# Public process provenance notes: family 088

Inspected on 10 October 2026 at repository commit `fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb`, recorded as the current tip in `fetch_metadata.json`. These notes concern public process disclosure only. They contain no mathematical correctness assessment or panel outcome.

## Case identity and public summaries

The manuscript map places the selected seven-page paper and its Petty companion in family 088. The overview likewise groups them together. A family is a catalogue grouping; this does not establish that both papers came from one model call or shared a discovery trajectory. [Manuscript map, family 088](https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/CONTENTS.md#L2161), [overview source](https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/overview.tex#L252).

README lists ten abridged reasoning-summary families: 007, 017, 087, 102, 159, 197, 221, 271, 287 and 362. Family 088 is absent. The complete, non-truncated `reasoning_traces` tree has those ten PDFs and one additional TeX source for the Mézard–Parisi summary, with no dedicated selected-paper entry. [README summary list](https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/README.md#L22), [pinned trace directory](https://github.com/openai/math/tree/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/reasoning_traces).

All ten PDFs were downloaded and their existing text extracted successfully; no OCR was used. A bounded keyword screen found no selected-paper title, Brannen reference or family-088 designation. The family-087 Mahler summary mentions projection bodies and the reverse Petty inequality in its own discussion. That incidental overlap is not a process account for the selected paper. `trace_fetch_manifest.json` and `trace_text_search.json` record hashes, extraction and search scope. This supports absence of a dedicated 088 summary in this public inventory, not absence of private traces or of every possible reference anywhere in the repository. [Mahler public summary](https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/reasoning_traces/symmetric-and-general-mahler-conjectures.pdf).

## What the collection-level description discloses

README attributes the collection to an unreleased internal OpenAI model, describes roughly 4,000 posed problems, and reports about three hours of ChatGPT Pro thinking compute per result on average. It describes aggregation into families/manuscripts. These are collection-level statements: they do not identify family 088's model version, exact prompt, elapsed time, compute budget, call count or tools. The named exceptions concern other work; that does not establish a complete case-specific workflow or absence of human intervention here. [Production description](https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/README.md#L40).

No case-specific prompt, tool log, intermediate attempt sequence, retrieval record or timing record was found in the inspected 088 catalogue entry, selected-paper README, global history or dedicated trace inventory. No prompt from another family's summary should be substituted for this case's missing prompt. The public final mathematical exposition is a derivation presented for readers; it is not a historical account of the model's private reasoning.

## Dates, versions and public artifacts

The selected manuscript and its own README carry 24 September 2026 as their date. The selected README has citation metadata and no version notes. The October 7 repository history lists revisions in other subject areas and does not name this paper; that limited fact does not exclude unrecorded internal drafts or edits. [Selected README](https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/A-product-counterexample-to-the-simplex-maximum-for-projection-body-volume-September-24-2026/README.md), [public history](https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/history.md).

A path-specific GitHub history query, restricted to the pinned commit's ancestry and `build/main.tex`, returns one public commit: `adc7f1241b42e322a6451854ab7e4b4c146bf78a`, labelled Initial commit, with committer timestamp 6 October 2026 21:58:50 UTC. This is public Git metadata for that source path, not a discovery timestamp or a full internal drafting history. `manuscript_public_commits.json` and `manuscript_commit_fetch.json` preserve the query and pagination information. [Commit record](https://github.com/openai/math/commit/adc7f1241b42e322a6451854ab7e4b4c146bf78a).

The linked Lean scope document advertises a dimension-twenty product witness and explicitly excludes the paper's eventual exponential-factor result. The catalogue links comparator configurations and a native product-counterexample module. The published module combines named arithmetic, brightness, zonotope and reconstruction components; this describes a public proof artifact, not the original discovery route or evidence that Lean was used during the originating model session. No compilation, dependency audit or comparator verification was performed for these provenance notes. [Family 088 Lean scope](https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/lean/docs/088.md), [formalization catalogue](https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/lean/formalization.yaml), [native artifact](https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/lean/OAI/Geometry/ProjectionVolume/ProductCounterexample.lean).

## Earlier work: acquisition remains unknown

The final manuscript acknowledges and cites Feng–Hu–Liu–Xu's 2026 counterexample work. This establishes that the published text refers to it. It does not show whether the originating model saw that work before producing the construction, received it in a prompt, retrieved it with a tool, encountered it through training or was given a later editorial citation. No such acquisition record for this case is disclosed in the inspected material. Publication dates or a final bibliography alone cannot settle this question. [Selected source, introduction](https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/A-product-counterexample-to-the-simplex-maximum-for-projection-body-volume-September-24-2026/build/main.tex), [bibliography](https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/A-product-counterexample-to-the-simplex-maximum-for-projection-body-volume-September-24-2026/build/references.tex).

Public summaries from other cases can illustrate the kind of information released. They cannot reconstruct this case's missing private reasoning, establish independent rediscovery, or determine the chronological origin of its central idea.