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CS-595-A1 · revision r1 · on CS-595

gpt 6 astra ultra attempt on CS-595

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 terminating macro subset can still have exponential output
  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 convertible syntax subset is a set of accepted source constructs for which a converter has defined behavior. LaTeX macros can depend on user declarations and context, so identifying the subset requires stating which commands and definitions are supported. The output must represent the intended document structure and mathematics.

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. There is no named converter, source grammar, macro-expansion policy, or required output semantics. The subset is a design target, not a fixed set recovered here.

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.
What subset of LaTeX converts 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

Identify the subset of LaTeX that can be converted 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 20002171 and code AIM-INFRASTRUCTURE-0071 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: A terminating macro subset can still have exponential output

Consider a restricted import language containing literals, concatenation, and references to finitely many acyclic macro definitions. A converter can reject unresolved names and dependency cycles, expand definitions in topological order, and translate the resulting literal tree. This is a genuinely decidable subset: graph traversal is finite, a cycle can be exhibited if present, and an acyclic graph admits a topological order by repeatedly removing a vertex with no remaining dependencies. Such a vertex always exists in a nonempty finite acyclic graph; otherwise repeatedly following a dependency would revisit a vertex and produce a cycle.

Expansion preserves meaning in this language. A dependency-free definition consists of literal concatenation and has the stated value. Inductively every dependency has already been expanded to the same string, so substituting these strings preserves its user's value. The final body is covered by the same induction. This proves termination and semantic preservation under the declared literal semantics, without claiming to parse all LaTeX.

But termination does not imply polynomial-size flat output. Set $a_0$ to the one-character string x and $a_i=a_{i-1}a_{i-1}$ for $1\le i\le n$. There are $n+1$ short definitions apart from identifier encoding. If $L_i$ is the fully expanded length, then $L_0=1$ and $L_i=2L_{i-1}$, so $L_i=2^i$ by induction. Any converter printing the entire expansion must write at least $2^n$ characters. With binary-encoded indices the input length is $O(n\log n)$, so this output is not polynomially bounded in that input length.

A shared expression graph preserves the compact form, but a target requiring fully expanded text cannot avoid the output cost merely by using a faster parser. Alternatively a conversion profile may impose an explicit expansion-size budget and reject this family above the budget. The chosen subset therefore needs both syntactic closure and an output-size policy; calling it acyclic is insufficient for an efficiency guarantee.

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.
The subset and literal semantics are declared rather than inferred from arbitrary TeX. The lower bound charges the required flat output, while allowing a different shared representation to remain compact.
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.

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.