Mathodology Agent Pipeline

Mathodology Agent Pipeline Archive

Scope

This skill preserves architectural knowledge about the former Mathodology Python worker and multi-agent pipeline.

The current GitHub branch does not contain the worker source. Use this skill to update archived guidance, explain the former design, or help reconstruct context from history. Do not instruct agents to edit or test missing worker files in this checkout.

Archived Concepts

The former worker coordinated specialized modeling agents around a mathematical modeling run:

• problem interpretation and task decomposition
• literature and evidence search
• model selection and method grounding
• code execution for numerical work
• draft generation and revision
• critique, audit, and final evidence checks

The worker also carried knowledge about HMML-style method retrieval, MATLAB or Octave execution, web and scholarly search tools, figure generation, and runtime skills used by the Coder role.

New Orchestration Use

This skill now also carries the reusable workflow pattern that replaced the removed worker source.

For Claude Code:

• Use .claude/workflows/mathodology-award-submission.md.
• Use .claude/workflows/mathodology-contest-variants.md when the contest is not the default MCM/ICM or CUMCM-style paper workflow.
• Dispatch .claude/agents/mathodology-*.md roles.
• Lead owns phase gates and synthesis.

For Codex:

• Use multi-agents mode.
• Dispatch separate agents for problem analysis, evidence, model design, experiments, critique, writing, and packaging.
• Keep a phase log and run an independent critic gate before advancing.
• Treat execution as phase-sized and resumable. Ask the user only for contest-critical details, then continue automatically when the gate passes.
• In Phase 0, classify the contest type and apply the adapter from docs/WORKFLOWS.md.

Human Confirmation Checkpoints

The workflow should not stop for every ambiguity. Most modeling details can be handled by conservative, explicit assumptions and later critic review.

Ask the user only when the answer would change official requirements, private data access, model route selection, compute or reproducibility constraints, or final submission decisions. The question should state the current phase, why the detail blocks progress, the recommended default, and the consequence of common answers.

For all other ambiguity, record the assumption in the phase log and proceed. If Codex must stop because a response boundary is reached, preserve the current phase, completed gates, unresolved risks, artifact paths, and next action so the next response resumes rather than restarts.

Phase Responsibilities

• Phase 0: problem analyst maps prompt clauses, scoring surface, contest type, deliverables, official constraints, dependencies, and material ambiguities; critic checks requirement coverage, adapter selection, and whether user questions are truly contest-critical.
• Phase 1: evidence researcher builds source ledger, data dictionary, proxy logic, benchmark inventory, citation plan, and evidence gaps; critic checks traceability and proxy defensibility.
• Phase 2: at least two model agents propose alternatives; lead compares at least three routes and selects one with rejection reasons; critic checks route fit, novelty, time feasibility, and absence of generic method stacking.
• Phase 3: modeler writes notation, assumptions, units, objectives, constraints, algorithms, pseudocode, validation metrics, baseline, ablation, sensitivity, and robustness plan; critic checks implementability and mathematical coherence.
• Phase 4: coder produces reproducible computation, environment notes, raw outputs, tables, figures, baseline, ablations, sensitivity, robustness outputs, and run logs; the figure/table set must cover model structure, primary results, sensitivity, robustness, decision tradeoffs, and final recommendations; critic checks number traceability, source data, density, and no cherry-picking.
• Phase 5: modeler and paper editor translate results into prompt-level answers, captions, recommendations, limitations, uncertainty notes, claim-source links, and a figure/table coverage map; critic checks answer coverage, support, and whether visual and tabular evidence is sufficient for a top-tier paper.
• Phase 6: paper editor builds summary, coherent paper narrative, references, appendix, AI-use statement when required, and final figure/table placement; critic checks summary quality, paper coherence, notation, citations, page/format risk, and whether results feel substantive rather than sparse.
• Phase 7: critic audits prompt coverage, math, evidence, reproducibility, writing, formatting, originality, and final scoring risk; lead reruns specialists until no blocker or high issue remains.
• Phase 8: packager assembles final paper, source, code, data notes, figures, tables, README, AI-use statement, and checklist; critic checks compliance, anonymity, size/page limits, secrets, scratch artifacts, and submit-readiness.

