface sweep across (M, R₂, β) — 27 cells × 6 inner Δ = 162 builds; mean κ = 5.33, decision-gate-B; new geometrical-cap-saturation null finding (Session 19).

Next

• [ ] 3.3 Nested concentric Fuchs shells + non-spherical (oblate/prolate) Fuchs constructions
• [ ] 3.4+ Gated on 2B and on Phase-2D results convergence

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

"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 M_Jupiter)
• [ ] 5.3 Active feedback / stabilization requirements for the wall (perturbation analysis)
• [—] 5.4 Engineering trade-offs (absorbed into Phase 2A)