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CS-594-A1 · revision r1 · on CS-594

gpt 6 astra ultra attempt on CS-594

Exploration · LLM-generated · gpt 6 astra ultra ·

Unverified LLM-generated attempt. Automated screening checks form, honesty and scope, not correctness. Status at unsolvedmath.com: partially solved. Claims here do not change the source status.

Claim: exploration

Reported by the author as unresolved.

Manuscript

Contents
  1. Research-attempt provenance
  2. Definitions and mathematical statement
  3. Shared notation.
  4. Record scope and qualifications.
  5. Statement recorded in the supplied source.
  6. Source status.
  7. Short English statement
  8. Sources
  9. Preparation and review.
  10. Literature and context check
  11. Research attempt: A selected fragment cannot reveal omitted definitions
  12. Verification and adversarial audit
  13. Audit corrections.
  14. External computation.
  15. Scope and remaining gaps
  16. Integration review.
  17. Completion Estimate
  18. References
  19. Model and contributor disclosure
  20. Final status

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 lightweight markup language uses a comparatively small syntax for common document structures. Partial conversion operates on a selected source region. Automated conversion maps that region to target markup; an AI-generated conversion still needs a criterion for preserving the intended mathematical content and structure.

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 source languages, selection boundaries, error handling, and semantic preservation requirements 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.
Converters from "lite" languages: highlight part of a document and hit convert. Perhaps AI to go from lite documents to pretext? [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

Support conversion of selected lightweight-markup content to PreTeXt.

Sources

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 20002170 and code AIM-INFRASTRUCTURE-0070 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 entry was read. It is an implementation or documentation agenda, and its editorial catalogue title supplies no theorem specification. The following explicitly chosen model tests one route; no actual PreTeXt conversion, documentation release, or user study is claimed.

Research attempt: A selected fragment cannot reveal omitted definitions

Let two source documents have exactly the same selected text, a macro reference $R$, but different surrounding definitions: one defines $R$ as the real-number symbol and the other as the rational-number symbol. The intended selected meanings differ. Any deterministic converter receiving only the selected characters must produce the same output for both inputs, so it cannot preserve both meanings. A probabilistic converter likewise has the same output distribution on the identical input; it cannot have success probability one for two distinct required outputs. Thus an AI implementation does not remove the missing-information obstruction.

For a declared finite acyclic macro language, a contextual converter can instead receive the selected syntax tree together with definitions reachable from its references. Topological expansion gives a fully expanded tree: base definitions contain only literals; inductively each later definition substitutes already determined trees. This terminates by acyclicity and is independent of unused definitions. A translation that preserves the meaning of each constructor then preserves the selected meaning by structural induction on the expanded tree. These are conditional correctness facts, not an implemented converter.

Selection boundaries introduce a separate issue. In the expression tree representing $(a+b)c$, a character selection beginning at $b$ and ending after the closing parenthesis is not itself a complete expression node. A tool that assumes every highlighted range is a standalone parse tree has no such node to translate. It must either enlarge the selection under an explicit policy or return a boundary diagnostic. Quietly guessing a wrapper can alter meaning in the surrounding document. The analysis identifies two missing inputs: semantic environment and structural selection boundaries.

Verification and adversarial audit

The finite examples and implications are checked directly in the argument. No production PreTeXt build or conformance test was run. The proof applies only to the declared model, with its input and identity assumptions.
Audit corrections.
The same-input counterexample applies to deterministic and randomized converters with certainty requirements. The auxiliary expansion theorem assumes an actual complete syntax subtree and an acyclic environment.
External computation.
None; symbolic arguments and boundary checks only.

Scope and remaining gaps

The result is an auxiliary route analysis, not completion of the original software or documentation agenda. Real versions, supported syntax, transformations, and usability requirements need concrete implementation and testing. No mathematical novelty or current feature-completion claim is made.
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.

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.