Agent Handoff Format

Every specialist must end with:

Agent handoff:
- Phase:
- Agent:
- Files or artifacts produced:
- Decisions made:
- Assumptions introduced:
- Evidence used:
- Commands or computations run:
- Known weaknesses:
- Questions for lead or user:
- Critic focus requested:

Prize-Level Gates

Block progression if any of these are missing:

• prompt requirement without an output
• major assumption without evidence, derivation, or sensitivity check
• selected model without rejected alternatives
• reported number without reproducibility path
• figure or table without interpretation
• sparse result presentation: for a paper-first contest, the final draft must contain a purposeful figure/table system, not only a few isolated visuals
• missing visual/tabular coverage for model architecture, primary comparison, sensitivity, robustness or uncertainty, scenario or policy tradeoff, and final decision summary, unless the contest format explicitly prevents it
• figure/table count inflated with decorative, duplicate, or unsupported artifacts
• figure-generation defects such as overlapping labels, clipped axes, unreadable text, duplicate caption prefixes, orphaned figures, or tables that wrap incoherently in the rendered PDF
• paper claim without support
• final package without README and requirement-to-file checklist
• phase artifact without independent critic review
• blocker or high-severity critic issue without a fix

Figure And Table Density Standard

For MCM/ICM O-prize, CUMCM national-first-prize, and comparable paper-first contests, treat visual and tabular density as a scoring gate, not cosmetic polish.

Minimum expected coverage before Phase 6 passes:

• one model-architecture diagram or algorithm flowchart
• one compact data, assumption, or parameter table
• one baseline or route-comparison figure/table
• one sensitivity figure or tornado/heatmap-style diagnostic
• one robustness, uncertainty, or stress-test figure/table
• one scenario, policy, cost, environmental, or implementation tradeoff figure/table when the problem is decision-facing
• one final decision dashboard or prompt-by-prompt answer table

These are role requirements, not a fixed count. A short sprint may merge roles into fewer artifacts; a full MCM/ICM or national contest paper should usually exceed this minimum while staying inside the page limit. Do not add filler figures. Every visual must carry a result that a judge can use to understand, verify, or compare the solution.

For the full generation and verification contract, use docs/WORKFLOWS.md / docs/WORKFLOWS_zh.md section "Figure And Table Generation Specification". The key operational rule is: generate from source data, render the final PDF, create a figure/page contact sheet, visually inspect it, and block any phase with overlap, clipping, illegible text, duplicated captions, or unsupported filler visuals.

How To Maintain This Skill

When updating archived pipeline guidance:

1. State clearly that the implementation is historical and not present on this branch.
2. Prefer conceptual boundaries over file paths.
3. Avoid commands that imply the current checkout can run the old worker tests.
4. If exact implementation evidence is needed, inspect Git history in a separate worktree.
5. Keep details reusable for future agents who need to understand or rebuild the pipeline.

Useful Questions

Use this skill for questions like:

• How did the former multi-agent modeling pipeline divide responsibility?
• What did the Coder, Critic, Search, MATLAB, or HMML concepts mean?
• Which archived behavior should be preserved in skills documentation?
• What must be recovered from Git history before rebuilding a worker?

Current-Branch Rule

Any current-branch edit should be limited to skills or documentation. Do not add worker source, tests, package files, run artifacts, or runtime skill directories back to this branch unless the user explicitly changes the repository strategy.

Source & license

This open-source skill is cataloged on AgentStack and links to its original source — we do not rehost the code.

• Author: sweetcornna
• Source: sweetcornna/mathodology
• License: MIT

Install and usage instructions live in the source repository linked above.