Residual-context certificates for PreTeXt snippets

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 editor snippet is reusable source text inserted during authoring, sometimes with editable placeholders. VS Code is an editor named in the extract. A useful snippet must be valid in its intended document context and make required dependencies clear.

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 specifies no snippet catalogue, supported schema version, or correctness criterion.

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.

More copy/paste snippets (in vscode) [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

Provide additional copy-and-paste authoring snippets.

Sources

• S1 Ulam AI and the UnsolvedMath Contributors, UnsolvedMath: A Curated Collection of Open Mathematics Problems, record 20002167 (AIM-INFRASTRUCTURE-0067). 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-0067. 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 20002167 and code AIM-INFRASTRUCTURE-0067 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 snippet interface must include its free dependencies

In a finite expression language, a snippet is built from literals, named references, and concatenation. Its free-dependency set is computed recursively: a literal has none; a reference to $a$ has $\{a\}$; concatenation has the union of its children's sets. If two environments agree on every name in that set, the snippet has the same value in both. Proof is structural induction: literal values agree; a referenced name agrees by hypothesis; concatenation of equal component values agrees. This establishes an exact residual-context interface for the declared language.

The interface is needed even for a snippet that looks self-contained. The reference $a$ can render as 2 in one environment and 3 in another. Copying only the reference cannot determine which value was intended. If environment values themselves are macro expressions rather than already evaluated strings, the dependency calculation must recurse through those definitions; a one-level name list can miss $a\to b\to c$.

Name dependencies do not exhaust every possible context. Extend the language with a token that prints the ambient theorem counter. Its output differs between counter states 4 and 5 even when all named strings agree. The prior interface theorem then fails because it omitted a newly observable input. The repair is to include that counter in the environment interface and prove the additional syntax case. This gives a concrete boundary to the strategy: an interface certificate is sound only when its dependency analysis covers every observable form in the accepted snippet grammar.

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.

The induction covers a specified grammar, not arbitrary editor snippets. Counter state supplies an explicit failure when context analysis omits an observable input.

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.