You are performing Pass 0 of a pre-registered adversarial review: a blind primary-source mathematical reconstruction.

INPUT BOUNDARY
- Use only the uploaded packet `math_blind_primary_packet_v1.zip` and the exact pinned primary-source URLs listed in its `PINNED_SOURCE_LINKS.md`.
- Do not use memory, personalization, prior chats, custom instructions, author credentials, social-media conduct, model consensus, or general web search.
- You may retrieve only the exact pinned URLs in `PINNED_SOURCE_LINKS.md`. Do not substitute a moving branch, later revision, summary, commentary, or search result.
- If any required pinned source cannot be opened completely, STOP the substantive review and return a source-access failure ledger. Do not guess or silently substitute.
- Do not use or infer the conclusions of *The Verdict as Axiom*, Red/Fable, Claude, ChatGPT, Grok, Gemini, Nielsen's social posts, or any local build audit. None is evidence in this pass.

DISCLOSURE FIRST
Before analysis, report:
1. provider and exact visible model/version label;
2. visible reasoning setting or effort;
3. tool, code-execution, URL, and web-search access;
4. whether memory, personalization, project context, connected apps, or prior conversation context is available;
5. any provider-lineage conflict with an artifact;
6. the uploaded packet filename and its expected SHA-256:
   146096dbc0819f4ed493de580ebb77ab2ea6fe01627e246e354208275ae072a0
7. whether you independently computed that hash or merely read it from the packet manifest.

SOURCE-ACCESS LEDGER
List every file and pinned URL actually opened. For each, state whether it was read completely, partially, or not at all. Do not claim complete review of a source you could not fully access.

TASK
Without relying on either side's prior prose conclusions, reconstruct and audit:
1. the exact OpenAI group, module, compact-group, Pontryagin-dual, action, crossed-product, and von Neumann-algebra definitions;
2. the exact meaning of `n = 0` in the OpenAI source, including whether it means an identity shift, an identically zero carry cocycle, or something else;
3. whether the OpenAI and unsigned Anthropic-hosted constructions are identical, related, or distinct, with a precise object-by-object comparison;
4. Ioana Theorem 8.2's applicable hypotheses and conclusions, using the full theorem rather than an introductory paraphrase;
5. whether Nielsen's displayed `Theta` satisfies each applicable hypothesis, including which algebra the non-intertwining condition concerns;
6. the entry conditions and data required by Ioana's Section 9 pipeline, and whether Nielsen has constructed them;
7. the torsion-dependent conclusion actually available from Theorem 8.2;
8. what Nielsen v47's Lean appendix proves, what it assumes or axiomatizes, and what follows only conditionally;
9. the strongest source-grounded defense of Nielsen v47;
10. the strongest source-grounded objections to Nielsen v47;
11. an explicit observation or source finding that would reverse each major conclusion.

OUTPUT REQUIREMENTS
Use this exact structure:
A. Reviewer disclosure
B. Source-access ledger
C. Object map
D. Meaning of OpenAI `n = 0`
E. OpenAI versus unsigned Anthropic-hosted construction
F. Ioana Theorem 8.2 hypothesis/conclusion table
G. Nielsen `Theta` hypothesis audit
H. Section 9 entry-condition audit
I. Torsion branch
J. Nielsen formal appendix: proved versus assumed
K. Strongest defense of Nielsen v47
L. Strongest objections to Nielsen v47
M. Falsifier/reversal matrix
N. Specialist questions and unknowns
O. Narrow final assessment

For every material claim, cite exact PDF page and theorem/lemma/remark number, or exact Lean identifier and line range. Quote sparingly. Distinguish these labels precisely:
- proved
- formally checked
- source-inspected
- finite computation
- inference
- specialist question
- unknown

Do not present model agreement as peer review or independent validation. Do not diagnose any person or infer private intent. Do not reveal hidden chain-of-thought; provide concise, checkable reasons and citations.

This is a one-shot frozen pass. Do not ask for substantive corrections or invite iterative debate. Ask a question only if a required source is inaccessible or corrupted.
