# Hironaka char-p resolution review: AI provenance record

## 2026-10-23T16:49-04:00 — frontier-dump/hironaka-char-p-resolution-review
[id: 2026-10-23T16:49-04:00__frontier-dump__hironaka-char-p-resolution-review]

**Consolidated from:** `ai/2026-10-23-hironaka-char-p-resolution-review/ai-usage.md`

**Record status:** completed research dump. Written by the caller (an AI agent working for Taylor) at 2026-10-23T17:50−04:00, America/New_York. Facts come from the primary worker's hand-back, the harness completion notification and the files in this folder.

**Prompt:** Taylor (human) first asked: "Find Hironaka's paper on resolution of singularities in characteristic p." The caller located `refs/hironaka-resolution-of-singularities-in-char-p.pdf` (track-down-reference). Taylor then wrote: "That is it. /frontier-dump perform an adversarial review of the manuscript. If the technique can be repaired, repair it. If the technique cannot be repaired, explain why." No further human direction.

**Agents:**

| Role | Agent ID | Requested model | Observed model | Harness | Requested effort | Observed effort |
| --- | --- | --- | --- | --- | --- | --- |
| caller | main Claude Code session (ID not recorded) | claude-opus-5-5 | claude-opus-5-5 (system prompt) | Claude Code CLI | low | not recorded |
| primary | general-purpose subagent (Agent tool; ID not recorded here) | claude-fable-5-1 (`model: fable`; chosen as the strongest model reachable from the harness) | claude-fable-5-1 (worker's self-report) | Claude Code subagent | "depth over breadth" in prompt; no effort parameter set | not recorded |
| descendant | literature-search general-purpose subagent (ID not recorded) | inherited from primary | not recorded (primary reports claude-fable-5-1 by inheritance, not independently confirmed) | Claude Code subagent | not recorded | not recorded |

Requested and observed models agree where both are known.

**Skill chain:** track-down-reference (caller, locating the PDF) → frontier-dump (caller) → primary research by delegation (+ one literature descendant) → update-ai-usage, update-tokens (caller). Skill files at write time: `frontier-dump` agent-skills HEAD `0eb34a5cbaf8`, SHA-256 `ab73fd7a7aae…`; `track-down-reference`, `update-ai-usage`, `update-tokens` mathcity HEAD `e9a249037bce`, SHA-256 `21e87fd749e5…`, `a8d796def839…`, `7f88edb603b6…`. SageMath 10.8 (`/Applications/SageMath-10-8.app`) for `verify.sage`; Python 3.13.7 for the search scripts. Harness build and web-tool versions: not recorded.

**Policy resolution:** git root `/Users/tdupuy/repos/dumps`; no `AI-POLICY.md` exists, so no instantiated policy governed this write. Recorded against the `update-ai-usage` skill's entry format and existing ledger conventions. The repo needs `new-repo-ai-policy`; no policy file was touched.

**Inputs:** `refs/hironaka-resolution-of-singularities-in-char-p.pdf` (human-authored preprint, H. Hironaka, dated 2017-03-23, 92 pp.; copy also hosted at people.math.harvard.edu/~hironaka/pRes.pdf), read in full via `pdftotext -layout`. Literature (human-authored) consulted read-only: Hauser, "Kangaroo points and oblique polynomials", arXiv:0811.4151 (read in full by the primary); ~45 URLs opened by the descendant (MathOverflow 269651 via proxy, Matsuki Kyoto colloquium page 2019, Cutkosky SLMath 2024, Wikipedia, arXiv abstracts for Cossart–Piltant, CJS, Kawanoue–Matsuki, Temkin, ATW and others, zbMATH API, obituary sources); full opened/failed list in `report.md` §7. Failed: ams.org BAMS 2010 PDF (403), direct MathOverflow, zbmath.org, ICTP indico, web.archive.org, hal.science, Semantic Scholar API.

