Closure-certified copyable PreTeXt starters

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 template is a reusable source skeleton from which a document can be created. A CLI is a command-line interface. A contributed repository hosts material maintained by community contributors. Templates can include content structure, metadata, configuration, and explanatory comments.

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 proposes possible distribution methods without choosing a template schema, review process, or supported versions.

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.

Sample small documents to copy/modify. Maybe as templates in the CLI or in a contributed repository [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

Supply small example documents as templates through a CLI or repository.

Sources

• S1 Ulam AI and the UnsolvedMath Contributors, UnsolvedMath: A Curated Collection of Open Mathematics Problems, record 20002168 (AIM-INFRASTRUCTURE-0068). 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-0068. 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 20002168 and code AIM-INFRASTRUCTURE-0068 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 copied starter can fail only when two copies are assembled

Suppose a starter contains an object identified by $q$ and an internal reference to $q$. A single copy has one target and a well-defined reference. Two byte-identical copies assembled in one document contain two objects with the same identifier. Their internal references no longer designate a unique target under a document-wide identifier rule. Thus successful rendering of one starter does not certify composability of multiple copies.

For a finite starter with identifier set $I$, assign each copy a distinct namespace $n$ and replace every local identifier $i$ by the ordered pair $(n,i)$. Rewrite every internal reference with the same pairing. Within one copy, equality of paired identifiers is equivalent to equality of the original identifiers. Across two copies, equal pairs would force equal namespaces, contradicting distinctness. Therefore all local targets remain unique and every rewritten internal reference reaches its corresponding copied target. This proves collision avoidance and internal-reference preservation in the pair-valued model.

A textual encoding of pairs must itself be injective. Naively concatenate namespace and identifier: $(\text{ab},\text{c})$ and $(\text{a},\text{bc})$ both become abc. A length-prefixed encoding, consisting of the namespace length, a separator, the namespace, and the identifier, is decodable uniquely by reading the length and consuming that many characters. It is therefore injective. Whether such an encoding is valid in the real target's identifier syntax is a separate conformance question.

External references should not be rewritten as local merely because their text equals a local identifier; the starter representation must distinguish local and external reference roles. The argument supplies a concrete requirement for copyable examples, but creates no CLI template and certifies no existing repository.

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.

Single-copy validity is tested against multiple-copy assembly. Ordered pairs are not assumed to remain injective under arbitrary string concatenation.

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.

• 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.