← AMRAL · PROGRAM-WSFC
Worm Sequence Freedom Closure · research-level provisional closure for the broadworm breadth sequence and the seven 2007 conjectures; not a Moser-area result
WSFC (Worm Sequence Freedom Closure) rewrites 'the worm problem' as a nested sequence of finite-freedom possibility spaces Γ0 ⊆ Γ1 ⊆ … and demands four gates — freedom exhaustion, effective approximation, task stability, value squeeze — so that finite-stage answers provably converge to the continuum answer. It is not a Moser-area result. Its only computed object is the broadworm breadth sequence t_n (the largest minimum width of a unit-length polygonal arc with at most n segments; t_n rises with n towards the known constant β ≈ 0.438925369), and its target is the seven general-n conjectures of the 2007 paper by Panraksa, Wetzel and Wichiramala. Moser appears only in R01, which itself says: 'the most important conclusion of this round is not a new Moser worm area bound.' 'Closure' here means finite-stage values converging to a known constant, not a new constant. The core manoeuvre restricts the candidate optimizers to a 'support-tangent class' (each side edge tangent to the unit circle about the opposite endpoint), which collapses the 2n − 2 vertex degrees of freedom to one or two parameters with closed forms.
Reconstruction update · 2026-10-08: reconstructed from surviving records, with sources and limits stated; originals and new implementations are distinguished. Overview and download bundle.
Honest status: the closed-form t_n inside the support-tangent class (n ≥ 4) match the 2007 table; the new t₇ = 0.438754439 and t₈ = 0.438816161 are floating-point minima of the reduced formulas, not certified enclosures. The load-bearing hypothesis G0 — the true optimizers lie in that class — reaches only 'research-proof-level provisional closure'. R27's calibrated statement: the correct authority level of the seven conjectures is not 'WSFC solves everything' but 2 classical source closures (convexity and drape, consequences of Adhikari–Pitman 1989) plus 5 WSFC provisional research closures, most of them conditional on G0. There is no proof assistant, independent review or peer review; none of the sixteen Lean files has been compiled, and the later ones are mostly theorem …_TARGET : True := by trivial placeholders. While preparing these pages this site recomputed every closed-form value the papers print, and all reproduce; a model-free differential-evolution search over all vertex coordinates reached the reduced-class value for n = 4, 5 (both seeds) and n = 6 (one of two seeds) and never exceeded it for n = 3 to 8 (n = 7, 8 under-converged) — none of which proves G0.
Authorship and provenance: the headers of the main documents of every round read 'Author: Neo.K; AI research collaborator: Aletheia / OpenAI GPT-5.6 Sol' (WSFC-00 adds the institution EveMissLab / 一言諾科技有限公司); key findings, state crystals and notes carry no author line. Traces of the execution environment (/mnt/data, artifact_tool, ChatGPT citation markers) indicate that GPT wrote and ran the rounds under Neo's direction; this is not Claude's work. The 'certificates' and 'MACHINE-CHECKED' are checks by the authors' AI in SymPy/Fraction/mpmath, mostly on toy cases, not a proof assistant. Priority is never claimed; R27 names outside review and contacting the authors as the next step.
The R28 'Independent Verification Pack' verified no mathematics: it is a protocol for future reviewers; its shipped script only checks file hashes and the dependency graph, the output was logged by the authors' AI runtime, and no human or third-party attestation exists. R28 itself says this round does not claim independent review complete, novelty, or formal verification; its status is NO AUTHORITY UPGRADE, and no Round-29 replay exists after it.
Missing files, recoveries, and one calibration: the original R19 is unavailable; an R18/R20-based reconstruction dated 2026-10-08 is now provided (R20 builds on it; the recovery bundle also lists it as MISSING and leaves only its intended topic, 'Refinement Chain / Closure Algebra', positioned between R18 and R20); the original standalone R22 package is unavailable; its complete R28 copy is now shipped as a standalone reconstructed package (intended topic 'G1 — Full-Domain Coverage', between R21 and R23). On 2026-10-07 GPT recovered, from the ChatGPT Library / Drive, R12 (with State Crystal 12; the original R12 package is unavailable; a new reconstructed implementation is now shipped) and the original R23 package (its main document is byte-identical to the R28 copy; the key finding, state crystal, verifier script and certificates now exist too), and decided that the canonical R04 is 'Support-Class Necessity I' (the earlier 'Finite Convexity and Obstacle Reduction' draft is kept and marked superseded); all 27 checksums in the bundle match (bundle SHA-256 5532652b…). WSFC-00 rests on five prerequisite documents that are neither on this site nor in this folder (SDRPC_00, MCC_OE_00/01, Projection_Possibility_Space_Paper_04, and the serializable-mathematical-constants proposition). One value bound is unreconciled: R01's 1/(n − 1) versus R22's 1/⌊n/2⌋. The baselines on the Moser's Worm Problem case (disc, 30-degree sector, Wetzel triangle) omit the Keller bound of 2026-09-18 that R01 cites; aligning them is suggested.
Reading path: start with R27 (the authority ledger) and WSFC-00 (the non-claims); for the mechanism read R01 → R03; to see how a real gap was found and repaired read R05 → R06; for the conditional structure of the global chain read R21 → R24 → R25–R26; R28 shows that no outside review has happened. R07–R18 are certificate and Lean-draft infrastructure (mostly toy examples) with no pages of their own: they are listed in the table below and available for download.
All 17 reader pages now offer complete Chinese and English texts, comprising 20 bodies (R12 and R22 each separate the paper from its reconstructed-package note; R25 and R26 share a page; the early and canonical R04 versions remain separate). Original or reconstructed sources and translations are distinguished; translation does not upgrade research evidence. Download-only material remains in its original form.
The original bytes of the documents with pages and of the remaining files, unmodified; the 25 original zips are attached too; the files recovered on 2026-10-07 are in the recovered/ subfolder. The other rounds carry a one-line claim and a flag ('none' = no overclaim found; 'mild' = wording a reader could over-read, or corrected later in the series). The complete archive is kept in AMRAL's research archive and verified per file by SHA-256. Original bytes are retained; reconstructed material is distinguished by its directory and page labels.