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:

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:

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.