← AMRAL · PROGRAM-GOLDBACH
Goldbach Reverse-Structure Closure Program · 2026-09-28 to 10-03 · 77 files (RG-SCP 28, SRBRD 26, TCDC 23)
The strong Goldbach conjecture (every even number greater than 2 is the sum of two primes) is open; the strongest related result is Chen's 1973 theorem that every sufficiently large even number is p + P2, and computers have verified the even numbers up to about 4×1018. This line of research does not claim to prove it: its 'reverse' is to assume a counterexample N, derive the structural conditions it must satisfy one by one, see whether they can contradict each other, and record at every step where the argument stalls. The 77 documents form three sub-series, in chronological order: RG-SCP (2026-09-28 to 30, 28 files) writes Goldbach as a counterexample universe, obstruction covers and demand–capacity inequalities, with self-audits and Lean-oriented specifications that are not machine-checked; SRBRD (2026-09-30, 26 files) re-encodes it exactly as a finite root-bounded relation domain, checks finite moment certificates one m at a time, and turns to the sieve–parity boundary after meeting a uniformization barrier; TCDC (2026-10-02 to 03, 23 files) writes down a methodology, reduces failure to a finite integer transport feasibility problem and prices the missing inputs along Chen-type weighting, two-sink capacity, parity defect and aggregate convolution levels.
Honest status: none of the 77 documents claims that Goldbach is proved, reduced to a finite check, or 'closed'. Every 'closure' sentence is conditional; every series ends with 'GOLDBACH STILL OPEN' and a list of 'NOT YET PROVED' items. 'PASS' is each paper's own acceptance gate, and 'Closure' is the program's vocabulary for the certificate it wants (an empty counterexample set, an empty failure surface), not an achieved result. RG-SCP reports no computation; the finite scans of SRBRD and TCDC (m up to 5000, 105, 106) come with no code or data. Nothing is machine-verified and nothing is refereed. The author line of all three sub-series is 'Neo.K; Aletheia (GPT-5.6 Sol)' (the RG-SCP conjecture draft and the three Notes are unsigned) without separating direction from execution.
What these pages are: the overview page of each sub-series carries an honest-status note, a note on what was reproduced, a list of how later papers correct earlier ones and a reading path; the selected pages load the original text in full (the originals are Traditional Chinese with English terminology; on English pages the title, abstract and claim statement are translated into English while the full-text translation is not finished), and the other documents are listed for download with a one-line claim and a flag. Dependencies between the sub-series run one way: TCDC cites SRBRD, and SRBRD cites the V1 specifications of RG-SCP. On the relation to DMSD: the M6 definitions used by DMSD (cited to no source in its text) come from the RG-SCP series here; DMSD's content and its assessment are on its own pages.
In chronological order; each overview page has its own status note and reading path.