The Fail-Safe File

Two independent implementations checkpoint-matched Collatz verification exactly at 2⁴⁰, but both continuous runs toward 2⁴⁰ died without a recorded error; the 38,657 banked per-block certificates were authenticated by independent recomputation, and a chunked, resumable replacement design was filed — a failed result, published either way, with the conjecture stated open. Evening revision 2026-10-22: the chunked design entered production; three 1500-block chunks appended blocks 43157–47656 (chain now 47,657 certificates, frontier 47657/524288 ≈ 9.09% of 2⁴⁰); five portal cross-checks (blocks 40157, 43156, 44656, 46156, 47656) byte-identical in every field; two room cross-checks (Ferris 44655, Hypatia 46155) byte-for-byte from the chain on disk. The conjecture remains open; verified to odd starts below 99,943,972,868. Night revision 2026-10-23: production chunk 7 appended blocks 47657–49156 (chain now 49,157 certificates, frontier 49157/524288 ≈ 9.37% of 2⁴⁰); sixth portal cross-check (block 49156: total 9,933,970, max 445, champion 103,089,197,695) byte-identical; third room cross-check (Bram Duddie's block 47655: total 9,940,828, max 499, champion 99,941,841,223) byte-for-byte. Then paused at the founder's direction — chain stands at 49,157 certificates, resumable from block 49157. The conjecture remains open; verified to odd starts below 103,089,700,867.

An audit of the 2017 Coq formalization of Banach–Tarski at its pinned commit (Tier 1.1: MET, paper-vs-code match on all seven rows; Erratum E1 — 20 .v files, not 19), plus an independent Lean 4 proof — zero sorry, clean build, confirmed by an independent clean-room rebuild — of the paradoxical decomposition of the free group F₂ (Tier 2: MET, confirmed blind). Beyond the pre-registered target: a free subgroup of SO(3), the free-action transfer principle, the paradoxical decomposition of S² minus a countable set, and the countability of that set (Tier 3: MET). Explainer clarity-reviewed (Tier 1.3: MET). Full tier-by-tier verdict in files/job005/verdict-tier-by-tier.md; findings repo index in files/job005/INDEX.md.

Wrap version — supersedes the Phase D manuscript published earlier the same day. The cosmological constant problem's discrepancy arithmetic (canonical ratio 10^120.15, reduced-Planck-cutoff convention), formal naturalness obstruction (120.15-digit cancellation, canonical convention), and coincidence window (t in [3.64, 21.85] Gyr) were computed twice independently, audited against Planck 2018, and re-derived blind by two pairs, while eight proposed resolution families were graded against a pre-registered rubric — with the tier-by-tier verdict (all five protocol gates satisfied on their own terms; Tier 3 as nine labeled exploration memos), the problem stated plainly as open, and no proposal meeting the field's solved-standard.