gpt 6 astra ultra attempt on CS-572

Research-attempt provenance

Definitions and mathematical statement

Shared notation.

Standard number systems are $\mathbb N,\mathbb Z,\mathbb Q,\mathbb R,\mathbb C$. Specialized notation and index ranges follow the cited source and the definitions below.

PreTeXt represents document structure and mathematical content using semantic markup. A rendered output is a presentation produced from that source, such as web or print output. A workbook collects exercises or activities from a larger work. Front matter supplies introductory material. Provenance links identify the original source and stable identifiers distinguish an extracted item from its location in the full document.

Record scope and qualifications.

The catalogue title is retained as metadata. Named certificates, contracts, bounds or frameworks in that title are not asserted as results of the original source extract. Selection rules, numbering, dependencies, front matter, and cross-reference behavior are implementation choices not fully specified by the extract.

Catalogue screening limitation: PreTeXt software design, documentation, or publication feature request; no mathematical problem is specified by the supplied passage.

The source snapshot labels this record partially solved; this is catalogue metadata rather than independent verification of a mathematical result or the current completion of a project.

Statement recorded in the supplied source.

From a book with worksheets or activities, extract a "workbook". It might have alternate frontmatter, but it should also have links to the original source. [S2]

Source status.

The supplied catalogue labels this source record partially solved; that metadata was checked against the supplied snapshot on 2026-10-11. The label is preserved for provenance and is not an independent verification of present open status or mathematical correctness.

Short English statement

Extract a workbook from a book while retaining links to the source.

Sources

• S1 Ulam AI and the UnsolvedMath Contributors, UnsolvedMath: A Curated Collection of Open Mathematics Problems, record 20002148 (AIM-INFRASTRUCTURE-0048). Catalogue curation and metadata: CC BY 4.0. The source extract is retained; definitions, English summaries and qualifications are editorial additions. https://huggingface.co/datasets/ulamai/UnsolvedMath.
• S2 AIM Workshop Problem Lists, source linked by catalogue record AIM-INFRASTRUCTURE-0048. https://github.com/PreTeXtBook/community/wiki/Moderated-Problem-Session.
• S3 Official PreTeXt Guide, Worksheets (context for worksheet and workspace terminology). https://pretextbook.org/doc/guide/html/overview-worksheet.html.

Preparation and review.

The original source and UnsolvedMath contributors retain attribution for the source extract. Codex (GPT-6; exact serving revision not exposed) assisted with definitions, English summaries, scope notes and formatting. No new human mathematical authorship or independently verified solution is asserted. Permanent source ID 20002148 and code AIM-INFRASTRUCTURE-0048 checked against the complete supplied registry and current repository. Distinct upstream records, including repeated questions and broad or damaged extracts, are retained for complete coverage of the source CS category. A repeated record is not a new independent conjecture. Complete mathematical-equivalence and current-literature review has not been performed. Preparation and final review follow contribution prompts C and D, with source gaps disclosed. Structural and rendering checks do not establish a new theorem or open status.

Literature and context check

The community-session source was consulted directly. Its entry is a feature or design request, without a complete formal specification. The catalogue title is editorial and is not evidence of an existing theorem. The following finite model is an auxiliary investigation; no PreTeXt implementation or project completion is asserted.

Research attempt: A minimal extraction closure and its provenance limitation

Model a book by a finite directed graph $(V,E)$, with an edge $u\to v$ meaning that retaining $u$ requires retaining $v$. These are mandatory conjunctive dependencies, not optional alternatives. For selected worksheets $S\subseteq V$, initialize $C_0=S$ and set $C_{k+1}=C_k\cup\{v:\exists u\in C_k,(u,v)\in E\}$. After at most $|V|$ strict additions this stabilizes at $C$. It contains every node reachable from $S$: induction on path length proves inclusion. Conversely every added node has a path from $S$, by induction on the insertion stage. Hence $C$ is precisely the reachable set and is the smallest dependency-closed superset of $S$. A queue implementation visits every retained node and outgoing edge once, giving $O(|V|+|E|)$ time for explicit adjacency lists.

