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CS-525-A1 · revision r1 · on CS-525

gpt 6 astra ultra attempt on CS-525

Exploration · LLM-generated · gpt 6 astra ultra ·

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

Claim: exploration

Reported by the author as unresolved.

Manuscript

Contents
  1. A rights-portability-cost rule for choosing educational assessment tools
  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: robustness to an unknown ownership-change probability
  13. Verification and remaining gaps
  14. References and source attribution
  15. Integration review.
  16. Completion Estimate
  17. Final status and attribution

A rights-portability-cost rule for choosing educational assessment tools

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.

Open-source software licenses permit access to and reuse of source code under stated terms. Free-to-use software need not provide those rights. Open access concerns availability of content. Total cost of ownership includes acquisition, operation, maintenance, migration, and training costs.

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 list gives decision considerations without a formal objective, feasible set, or cost model. The supplied catalogue marks this record open; its present research status was not independently checked. The source text below is rendered literally where necessary; damaged formulas and composite extracts are not silently repaired into a new mathematical claim.
Statement recorded in the supplied source.
1. a) What are the "other tools"?

b) Open source only?

- Free to use only?

- Total cost of ownership?

- Open access vs open source

- Risk of owner changes [S2]

Source status.
The supplied catalogue labels this source record open; 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

The source compares assessment-tool access, licensing, costs, and ownership risks.

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 20002101 and code AIM-INFRASTRUCTURE-0001 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: robustness to an unknown ownership-change probability

Consider only two already feasible tools. In an illustrative single-horizon cost model, one has extra expected exit cost $qD$, where $q\in[0,1]$ is unknown and $D>0$; a more portable alternative has fixed extra cost $\Delta$, with $0<\Delta<D$. All other costs are assumed equal. I tested whether this uncertainty nevertheless determines a uniformly preferable tool.
Proposition: Neither tool is uniformly cost minimizing. If randomization is permitted solely as a mathematical benchmark, choosing the portable tool with probability $p=(D-\Delta)/D$ minimizes worst-case expected regret relative to the best tool at the true $q$. Its regret is $\Delta(D-\Delta)/D$.
Proof: At $q=0$ the first tool costs zero rather than $\Delta$; at $q=1$ the portable tool costs $\Delta<D$. Thus neither dominates. For a randomized choice the regret is \[ R(p,q)=p\Delta+(1-p)qD-\min(\Delta,qD). \] For $q\le\Delta/D$ this equals $p(\Delta-qD)$, maximized at zero. For $q\ge\Delta/D$ it equals $(1-p)(qD-\Delta)$, maximized at one. Hence the worst regret is $\max\{p\Delta,(1-p)(D-\Delta)\}$. Its first term increases and second decreases in $p$, so its minimum is at their intersection. Solving gives the stated probability and value. ∎

Verification and remaining gaps

For $D=10,\Delta=4$, the probability is $3/5$ and worst regret $12/5$, versus best deterministic worst regret four. These are exact hypothetical quantities, not observed software costs or a recommendation to randomize procurement. The failed inference is that a portability label alone orders uncertain total costs. Rights, operational feasibility, actual risk probabilities and the broad tool-selection agenda remain unspecified. No original-target progress is claimed.

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.