capwitf/my-mathmodeling-skills/math-verifier

数学核验

用途

Verify the math before it becomes paper language. Treat this skill as an independent hard gate for dimensional consistency, formula back-substitution, boundary behavior, feasibility claims, and assumption loss.

核心规则：不要解新问题，也不要发明缺失的模型部件。只按题面、建模交接、符号表和证据产物核验已经写出、算出或声称的内容。

国一候选门槛：数学核验必须保证题目贴合、建模洞察、证据可信、可复现、边界清楚有公式、单位、约束和边界案例支撑；这是提交质量门槛，不承诺获奖。漂亮结论只要无法回代、无法闭合单位或无法说明边界，就不能进入论文就绪状态。

硬门禁：单位、定义域、约束、边界条件、公式回代或可行性措辞只要未检查、不一致或未知，模型结论就不能进入论文就绪状态。

返回规则：本技能只把发现返回 math-hub。可以建议修复面，但不能直接路由、派发或调用另一个技能。

必要输入

Collect the smallest available set:

• current problem/subquestion and required deliverables;
• problem_brief.md, model_handoff.md, assumption_log.csv, and symbol_table.csv when available;
• formulas, constraints, objective, parameter values, units, and domains;
• result tables, result_registry.csv, run_record.csv, and claim_ledger.csv for computed claims;
• official or user-provided tolerances, hard constraints, and feasibility definitions.

If a needed source is missing, mark the affected check blocked or diagnostic-only; do not fill the gap from memory.

核验检查

Run only checks relevant to the active claim or model route:

不要奖励复杂度。单位闭合、边界已检查的简单模型，优先于隐藏可行性缺口的复杂模型。

产物约定

When maintaining math_verification.csv, use:

check_id,subquestion,artifact,location,claim_id,check_type,input_ref,expected_relation,observed,status,severity,minimum_fix,owner

Statuses:

• pass: check is directly satisfied by cited evidence.
• blocked: required source, unit, formula, constraint, or tolerance is missing.
• fail: evidence contradicts the model or claim.
• diagnostic-only: check reduces uncertainty but is not enough for paper-ready use.

Severity:

• P0: contradiction, fabricated value, missing required deliverable, or rule-breaking feasibility wording.
• P1: unit, constraint, boundary, reproducibility, or validation gap blocking paper-ready status.
• P2: weak assumption explanation, missing stress case, or fragile boundary claim.
• P3: wording, notation, or presentation cleanup after the math is sound.

输出约定

Return:

Verification lock:
Checked artifacts:
Hard check results:
P0/P1 blockers:
Claims allowed as paper-ready:
Claims downgraded to candidate/diagnostic:
Assumption and boundary losses:
Math verification rows:
Smallest repair order:
Return to hub: math-hub
Recommended repair surface:

Recommended repair surface may name model, code, table, figure, abstract, latex, or hub QC, but the handoff always returns to math-hub.

红线

Stop and mark a blocker when:

• a symbol has no unit, domain, or first-use definition;
• two terms are added or compared with incompatible dimensions;
• a hard constraint is absent from the model, code, or feasibility check;
• a reported result cannot be reproduced by formula back-substitution or a cited run;
• a relaxed, violated, or candidate solution is described as strict feasible;
• a boundary case contradicts the claimed mechanism or trend;
• an assumption removes a real constraint without naming the loss;
• verification starts designing a new route instead of checking the current one.

Do not hide failed checks in prose. Downgrade the claim or return the missing evidence to math-hub.