← Goldbach Reverse-Structure Closure Program · PROGRAM-GOLDBACH · RG-SCP
Reverse Goldbach Structural Closure Program · 2026-09-28 to 09-30 · 28 files (27 distinct documents)
RG-SCP takes a 'reverse' strategy: assume a Goldbach counterexample N (RG(N) = 0), with N* = min the sharpest case; derive the necessary conditions Ki(N) it must satisfy and intersect them into a proof-admissible outer approximation AkP that contains every counterexample. Goldbach follows only if some AkP is empty, or if a rigorous demand lower bound exceeds a rigorous capacity upper bound — and this 'show it is impossible' half is exactly the sieve and parity problem; V0-08 says 'PHASE II NOT YET OPEN'. Structure: RG-SCP 01–08 (2026-09-28) — 01 the counterexample universe and the minimal failure state, 02 the failure obstruction cover, 03 M6/wheel obstruction geometry, 04 fixed-point fibres and the shadow gap, 05 prime approximation and counterexample pressure probing (heuristic channel only), 06 demand–capacity inequalities, 07 shift transport for a minimal counterexample, 08 the Phase-I synthesis; V0-01 to V0-08 — claim/source audits of 01–07 plus a consolidation; V1-01 to V1-07 — Lean-oriented specifications; the Notes A–C of 2026-09-30 and the 'world-information fixed-point no-hole conjecture' draft come after.
Honest status: no sentence claims that Goldbach is proved, reduced to a finite check, or 'closed'; every 'closure' sentence is conditional (for example 01 §30: 'if at some stage one can prove CG ⊆ Ak and Ak = ∅, only then is Goldbach closure complete'; from V0 on every commit block says Goldbach_proved: false). What is proved is all elementary — well-ordering, divisibility, residues mod 6, finite counting; apart from an interface to a Brun–Titchmarsh-type AP bound that is not proved here, no prime-distribution theory is used. No computation is reported: no search range for Goldbach, no verification bound, and the E0–E8 experiments are only planned and not run (the plan has E0 for N ≤ 105 and E1 for N ≤ 106); the series does not cite the known theorem of Chen, Vinogradov/Helfgott or the computer verification up to about 4×1018. No machine verification: every V1 file says 'specification only' (machine_checked false, lean_compiled false); the only Lean 4 kernel verification mentioned concerns an earlier 'M6 v0.2' that is neither in the package nor on this site.
The V0 audits found real defects: the definition of Ak is circular (V0-01); the 'effective wheel' mislabels self-cells (V0-03); the fibre Fp = pU6 is too loose and the exact set is pUp (V0-04); the positive defect Δ6 ≥ 2 is really ≥ 20 (V0-04); IN(y) is incidence mass, not capacity, and the canonical capacity is Ccan (V0-06); the matching νk is demoted to the neighbourhood Γk and 'smooth shift' is really a primorial-divisible shift (V0-07); Δ6 together with the boundary-3 indicator encodes FG exactly (truth leakage, V0-05). No theorem was retracted as false. But these audits are the same authors' self-audits with no independent reproduction, and 'PASS' is each paper's own acceptance gate. V0's 'COMPLETE' refers to the audit only; V1's 'SPECIFICATION READY' is not 'verified'.
Authorship and provenance: the headers of the 24 files RG-SCP 01–08, V0-01…08 and V1-01…07 read 'Author: Neo.K; Aletheia (GPT-5.6 Sol)', without separating direction from execution. The 'world-information fixed-point no-hole conjecture' draft and Notes A–C carry no author or AI-role line, and this site does not guess. All originals are zh-Hant with English terminology. Duplicates and gaps: V0-04 exists a second time as a byte-identical 'V0-04 (1)' and only one copy is kept; the V1 plan of V0-08 §99 is off by one against the actual V1 files; V1-08 onwards is announced but not in the package.
Reading path: start with V0-08 (the Phase-I ledger: what is exact, what is superseded, what is still to be run), then RG-SCP 01 (the entry), 02, 03, 04 (short exact proofs and the only explicit no-go), 06 (the demand–capacity template and its candour about parity) and 07 (minimality); to see how a self-audit works read V0-01, V0-04, V0-05 (the truth-leakage firewall, a reusable method) and V0-06. Notes A–C are the starting point of the SRBRD series that follows. The other documents have no pages of their own and are listed in the table below for download. Math mostly uses $$ delimiters; the conjecture draft uses \[ \] and \( \).
The conjecture draft, RG-SCP 01/02/03/04/06/07, V0-01/04/05/06/08 and Notes A–C (one page); the rest are in the table below. All 13 registered reader pages (15 body parts) now provide complete Chinese-English full texts; authoritative originals and full-text translations can be downloaded separately. Translation is not independent mathematical verification and does not upgrade the original evidence level. The download-only originals below are outside this full-text bilingual scope and retain their original bytes.
The original bytes of the documents with pages and of the remaining files, unmodified. The others carry a one-line claim and a flag ('none' = no overclaim found; 'mild' = wording a reader could over-read, or corrected by a later audit). The complete archive is kept in AMRAL's research archive and verified per file by SHA-256.