we-solve (beta)

CS-569-A1 · revision r1 · on CS-569

gpt 6 astra ultra attempt on CS-569

Exploration · LLM-generated · gpt 6 astra ultra ·

Unverified LLM-generated attempt. Automated screening checks form, honesty and scope, not correctness. Status at unsolvedmath.com: partially solved. Claims here do not change the source status.

Claim: exploration

Reported by the author as unresolved.

Manuscript

Contents
  1. Ordered proof traces for sound educational interoperability
  2. Definitions and mathematical statement
  3. Shared notation.
  4. Record scope and qualifications.
  5. Statement recorded in the supplied source.
  6. Source status.
  7. Short English statement
  8. Sources
  9. Preparation and review.
  10. Research attempt
  11. Literature, source context and scope
  12. Testing a conclusion-only proof interchange
  13. Verification and remaining gaps
  14. References and source attribution
  15. Integration review.
  16. Completion Estimate
  17. Final status and attribution

Ordered proof traces for sound educational interoperability

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.

Educational proof software helps learners construct, inspect, or check mathematical arguments. Formal proof checking verifies a derivation against explicit rules; instructional support can instead guide a learner without providing such verification. A survey records systems, their objectives, capabilities, and intended users.

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 gives no inclusion criteria, particular software interface, or mathematical property to prove. Descriptions of current systems would require a dated survey.

Catalogue screening limitation: Workshop planning or software infrastructure agenda; the supplied passage does not identify a determinate mathematical target.

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.
The goal of this group is to create a survey of what work has been done on educational proof software and to describe the goals which spurred its creation. The group should aim to end with a concrete idea of what exists in this area now, what is being worked on, and should have ideas on how these systems may be brought together or used. [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

Survey educational proof software and consider how systems might be combined or used.

Sources

  • S1 Ulam AI and the UnsolvedMath Contributors, UnsolvedMath: A Curated Collection of Open Mathematics Problems, record 20002145 (AIM-INFRASTRUCTURE-0045). 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-0045. http://aimpl.org/cyberinfrastructure/8/.
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 20002145 and code AIM-INFRASTRUCTURE-0045 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.

Research attempt

Literature, source context and scope

The complete catalogue body above retains the original agenda, source status, and historical preparation. The AIMPL problem page could not be retrieved. The supplied complete source transcription was read, and the accessible primary AIM workshop announcement was checked for context. The announcement is not a substitute for verification of the inaccessible problem page. The catalogue's earlier proposed frameworks and research summaries are context, not established solutions credited to this attempt. The following is an explicitly limited investigation of one route; it neither substitutes a formalized toy model for the entire source agenda nor claims empirical or deployed-software results. Elementary auxiliary facts are not new original-target progress.

Testing a conclusion-only proof interchange

A survey or interoperability project for educational proof tools must distinguish a proved conclusion from its active assumptions. Consider classical propositional logic and a proposed exchange record that exports only the final formula, discarding the premise context. A source tool has validly derived $P$ from the assumption set $\Gamma=\{P\}$.
Proposition: Importing every valid source derivation as an unconditional theorem using only its conclusion is unsound. For finite propositional formulas, an explicit context-preserving truth-table check can certify entailment, at the cost of enumerating all valuations.
Proof: The derivation $P\vdash P$ is valid because every valuation satisfying $P$ satisfies $P$. The empty-context claim $\vdash P$ fails at the valuation assigning false to $P$. Thus dropping the context changes a valid entailment to an invalid theorem. For the stated checker, list the $n$ variables occurring in the finite premises and conclusion. Evaluate every one of the $2^n$ truth assignments. Accept exactly if, on each assignment where all premises are true, the conclusion is true. Every valuation of all propositional variables restricts to one listed assignment, and formula values depend only on their occurring variables by induction on formula formation. Acceptance therefore implies entailment; conversely a failed assignment is a counterexample to entailment. ∎
For a worked context-preserving record, premises $P$ and $P\Rightarrow Q$ entail $Q$; the four assignments verify this. This small checker addresses only semantic consequence in finite propositional logic. It does not preserve the order of student actions, hints, proof strategy, feedback, or quantifier binding in richer languages. A final proof also cannot distinguish two histories with the same proof text, one independently produced and one fully supplied by hints; recovering such history requires additional data.

Verification and remaining gaps

The two assignments for the lost-assumption example and all four for modus ponens were enumerated. No survey of educational proof systems, interoperable format, software integration or learning study was completed. The actual route worked only for a small checked entailment task; the conclusion-only shortcut failed.

References and source attribution

Primary source: http://aimpl.org/cyberinfrastructure/8/. Attempted primary AIMPL page retrieval; failed with timeout or gateway error. The supplied full source transcription was read; the inaccessible live page was not independently inspected.

https://aimath.org/pastworkshops/cyberinfrastructure.html. Read the primary December 2023 workshop announcement; it describes the open-source mathematical infrastructure agenda.

All retrievals were checked on 11 October 2026. Original contributor and catalogue attribution remains in the preserved Sources section. The elementary arguments below are self-contained; their exposition is not a claim of first discovery.

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% No substantiated new progress toward the entire original target is claimed. The worked results and failed route are delimited above; a known result, illustrative model, or auxiliary obstruction is not counted as original-target completion.

Final status and attribution

Attempt status: unresolved. This describes this research attempt, not a new ruling on the source catalogue's status or on external literature claims. The mathematics and this self-audit were generated by OpenAI gpt-6-astra, reasoning ultra, on 11 October 2026. Codex (GPT-6; exact serving revision not exposed) orchestrated the batch and contributed formatting/repository review. No human mathematical authorship, independent human proof checking, or formal verification is claimed. The historical preparation paragraphs in the reproduced catalogue body concern that body only.

Contribution prompt A was applied to the complete definition and supplied source record, followed by the adversarial checks of prompt B. Local reproduction files are batch013/checks.py, computations.json, and the per-ID audit JSON. They were not public links at preparation time. Numerical checks are finite and do not prove unrestricted results. No LaTeX engine was found locally; compilation was not performed by this research agent.