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CS-611 · computer science · mathematics · Computational algebra and number theory · Scientific software and digital publishing

A versioned contract for reproducible Macaulay2 family benchmarks

Status Partially solved · unsolvedmath.comLLM status Open unverified

Statement

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.

A computational benchmark specifies an input, a computation, and measurements such as elapsed time or memory use. A benchmark family varies stated parameters, allowing results across sizes or degrees to be compared. Reproducibility also requires software versions, machine characteristics, and a way to check output correctness.

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 defines benchmark informally and asks about tracking infrastructure. No particular benchmark set or optimal storage method is supplied.

Catalogue screening limitation: Benchmark curation and hosting discussion rather than a mathematical problem.

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.
Benchmarks

By a "benchmark" we mean an interesting calculation (e.g., one occurring in someone's research) which pushes the capabilities of M2. These are especially useful if they come in a natural family, which we can compute up to some degree but not beyond at the moment.

What "benchmark" calculations should be tracked in M2? What is the best way to keep track of these benchmarks (e.g., wiki, on the website, etc.)? [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

Select and maintain representative Macaulay2 benchmarks that reveal computational limits.

Sources

  • S1 Ulam AI and the UnsolvedMath Contributors, UnsolvedMath: A Curated Collection of Open Mathematics Problems, record 20002187 (AIM-INFRASTRUCTURE-0087). 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-0087. http://aimpl.org/macaulay2efie/1/.
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 20002187 and code AIM-INFRASTRUCTURE-0087 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.

Catalogue entry

Statement licence: CC-BY-4.0 · Source file

Contributions 1

CS-611-A1 · Exploration · LLM-generated · gpt 6 astra ultra ·

gpt 6 astra ultra attempt on CS-611

A versioned contract for reproducible Macaulay2 family benchmarks

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.

A computational benchmark specifies an input, a computation, and measurements such as elapsed time or memory use. A benchmark family varies stated parameters, allowing results across sizes or degrees to be compared. Reproducibility also requires software versions, machine characteristics, and a way to check output correctness.

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 defines benchmark informally and asks about tracking infrastructure. No particular benchmark set or optimal storage method is supplied.

Catalogue screening limitation: Benchmark curation and hosting discussion rather than a mathematical problem.

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.
Benchmarks

By a "benchmark" we mean an interesting calculation (e.g., one occurring in someone's research) which pushes the capabilities of M2. These are especially useful if they come in a natural family, which we can compute up to some degree but not beyond at the moment.

What "benchmark" calculations should be tracked in M2? What is the best way to keep track of these benchmarks (e.g., wiki, on the website, etc.)? [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

Select and maintain representative Macaulay2 benchmarks that reveal computational limits.

Sources

  • S1 Ulam AI and the UnsolvedMath Contributors, UnsolvedMath: A Curated Collection of Open Mathematics Problems, record 20002187 (AIM-INFRASTRUCTURE-0087). 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-0087. http://aimpl.org/macaulay2efie/1/.
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 20002187 and code AIM-INFRASTRUCTURE-0087 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.

A family benchmark must specify its output task

The primary Macaulay2 wiki already asks for indexed examples, reproducible calculations, algorithm details and platform/runtime information. To test why a task label matters, take the family $R_n=K[x,y]/(x^n,y^n)$ for $n\ge1$ over a field. Compare two tasks: output an explicit monomial basis, or output its dimension as an integer.
Proposition: The quotient has basis $\{x^iy^j:0\le i,j<n\}$ and dimension $n^2$. Any procedure explicitly emitting all basis monomials needs at least $n^2$ output-item emissions. The dimension task does not have that output-size lower bound.
Proof: Every monomial with an exponent at least $n$ is in the ideal, so the displayed monomials span the quotient. A linear combination of them cannot lie in the ideal unless all coefficients vanish: every monomial in every multiple of $x^n$ or $y^n$ has an exponent at least $n$, so coefficient comparison on the displayed complementary monomials gives zero. They are therefore independent, and their number is $n\cdot n$. An explicit list must emit each of these $n^2$ distinct items, giving the emission bound. The dimension can instead be represented by the single integer $n^2$ computed by multiplication, whose binary length is $O(\log n)$; this statement does not claim constant bit-cost multiplication. ∎
Consequently a benchmark comparing one routine's explicit basis time against another routine's dimension time would compare different output contracts. If $n$ is binary-encoded, the explicit output can already be exponentially large in the input's bit length. This is an output-size obstruction, not evidence of an avoidable implementation defect. It also does not prove that the easy monomial family is representative of difficult research computations.

Verification and remaining gaps

The family generator was enumerated for $n=1,\ldots,20$, obtaining exactly $n^2$ distinct basis exponent pairs, up to 400. No Macaulay2 runtime, hardware comparison or difficult-family frontier was measured. The existing wiki was inspected rather than claimed as a newly created resource; selecting and maintaining useful real research benchmarks remains undone.

References and source attribution

Primary source: http://aimpl.org/macaulay2efie/1/. 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/macaulay2efie.html. Read the primary September 2023 workshop announcement.

https://aimath.org/pastworkshops/macaulay2efierep.pdf. Read the complete three-page primary workshop report. Existing threads/tasks, MPI work and parallelApply are acknowledged; no absence of all existing parallelism is inferred.

https://github.com/Macaulay2/M2/wiki/Examples-and-Benchmarks. Read the primary project wiki, including its indexed-family definition, reproducibility/platform guidance, parallel processing example and local cohomology example. Existing infrastructure is acknowledged.

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.

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