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, andsymbol_table.csvwhen available;- formulas, constraints, objective, parameter values, units, and domains;
- result tables,
result_registry.csv,run_record.csv, andclaim_ledger.csvfor 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:
| Check type | What to verify |
|---|---|
dimensional | Every term in an equation has compatible dimensions and declared units. |
domain | Variables, indices, sets, binary/slack roles, and parameter ranges match the problem and code handoff. |
constraint | Hard constraints are represented, measurable, and not silently softened. |
formula back-substitution | Substitute baseline, boundary, or reported values into formulas to catch algebra/sign/unit errors. |
boundary | Extreme, zero, saturated, or limiting cases behave in the expected direction. |
conservation | Flow, mass, count, probability, budget, or balance laws close within tolerance. |
feasibility wording | Claims use strict feasible, relaxed diagnostic, candidate, not identifiable, or unavoidable gap correctly. |
assumption loss | Simplifications name what realism, constraint, or uncertainty they remove. |
result schema | The table/figure needed to prove the claim can hold all required units, scenarios, baselines, and tolerances. |
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:
csvcheck_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:
textVerification 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.