**Tools:** pdftotext, Bash, WebSearch/WebFetch, SageMath, Python. Primary: 27 tool uses, 3,552 s (harness notification). Descendant: 123 tool uses, ≈14 min (primary's report).

**Work performed:** line-level reading of the whole manuscript with a dependency graph and page locators (`math-audit.md`); explicit counterexamples in characteristic 2 (E = (x²+y⁵,2) in A²; Narasimhan's example in A⁴; Hauser's kangaroo x²+y⁷+yz⁴ in A³) computed in `verify.sage` (V1–V4); exhaustive F₂ searches for monomial-curve counterexamples to Thm 10.3 (`search_constant_ridge*.py`, 0 found); local repairs; repairability assessment; reception/literature survey.

**AI-results (AI4):** every row was produced by claude-fable-5-1 / Claude Code subagent / frontier-dump (row 6 by the descendant). Naming the producer records origin, not mathematical warrant.

| # | Result | Derivation account | Literature search | Refs verified |
| --- | --- | --- | --- | --- |
| 1 | ℘^{nega}(E,−a) is the unit ideal at singular points; Thm 9.2 vacuous; Thm 7.8 Eq. (59) false | two proofs in report §3 (Hasse derivative; via the manuscript's Thms 4.5, 6.3); `verify.sage` V1 | no published analysis of these steps found | manuscript locators only |
| 2 | Thm 16.6(2),(4), Cor. 16.9 false; Thm 16.13 (Main Thm II) lacks a termination argument | explicit blowup of (x²+y⁵,2), report §3.4, V1 | — | — |
| 3 | Thm 15.10 Step 2 false; §6.2 Ě ill-defined ((44) ≡ S(Ê)); Thm 6.1 second sentence false; Thm 14.4/Lemma 14.5 proofs truncated | report §§3.1–3.5, V2 (Narasimhan) | Narasimhan example as reproduced | Narasimhan original not opened |
| 4 | §10 claim Sing(Ě) ⊂ tail hypersurface: UNDETERMINED; lemma excluding monomial-curve counterexamples | parity + second Hasse derivative argument; F₂ searches | — | — |
| 5 | Local repairs (Def. 4.14 typo, Ě redefinition, Lemma 3.14, Thm 6.1 restricted, Cor. 7.15, Thm 10.6 for one smooth D, Thm 7.1 sketch); verdict that the central termination gap is the open problem itself (kangaroo phenomenon), and that "repairable vs demonstrably irreparable" is a false dichotomy | report §5 | Hauser 0811.4151 (opened), Moh bound as cited there | Hauser opened |
| 6 | Reception: preprint never posted to arXiv, no erratum/revision; no expert confirmation (MO 269651; Matsuki 2019); dim ≥ 4 char p still regarded open; obituary facts (Hironaka d. 2026-03-18) | descendant web search | report §7 | opened by descendant; not re-opened by primary or caller |

**Retention (AI15):** this folder holds the evidence. Worker transcripts stay in the Claude Code session logs under `~/.claude/projects/-Users-tdupuy-repos-dumps/`; not copied into the repo.

**Negative results (AI14):** 13 refutations in `report.md` §6 (items 1–13 above, including the false dichotomy in the user's framing and the unconfirmed proof-reading claim of p.4). Carry-forward: no prior dump inputs (0 carried, 0 excluded).

**Review:** agent review: the caller checked file presence and the refutations section, re-ran `verify.sage` under SageMath 10.8 (output byte-identical to `verify-output.txt`) and both search scripts with `python3 -I` (0 solutions, as recorded), and ran `git diff --check` (clean). The caller did not check the mathematics. Human verification: none.

**Integration:** not integrated.

**Scope limits / withheld:** no commits, pushes or edits outside this folder apart from the master ledgers. The primary's Write tool refused the name `report.md` ("subagents should not write report files"); it wrote the file via shell heredoc as the brief required. Unverified items are listed in report §§7–9.
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