Selecting only worksheet-tagged nodes fails on the three-node instance $w\to m\to b$: the worksheet $w$ uses a macro $m$ whose expansion depends on a bibliography object $b$. Retaining $w,m$ but not $b$ is still insufficient. This tests transitive rather than merely direct closure.

Closure alone does not preserve provenance. Suppose editions $v_1,v_2$ both have a worksheet with local identifier $w$, but different statements. An extraction retaining only $w$ and a mutable latest-edition URL has the same stored provenance for the two different origins. No resolver using only those fields can recover both origins correctly: identical input forces identical output. A provenance record must distinguish the edition and original item, for example the triple $(\text{publication},\text{edition},\text{id})$, and any actual link must be checked against that edition's manifest. This additional datum does not follow from dependency reachability.

The closure proof deliberately excludes alternatives, conditional imports, and dynamically generated references. With an either-or dependency, requiring both endpoints can cease to be minimal; those cases need a different model.

Verification and adversarial audit

The argument is an exact analysis of the stated finite model. Its counterexample was checked by direct substitution; no PreTeXt build, browser test, or user study was run. The model's assumptions are explicit and are not asserted to describe every real document.

Audit corrections.

Dependency completeness and origin identity are separate requirements. The minimality claim is restricted to a fixed graph of mandatory edges; no general minimum workbook problem is silently solved.

External computation.

None; symbolic arguments and boundary checks only.

Scope and remaining gaps

The calculation identifies a concrete failed route or a restricted correctness property. Actual schema integration, transformations, usability, and compatibility with the full original feature request remain unimplemented and unverified. Thus the original agenda remains unresolved, with no claimed mathematical novelty.

Integration review.

Codex (GPT-6; exact serving revision not exposed) reviewed the written arguments and expanded layout and source-reference wrappers. Repository metadata and the production web renderer were checked using Python 3.13 and JavaScript with MathJax 3.2.2. This model-assisted review is not independent human proof verification; no PDF compilation or formal proof checking is asserted.

Completion Estimate

COMPLETION: 0% The calculations below the preserved source statement investigate a concrete route, but establish no substantiated new progress toward the entire original target. Known special cases and failed sufficient conditions are not credited as a solution.

References

The original source references and catalogue attribution are preserved in the Sources section above. The following URLs were actually consulted for this attempt; retention of an additional original reference does not claim fresh consultation of it.

• https://github.com/PreTeXtBook/community/wiki/Moderated-Problem-Session (consulted 2026-10-11).
• https://pretextbook.org/doc/guide/html/overview-worksheet.html (consulted 2026-10-11).

Model and contributor disclosure

OpenAI gpt-6-astra, requested reasoning configuration ultra, generated this research attempt on 2026-10-11. The exact serving revision is not exposed. Codex GPT-6 performed orchestration, repository-format review, and a model-assisted mathematical audit of the written arguments; its exact serving revision is also not exposed. The mathematical route, boundary checks and final adversarial self-audit followed contribution prompts A then B in docs/contribution_prompts.md, after reading CONTRIBUTING.md. Python 3.14.2 assembled the standalone documents; any mathematical computation is specified in Verification. No theorem prover was used. No human mathematical authorship, substantial human proof correction, or independent human proof checking is asserted. Model-assisted review, source retrieval, and structural checks do not establish correctness or novelty. Full private reasoning transcripts are unavailable as reproducibility artifacts; the complete arguments, inputs and outcomes actually used are stated here or in the companion batch audit.

Final status

Unresolved as a new research contribution. This is a concrete route investigation, not a claim of new complete resolution or a current-status certification. A known answer reproduced for context does not become a new contribution. The catalogue's source-status label is preserved; this attempt status does not assert that a source-labelled solved question is open.