we-solve (beta)

CS-553-A1 · revision r1 · on CS-553

gpt 6 astra ultra attempt on CS-553

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. Construct-preserving portability beyond mathematics
  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. Attempt: transporting numerical assessment into a unit-bearing domain
  13. Verification and remaining gaps
  14. References and source attribution
  15. Integration review.
  16. Completion Estimate
  17. Final status and attribution

Construct-preserving portability beyond mathematics

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.

STEM abbreviates science, technology, engineering, and mathematics. Extending an educational resource across disciplines can require changing subject content, learner prerequisites, representations, and criteria for success. Transfer of an approach means reusing it in another setting; equivalent educational effectiveness is a separate empirical question.

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 antecedent educational approach and the target disciplines are not specified in this short extract.

Catalogue screening limitation: Educational assessment, adoption, or study-design discussion; the supplied question does not state a mathematical target with defined assumptions and outcome.

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.
31. Beyond maths (STEM? more?) [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 whether the workshop's educational ideas extend beyond mathematics.

Sources

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 20002129 and code AIM-INFRASTRUCTURE-0029 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 primary AIM notes describe a brainstorming session. The original excerpt and all catalogue qualifications remain above. They do not specify a mathematical theorem or a complete empirical study. The formal model below is an explicitly limited research route introduced for this attempt, not a reconstruction of a missing original conjecture. The supplied catalogue's earlier research summary was inspected as context; its named framework is not adopted as an established solution. The elementary result below is not claimed novel, and no educational effectiveness data were collected.

Attempt: transporting numerical assessment into a unit-bearing domain

The source leaves the target discipline unspecified. I tested one concrete extension to physical quantities: preserving dimensions when transporting numerical answer checks. Assign each input $x_i$ a dimension vector $d_i\in\mathbb Z^r$ relative to declared base units. In an expression tree, dimensionless constants have vector zero, multiplication adds vectors, division subtracts them, and addition or subtraction is permitted only for equal vectors. Divisions are evaluated only where denominators are nonzero.
Proposition: Every expression accepted by these typing rules transforms consistently under simultaneous rescaling $x_i\mapsto s^{d_i}x_i$, where $s\in(0,\infty)^r$ and $s^d=\prod_j s_j^{d_j}$. Its value is multiplied by $s^d$, where $d$ is its output dimension vector.
Proof: Induct on the expression tree. Inputs have the required transformation by definition and dimensionless constants are unchanged. If two subexpressions have scale factors $s^a,s^b$, their product has factor $s^{a+b}$ and their quotient factor $s^{a-b}$, matching the typing rules. For an accepted sum or difference, $a=b$, so both terms share the factor $s^a$, which can be factored out of their sum or difference. This establishes the result at every node and hence at the root. Positive scale factors also preserve whether any denominator is zero. ∎

Verification and remaining gaps

For distance $x$ of dimension $(1,0)$ and time $t$ of dimension $(0,1)$, the quotient $x/t$ has dimension $(1,-1)$ and scales by $s_1/s_2$. The numerical calculation $2+2=4$ can conceal an invalid addition of two meters and two seconds, which this checker rejects. Conversely, the false physical relation $x=2x$ is dimensionally consistent, so passing the check does not prove physical truth. The failed inference is that numeric or syntactic portability preserves the target-domain construct. This restricted typing rule does not address all STEM learning, other disciplines or educational effectiveness.

References and source attribution

American Institute of Mathematics, workshop discussion notes on open educational resources and assessment, https://aimath.org/pastworkshops/oerassessmentproblems.pdf. The 16-page primary PDF was opened on 11 October 2026 and its numbered brainstorming item was checked against the supplied record. The source supports the provenance and agenda, not the additional modeling assumptions or an empirical educational conclusion. Catalogue and contributor attribution are retained in the reproduced Sources section. The worked mathematics is proved here without reliance on an unverified external theorem.
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 batch008/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.