gpt 6 astra ultra attempt on CS-597

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.

A CLI processes commands and options supplied as text. Creating a document through a CLI can instantiate a template and configuration. A syllabus and a worksheet have different intended structures and uses even when they share an authoring system.

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. The required commands, templates, validation rules, and implementation status are not specified.

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.

Create by CLI: syllabus, worksheets. [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

Create syllabus and worksheet documents through a command-line interface.

Sources

• S1 Ulam AI and the UnsolvedMath Contributors, UnsolvedMath: A Curated Collection of Open Mathematics Problems, record 20002173 (AIM-INFRASTRUCTURE-0073). 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-0073. https://github.com/PreTeXtBook/community/wiki/Moderated-Problem-Session.

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 20002173 and code AIM-INFRASTRUCTURE-0073 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 primary community-session source was consulted. The record is a broad software-design request, and no mathematical theorem follows from its editorial catalogue title. The finite model below is explicitly auxiliary; it does not certify an actual implementation or current feature status.

Research attempt: Scaffold generation needs more than valid individual files

Consider a generator producing two linked files, a syllabus $s$ and worksheet $w$, with a reference from $s$ to $w$. If it writes $s$ successfully and then fails before writing $w$, each completed file may be syntactically valid, yet the generated project is incomplete. Prevalidating the two file contents does not eliminate this failure between writes.

In an abstract transactional filesystem, a stronger algorithm is: reserve a fresh destination namespace exclusively; create all files in a private staging area; validate the finite manifest and its internal references; atomically publish the completed namespace. Assuming atomic publication and that failures before publication leave staging invisible, every visible new project is complete. The proof has two cases. Before the atomic event the new project is not visible; after it, all manifest entries have already been written and checked. There is no model state in which only a proper prefix of its files is publicly visible.

The freshness check also needs an atomic reservation under concurrency. A separate check-then-write is insufficient: two generators can both observe an absent name, then both write it, with one overwriting the other's content. This interleaving obeys both local prechecks. Exclusive reservation permits at most one successful creator of that name, so the losing operation can report a collision before modifying the reserved project. These are assumptions of a selected abstract service, not evidence that any actual CLI implements the protocol.

Even the proven transaction property does not choose a useful syllabus schema or worksheet pedagogy. It only prevents a specific partial-creation and overwrite route from being mistaken for a successfully generated component collection.

Verification and adversarial audit

The construction and counterexample are checked in the written finite model. No actual PreTeXt build, browser, EPUB reader, or publishing service was tested. All runtime and identity assumptions used by the proof are stated explicitly.

Audit corrections.

Atomic publication and exclusive reservation are explicit premises. Content validation, project completeness, and concurrency correctness are separate claims.

External computation.

None; symbolic arguments and boundary checks only.

Scope and remaining gaps

This is a restricted route investigation. The full feature requires implementation, supported-version decisions, conformance tests, and user-facing evaluation that were not performed here. The original agenda remains unresolved, and no novelty or completed software feature is claimed.

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).

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 and repository-format review; 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.