Collision-safe assembly of legacy 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.

Legacy material is existing content created under earlier formats or workflows. Assembly combines selected items into a new organized work. Provenance, identifiers, cross-references, and required assets may need reconciliation when worksheets from multiple sources are combined.

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 source formats, assembly rules, rights information, or fidelity criterion are supplied.

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.

Assembling legacy material (book of worksheets). [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

Assemble existing worksheets into a reusable collection.

Sources

• S1 Ulam AI and the UnsolvedMath Contributors, UnsolvedMath: A Curated Collection of Open Mathematics Problems, record 20002177 (AIM-INFRASTRUCTURE-0077). 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-0077. 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 20002177 and code AIM-INFRASTRUCTURE-0077 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: Legacy assembly cannot infer ambiguous reference intent

Suppose legacy worksheet $A$ has a local target named intro, and worksheet $B$ has a different target with the same name. A reference intro inside $A$ intends the first target. Concatenating the two worksheets creates duplicate identifiers; resolving to the first matching string can silently change behavior if the assembly order is reversed.

If each original worksheet has unique local identifiers and its references are explicitly classified as local, assign source namespaces $a,b$. Map a target $i$ from source $n$ to $(n,i)$ and every local reference to the same pair. Distinct sources give distinct pairs, and within one source the map is injective. Consequently each original local reference resolves to the image of exactly its original target, independent of assembly order. This is a complete preservation argument for the specified typed reference model.

The hypotheses cannot be inferred from arbitrary legacy text. If one source already has two targets named intro and an unqualified reference intro, even the pair $(a,\text{intro})$ remains ambiguous. Two possible author intentions produce the same input bytes, so no deterministic renamer can reconstruct both intentions without more information. Such a case requires an explicit diagnostic or an external disambiguation decision, not a proof that automatic namespacing always succeeds.

Plain textual replacement has a different error: changing every occurrence of intro may alter prose that merely discusses that word. A typed-tree rewrite changes only identifier definitions and reference fields and leaves literal prose fixed. By induction over tree nodes, every prose node is unchanged and every reference node receives exactly its mapped target. This proves the benefit in the chosen representation; parsing real legacy formats into that representation remains an unimplemented part of the original request.

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.

Namespacing presumes unambiguous original local identities. The proof does not silently repair missing author intent, and typed rewriting is distinguished from global string replacement.

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.