gpt 6 astra ultra attempt on CS-600

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.

An instructor version is a presentation intended for teachers, potentially containing material such as solutions or guidance. Private publishing can mean restricting distribution or separating audiences. Omitting material from a rendered page and enforcing access control are distinct operations.

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 extract does not state the confidential material, access-control model, audience policy, or security requirements.

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.

Need to pay more attention to the Instructor ("Private Publishing") [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

Improve workflows for instructor-oriented or private publication.

Sources

• S1 Ulam AI and the UnsolvedMath Contributors, UnsolvedMath: A Curated Collection of Open Mathematics Problems, record 20002176 (AIM-INFRASTRUCTURE-0076). 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-0076. 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 20002176 and code AIM-INFRASTRUCTURE-0076 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: Hiding instructor text is weaker than excluding it from public output

Choose a byte-observation model for private instructor material. A document has public part $p$ and secret part $s$; public publication produces a byte string $R(p,s)$. Hiding a secret answer with a visual style does not ensure confidentiality in this model. For example the public bytes containing a hidden answer 2 differ from those containing a hidden answer 3, even if the displayed page looks identical. An observer reading the delivered bytes distinguishes the secrets.

The exact noninterference condition for this model is \[ R(p,s_1)=R(p,s_2)\quad\text{for all }p,s_1,s_2. \] On a nonempty product domain this is equivalent to the existence of a function $G$ of public input alone with $R(p,s)=G(p)$. One direction follows by substitution. For the other, fix any secret $s_0$ and define $G(p)=R(p,s_0)$; the displayed equality makes this independent of which secret is actually supplied. This is a proved factorization property, not a security audit of any renderer.

A cache can invalidate an otherwise separated pipeline. Suppose the same cache key $k$ is used for an instructor rendition and a public rendition, and lookup returns the first stored bytes. If instructor output is stored first, a later public request can receive it unchanged. Including audience and relevant source revision in the cache identity prevents this particular alias, provided distinct keys really address distinct entries. The result says nothing about access-control enforcement, logs, network metadata, or deployment behavior. Those are outside the byte-string model and must not be inferred from the factorization lemma.

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 observer and secret domain are explicit. Visual hiding is not treated as byte-level exclusion, and a mathematical noninterference condition is not advertised as actual privacy certification.

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.