← Goldbach Reverse-Structure Closure Program · PROGRAM-GOLDBACH · TCDC
Target–Condition Dual Closure · 2026-10-02 to 10-03 · 23 files (TCDC-00 to 22)
TCDC is a method plus a chain of reductions: specify a target, reverse-solve the conditions under which it holds, then separately establish existence, branches and a basin or capacity closure (00). Applied to Goldbach: for a fixed 2m, failure is a finite symmetric integer transport feasibility problem on cube-root-rough survivor states, with the exact identity MPP = nP − nSP + MSS (01). 01–03 reduction, capacity cuts and barriers (raw geometry and one-dimensional Brun–Titchmarsh both fall short); 04–07 a Chen-type weighted architecture (pressure scale m/log³ m; a direct cube-root linear sieve needs level > 2/3; a pointwise half-weight lemma with margin 0.0841 → 0.4067; a separate prime upper bound of 0.7421 cannot be paid; a conditional two-sink closure); 08–13 failure-support LPs, shadow prices, two-sink capacity and receiver blackout (effective only in a critical layer); 14–17 the exact one-variable branch ratio 1 : log 2, 'transfer to the joint survivor is itself of Goldbach strength', the parity-defect plane and the bad-mass simplex; 18–22 aggregate convolution providers: the harmonic level and the critical exponent θc = 0.641107 (3/5, 66/107 and 5/8 all lie below it), a port audit of an external theorem (Yang v2), and an end point that stops at 'the P ∩ R ∩ L provider does not yet exist'.
Honest status: none of the 23 papers contains a sentence claiming that Goldbach, a Chen-type theorem for the TCDC objects, or any 'closure' has been established. The Commit Decision of every one of TCDC-01 to 22 says Goldbach_proved: false; 21 of them have 'GOLDBACH STILL OPEN' in the verdict box (the verdict box of TCDC-05 says 'HSP STILL NOT PROVED' and its status line says Goldbach is still unproved), and TCDC-00 carries an explicit denial instead. 'PASS' is each paper's own acceptance gate, not independent verification, and 'closure' here names the target of an emptiness certificate for the failure surface, not an achieved result (14 of the 23 H2 titles contain the word). Several theorems are conditional implications (T14 of TCDC-06, T09 of TCDC-12, T18 of TCDC-16: if some inequality held, Goldbach failure would be impossible) whose hypotheses are never established.
Thresholds are priced inside an idealised benchmark: all constants and thresholds of TCDC-14 to 22 (2.0439, 1.0785, 7.85%, θc = 0.641107, 5.19%, 2.99%, 1.95%, 2.81%, …) presuppose a heuristic rank-one Buchstab matrix, an ideal neutral lower bound and an ideal mixed upper bound, so they are floors in an idealised model: do not read 'only about 1.954% at 5/8' as 'the problem is close'; the paper itself writes that no extrapolation to m → ∞ is legal. TCDC-14 states directly that transferring the one-variable 1 : log 2 to the joint survivor 'is itself an asymptotic theorem of Goldbach strength'.
Later papers correct earlier ones: TCDC-04 corrects the scale of TCDC-03 (m/log² m → m/log³ m); TCDC-06 supersedes the thin margin of TCDC-05; TCDC-10 corrects the one-prime corridor upper bound of 02/09 (one logarithm off); TCDC-13/14 temper the receiver blackout of TCDC-12 (a critical-layer effect only); TCDC-20 corrects the over-conservative description of Yang in TCDC-19; TCDC-22 corrects the scope of PVL in TCDC-21. No theorem is retracted; two of the six corrections move toward optimism and both depend on how the authors read external theorems. External theorems and version drift: Yang arXiv:2608.13299 treats largest-prime-factor questions, not Goldbach; the theorem numbers and levels quoted in TCDC-18/19/21 belong to v1 while TCDC-20/21 audit v2. A pre-publication read of v1 suggests that its upper-linear-sieve weights carry the full L(ν) on [1/3, 1], which would make the flat 5/8 used by the series a floor rather than the state of the art; that reading has not been re-derived and v2 restructures the theorem. Please read the series' '5/8 ceiling' as a floor.
What the pre-publication read-through reproduced: about 45 closed-form and numerical constants (0.4994, 0.8306, 0.0841, 0.4063/0.4067, 0.7421, 1.6250, 0.5906, 2.4427, 2.0439, 1.0785, 0.6411, 0.6572, …) to the printed digits; finite exact states for 3 ≤ m ≤ 5000 (RootRough, the prime/semiprime split and identities such as MPP = S − nSP − MPS) with zero violations; the pointwise lemma of TCDC-05/06 on 581,148 triples (y, w, X) with zero violations. The LP scans of TCDC-08, 09 and 12 were not reproduced, the Hall-type and network-amplification theorems were read but not re-derived, and Pascadi's thesis Prop. 4.15 and Maynard III Props. 5.1–5.3 (the basis of TCDC-22) were not verified. This checks arithmetic inside the finite models and is not an independent referee.
Authorship and provenance: the headers of all 23 files read 'Author: Neo.K; Aletheia (GPT-5.6 Sol)' and 'research line: RG-SCP / SRBRD', with no author or AI-role line, and no file mentions Claude. Header dates are 2026-10-02 (00–19) and 10-03 (20–22); the file date of TCDC-19 is 10-03 17:43 although its header says 10-02. Every file uses $$ \boxed{…} $$ and YAML contract blocks; the language is mixed, with 00 leaning Chinese and 16–22 almost entirely English. TCDC cites SRBRD-00…26 for every definition (the identity of TCDC-14 is SRBRD-14), so reading SRBRD first is recommended. The announced TCDC-23 (growing-residue uniformity / Goldbach-shift adapter) and TCDC-24 are not in the package.
Reading path: 00 (method and non-claim) → 01 (the exact reduction) → 04 (the Chen-type architecture and the cube-root barrier) → 05 (the one sieve-style lemma) → 06 (the conditional two-sink closure and the 0.7421 no-go) → 14 (1 : log 2 and joint transfer of Goldbach strength) → 15 (the parity-defect plane) → 17 (the bad-mass simplex) → 18 (the harmonic level) → 21, 22 (the port audit and the end). The other 12 documents have no pages of their own and are listed in the table below for download with a one-line claim and a flag.
00, 01, 04, 05, 06, 14, 15, 17, 18, 21, 22; the rest are in the table below. All 11 registered reader pages (11 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 12 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 12, 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.