The Verdict as Axiom: A Source-Level, Reproducibility, and Information-Ecosystem Audit of Nielsen Versions 1, 17, 47, and 50

We audit J. L. Nielsen's rapidly revised manuscript on Connes' rigidity conjecture, with version 47 as the frozen full-audit target and version 50 as a bounded post-freeze update. We directly compare the distributed version-1, version-17, version-47, and version-50 objects, while using the Codex documentary inventory and cited PhilArchive endpoints for transitions assigned to versions 18, 22, and 46; those three raw objects are not redistributed in Supplement S1. We inspect the public OpenAI Lean source; compare the original reproducibility audit, a documentary audit of its receipts, and two fresh technical reruns; read Ioana's 2011 Theorem 8.2 and Section 9 pipeline; examine an unsigned Anthropic-hosted counterexample preprint; rerun an exact-arithmetic regression test for its load-bearing gauge identity; and analyze public AI-review transcripts, X exchanges, Facebook/Meta AI summaries, and unattributed Hacker News advocacy. Our mathematical conclusion is version-specific and deliberately narrow: neither version 47 nor the changed and repeated load-bearing claims inspected in the identified version-50 object establish Nielsen's advertised refutation of the supplied counterexamples or proof of Connes' rigidity conjecture. Part I continues to attack objects that the OpenAI source does not construct. The final OpenAI groups are literal semidirect products $\Lambda=D\rtimes K$ and $\Gamma_n=E_n\rtimes K$; the carry cocycle constructs the internal abelian group whose dual is $E_n$. Moreover, $n=0$ means the unshifted carry construction, not the identically zero cocycle. The original Claude Code audit compiled the pinned target and obtained only `propext` plus Lean's standard classical-choice and quotient-soundness axioms in the inspected dependency chains, but its passing Comparator replay used an unsandboxed shim. Codex A later audited the receipts and upheld the core source, build, and native-axiom results while narrowing the Comparator/nanoda independence claim and the asserted `landrun` failure mechanism. Codex B independently rebuilt the target, checked the two roots and 4,098 supporting declarations, and completed a genuine-sandbox positive checker path under an official dependency pin, but stopped conservatively before its remaining controls. Codex B2 completed those controls in a new environment. The exact source and narrow build passed; both roots reached only the three standard axioms with zero `sorryAx`; the official pinned `landrun` source passed non-root, capability, `NoNewPrivs`, filesystem, network, and nested-argument controls; Comparator, the Lean kernel, persistent exports, and direct nanoda accepted the protected artifact; and deliberately invalid statement, `sorryAx`, custom-axiom, and tampered-export fixtures were rejected for their intended reasons. According to the Stage 20 through 22 closure receipts, the deterministic 623,745,218-byte archive contains 3,118 members and has SHA-256 `3b0d30af7d11857a189964b4c460e59831c3a0da206c58d89263eeafbbcdb7d9`. A separate verifier program executed outside the staging tree on the same operator-controlled host rehashed the archive, safely extracted it, and matched the result against a self-excluding global manifest with SHA-256 `435e27c3310b13b3f96e76918866f7d4c071ffffe8c26710b9e3f305fbb576a1` [48]. The approximately 624 MB raw archive was retained locally and was not independently rehashed inside this manuscript-production environment. This is strong technical reproducibility evidence, not an automatic verdict on every semantic bridge from the formal statement to conventional operator-algebra language. Part II still fails at its load-bearing application of Ioana's Theorem 8.2. Nielsen defines $\Theta(fu_g)=fu_g\otimes\Phi(u_g)$, so $\Theta(A_G)$ is literally contained in $A_G\bar\otimes L(H)$. Ioana's theorem requires the full image not to intertwine into precisely that subalgebra before the group-like conclusion is available. Literal containment supplies the prohibited