Task portability for heterogeneous embeddables

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 embeddable is content or functionality incorporated into another document or platform. A diagram represents relationships visually; sonification represents selected data properties through sound. A dataset object packages data and associated access information. Different modalities and interactive tools require different interfaces and dependencies.

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 named systems are examples from the historical source. No supported integration interface, version, accessibility requirement, or resource limit is specified.

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.

Other embeddables: Penrose diagrams, Lurch, Sonification for data (multimodal), large data sets (see Runestone data file object). [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

Explore embedding diagrams, proof tools, sonification, and datasets in educational documents.

Sources

• S1 Ulam AI and the UnsolvedMath Contributors, UnsolvedMath: A Curated Collection of Open Mathematics Problems, record 20002179 (AIM-INFRASTRUCTURE-0079). 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-0079. 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 20002179 and code AIM-INFRASTRUCTURE-0079 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: A static fallback may preserve one data task and lose another

Take an embedded data object consisting of an ordered pair $(x_1,x_2)$. A static fallback showing only the unordered multiset of the two values preserves tasks that depend only on that multiset, such as their sum. It fails the task of identifying which index has the larger value: inputs $(0,1)$ and $(1,0)$ produce the same multiset but have different maximizing indices. Any answer computed only from that fallback must be the same for both and hence cannot be correct on both.

For the specific maximum-location task on pairs with unequal entries, a different fallback can store $(i_*,x_{i_*})$, where $i_*$ is the unique maximizing index. A decoder returning the stored index and value answers that task exactly. But this fallback loses arbitrary entry queries. Inputs $(0,2)$ and $(1,2)$ have the same maximum summary $(2,2)$, while the first entries differ. Thus success on one declared task does not imply preservation of the whole embedded object or all interactive queries.

The general finite statement is simple but useful. For a representation map $F:X\to Y$ and task $q:X\to Z$, a decoder $d$ with $q=d\circ F$ exists exactly when $q$ is constant on every fiber of $F$. Necessity follows because equal $F$ values give equal decoder outputs. For sufficiency, define $d(y)$ to be $q(x)$ for any $x$ with $F(x)=y$; fiber constancy makes this well-defined on the image. Values outside the image can be left undefined. The two examples respectively satisfy and violate this condition for different tasks.

This supplies an exact test of claimed fallback semantics in a finite model. It does not equate diagrams, proof tools, audio, and datasets, nor determine accessibility or embedding APIs for the systems named in the source.

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.

Portability is qualified by a declared task. Preserving one query is not confused with invertibility of the entire data object or with equivalence of all media.

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.