Context closure for stand-alone PreTeXt worksheets

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 standalone worksheet is a document that can be produced independently of its enclosing book or course. Its required resources can include metadata, images, styles, and definitions of cross-reference targets.

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. No completeness criterion for dependencies or required output formats is given.

Catalogue screening limitation: The supplied catalogue records the problem as solved; excluded from an unsolved-problem import.

The source snapshot labels this record 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.

There should also be "stand alone" worksheets. [S2]

Source status.

The supplied catalogue labels this source record 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. This is documentation of a source-labelled solved record, not a newly proposed unsolved problem.

Short English statement

Support worksheets that can be produced and shared independently.

Sources

• S1 Ulam AI and the UnsolvedMath Contributors, UnsolvedMath: A Curated Collection of Open Mathematics Problems, record 20002150 (AIM-INFRASTRUCTURE-0050). 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-0050. 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 20002150 and code AIM-INFRASTRUCTURE-0050 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 standalone fragment can capture hidden macro context

Use a small expansion language: expressions are literal strings, concatenations, or macro names. An environment maps finitely many names to expressions; its macro-dependency graph is acyclic. The value of a fragment is obtained by recursively expanding names. Let the fragment be the single macro $a$. In one environment $a=b$ and $b$ expands to the string 2; in another $a=b$ and $b$ expands to 3. Copying the fragment and the direct definition of $a$ produces identical copied bytes in both cases, yet the intended output differs. No standalone renderer receiving only that copy can preserve both meanings.

There is an exact repair for this restricted language. Collect every macro reachable from the fragment and copy each definition from its original environment. Expanding the copied fragment then produces the original value. To prove this, order the reachable macros topologically so each dependency precedes its user. Macros with no dependencies contain only literal concatenations and have the same value. Inductively, every referenced macro has the same copied value, so replacing it inside a concatenation preserves the user's value. Finally apply the same structural induction to the fragment itself. Acyclicity ensures termination; the proof does not cover recursive expansion.

Even all copied macro definitions can be captured by an ambient wrapper if duplicate names are resolved in favor of the wrapper. With copied $b=2$ and wrapper $b=3$, the fragment changes meaning. Either isolate the copied environment or rename its macro names injectively and update every reference. Injective consistent renaming preserves the dependency graph and the preceding induction. A wrapper that only makes a file syntactically complete therefore does not establish context independence.

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.

The macro language is a declared model, not a claim about arbitrary PreTeXt or TeX expansion. Direct dependencies, transitive dependencies, and host name capture are separately tested.

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.