← Goldbach Reverse-Structure Closure Program · PROGRAM-GOLDBACH · SRBRD
Symmetric Root-Bounded Relation Domain · 2026-09-30 · 26 files (SRBRD-00 to 25)
SRBRD begins with one exact step: for every m ≥ 3, 'does 2m have a Goldbach pair?' is rewritten as a finite symmetric root-bounded relation domain (Ωm, Σ×Qm, Rm) — 2m has a prime pair iff the residual set is non-empty; a counterexample iff this finite domain is completely covered by finitely many residue cells (00). Then three stretches: 00–10 give non-cover certificates from finite occupancy moments (Bonferroni, spanning forests, danger complexes, moment-polytope LPs) for each fixed m, until at paper 10 the authors themselves judge 'phase-free uniformization fails'; 11–18 turn to sieves: root completion, cofactor states, the semiprime boundary, the exact transport identity MPP = nP − nSP + MSS, the Buchstab-row-flow master identity and a constant ledger (ideal margin 1.70163, naive row cost 60.5588, fixed-row BV cost 29.63, level threshold θ* = 0.96288, row multiplier required R < 1.23315); 19–25 audit which external large-modulus theorems (BFI, Maynard II/III, Lichtman, Pascadi, Yang 2026) could supply the missing input, localise the gap to a narrow 'complement-exponent band' in the low row t ∈ [1/3, 2/5], and end with 'GOLDBACH STILL OPEN; RSFLD NOT YET PROVED; CONSTANT CROSSING NOT YET PROVED'.
Honest status: none of the 26 papers contains a sentence claiming that Goldbach, a Chen-type result or any partial result is proved by the series; every Commit Decision sets goldbach_proved / uniform_goldbach_closure / global_noncover_proved to false, and every status line carries a 'not proved' formula. 'PASS' is each paper's own acceptance gate and 'Closure' is the program's finite-closure vocabulary (19 of the 26 titles contain the word); neither is external verification and neither means a closure has been achieved. Every certificate is a finite certificate for one m at a time; nothing uniform is stated. All files are v0.1, written on the same day, unrefereed and not machine-verified (SRBRD-00 itself says 'not yet Lean-verified').
What the pre-publication read-through reproduced: by brute force, #Res(m) = RG−(2m) for m = 3…3000, the 8-row table of SRBRD-01 Appendix B, odd-Bonferroni certification with q ≤ 5 for every 3 ≤ m ≤ 5000, the transport identity of SRBRD-14 (m = 3…4000), the row lock and triangular support of SRBRD-15 (m = 3…6000) and the numerical tables of SRBRD-16 and 18, and it recomputed all the constants. That checks arithmetic inside the finite models, not the models; the read-through is not an independent referee, and its scripts are not part of this package. The scan claims of SRBRD-05 to 09, the numerics of SRBRD-10 and the external proof-dependency audit of SRBRD-21 were not reproduced.
Later papers correct earlier ones: SRBRD-13 corrects the rough predicate of SRBRD-11 (primes ≤ z were wrongly treated as obstructions); SRBRD-20 narrows the 'missing intersection' headline of SRBRD-19; SRBRD-21 retracts the 'possible easy outcome' of SRBRD-20; SRBRD-25 clarifies the mixing of weight classes under which 3/5 was attributed wrongly in SRBRD-18/22/23. The earlier originals are unmodified, so read along this chain. External inputs and version drift: SRBRD-19, 20, 23 and 25 cite Yang arXiv:2608.13299 as v2 (2026-09-03) but quote theorem numbers and levels of v1 (2026-08-13); until re-checked against v2, do not read 'the current linear-sieve level is 3/5' as today's state of the art. Chen's theorem appears only as an external benchmark and is neither re-proved nor used.
Authorship and provenance: the headers of all 26 files read 'Author: Neo.K; Aletheia (GPT-5.6 Sol)' without separating direction from execution; apart from one sentence in SRBRD-11 crediting the 'second division' intuition to the user, no file states any role, and this site does not guess. SRBRD-00 to 10 and 12 to 14 have no bibliography, and no code or data accompanies the finite scans (m up to 5000, 105, 106). The folder name 'SRBRD-0 — Exact Representation Kernel' is the title of paper 00, not of the whole series. Every file ends with a 'next round' section that opens with a heading stub of the next paper, so splitting on H1 mis-splits.
Reading path: 00 (the exact re-encoding) → 01 (first compression and no-go) → 03 (center–frontier) → 09 (the strongest finite certificate family) → 10 (the first uniformization barrier) → 11 (the parity audit) → 14, 16 (exact identities) → 17, 18 (constant ledger) → 20, 21 (the hypothesis audit and its retraction) → 25 (the end). The other 13 documents have no pages of their own and are listed in the table below for download with a one-line claim and a flag. The originals are Traditional Chinese with English terminology; the display math has one symbol per line and is rendered in the browser when the page loads.
00, 01, 03, 09, 10, 11, 14, 16, 17, 18, 20, 21, 25; the rest are in the table below. All 13 registered reader pages (13 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 other 13 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 other 13, unmodified. The others carry a one-line claim and a flag ('none' = no overclaim found; 'mild' = wording a reader could over-read, a stale citation, or a correction by a later paper). The complete archive is kept in AMRAL's research archive and verified per file by SHA-256.