Goldbach's Conjecture — a complete research archive

Every major paper, every line of attack, a verified map of every known dead end — with the constructions that close them — and an original measurement program on Goldbach fluctuations. Built in ~36 hours by an AI-orchestrated research fleet (Claude Fable orchestrating Claude and GPT subagents), with adversarial cross-model audits, full reproduction manifests, and an append-only log of every action including every mistake.

Did it solve Goldbach? No. Nobody is close, and this archive can show you precisely why — which is its point. What it offers instead: the fastest possible on-ramp for anyone who intends to try (FOR-SOLVERS.md), and one apparently-new empirical contribution: the variance/rigidity law of the Goldbach representation function (FINDINGS.md Tier 1).

Navigation

entry point	what you get
FOR-SOLVERS.md	Start here to attack the problem: reading path, the wall with constructions, named hinges, live openings ranked
FINDINGS.md	What this project found — honest five-tier ledger, retractions preserved
ANALYSIS.md	The strategic synthesis: scoreboard, three barriers, verdict per approach, program postscript
ATTACK.md	The deep map: one wall in five coordinate systems (L1–L5), six mounted attacks, near-miss catalog
notes/	Six research-level dossiers over the literature (index)
papers/	~108 primary sources — third-party works, see attribution
work/	The active-research program: 13 numerics campaigns, derivation attempts, cross-model probes and audits (index)
REPRODUCE.md	Every empirical claim → script → expected output (~10 min total on a Raspberry Pi 5)
WORKLOG.md	Append-only audit trail of every action, correction, and retraction

Headlines (calibrated)

• Measured (apparently new; twice-audited): Goldbach counts are ~3.4× more rigid than the Cramér model (Var ≈ 0.58·J), twin counts more rigid still (0.25–0.34× Poisson), with an empirical drift law and the rigidity localized — after a four-attempt derivation program — to a pair-correlation/GUE-class object. Details: work/VARIANCE-NOTE.md.
• Mapped: the parity wall verified across argument classes with explicit killing constructions; the fixed-sum hinge identified and — via adjudication — correctly attributed to Huang–Li's published equivalence.
• Opened: the E(X) < X^0.72 record reduced to one inequality at margin 9×10⁻⁵ with a complete attack spec (work/pintz-optimization-spec.md).
• Method: two-control empiricism, cross-model adversarial audits, and two-track novelty adjudication — four of our own headline claims were killed or downgraded by this pipeline before anyone could be misled. What remains stood the same fire.

Reproduction

apt install python3-numpy   # the only dependency
python3 work/numerics06-recheck.py   # the flagship measurement, ~50 s

Full manifest: REPRODUCE.md.

License

Original content (documents, notes, scripts) is licensed under Apache-2.0 (LICENSE). The papers/ directory contains third-party works that remain the property of their respective authors and publishers — they are not covered by this repository's license and are included for scholarly convenience with full attribution (papers/README.md).

Citation

See CITATION.cff. If this archive saves you months of literature work, that was the idea.