Answer Plausibility Checker

Purpose

Audit a candidate physical result before trusting it. This skill is a screen, not a proof: passing the checks does not establish that a derivation or experiment is correct, while one well-founded failure is enough to reopen the work.

Inputs

Ask only for missing information that can change the verdict:

• candidate value, uncertainty, and unit;
• quantity being estimated and the system/context;
• relevant input scales and assumptions;
• an expected range or comparison value, with source and date when available;
• applicable limiting cases;
• for an open-ended model or experiment, conserved totals and their initial/final or input/output values.

Do not invent missing units, reference values, uncertainties, or conservation terms. Mark unavailable checks not run.

Workflow

1. Restate the claim

Normalize the result as:

quantity = value ± uncertainty unit
conditions = ...
source = calculation | estimate | fit | simulation | measurement

Keep measured, assumed, and derived values distinct.

2. Run independent checks

Use as many independent anchors as the evidence permits.

1. Units and dimensions

   • Confirm that the stated unit matches the requested physical quantity.
   • Check dimensions in the final expression when the expression is available.
   • A dimensionally correct answer can still be physically wrong; never stop here.

2. Sign and domain

   • Check required bounds: mass and absolute temperature are nonnegative; a probability lies in [0,1]; speed is below the applicable model limit; geometry obeys its domain.
   • Distinguish signed components from magnitudes. A negative component may be valid.

3. Order of magnitude

   • Compare the result with a justified scale from the problem, a transparent Fermi estimate, or a sourced reference value.
   • Report the ratio and base-10 order gap. Do not call a difference “huge” without quantifying it.
   • Treat reference tables as prompts to verify, not timeless authority. Follow references/reference-values.md.

4. Limiting behavior

   • Vary one controlling parameter toward a meaningful small, large, zero, symmetry, or known-special-case limit.
   • State the expected physical behavior before comparing it with the candidate formula.
   • If symbolic limit evaluation or series expansion is the main task, hand off to limiting-case-validator.

5. Conservation or balance

   • For energy, momentum, charge, mass, particle number, or another applicable total, write a complete balance:

     initial + inflow + generation = final + outflow + dissipation
     

   • Never label a total “not conserved” until exchanges with the environment and source/sink terms have been considered.

   • For research or modeling work without a standard answer, require both an order-of-magnitude anchor and at least one applicable balance anchor. If no conserved total applies, explain why and substitute another independent physical constraint.

6. Uncertainty compatibility

   • When uncertainties are available, judge compatibility with a stated statistical rule—not central values alone. Default rule: with standard uncertainties (coverage factor k=1) u and u_ref, compute z = |value − reference| / sqrt(u² + u_ref²) and treat the two as compatible when z ≤ 2. If you use another threshold, state it.
   • Convert an expanded uncertainty (for example k=2) to a standard uncertainty by dividing by its coverage factor first. Do not judge by whether the ±u intervals overlap: with equal uncertainties they stop overlapping at z ≈ 1.4.
   • Do not infer significance from an uncertainty-free comparison.

3. Use the deterministic checker when useful

scripts/check_plausibility.py checks finite values, bounds, expected-range membership, order gap, uncertainty compatibility (the z rule of check 6), and additive conservation balances from a JSON record. It does not understand physical meaning or unit conversions; normalize all compared values to the same unit first.

python3 scripts/check_plausibility.py case.json
python3 scripts/check_plausibility.py case.json --json

Input format:

{
  "quantity": "launch speed",
  "value": 11200,
  "unit": "m/s",
  "bounds": {"min": 0},
  "expected_range": {"min": 10000, "max": 13000, "source": "source URL", "checked": "YYYY-MM-DD"},
  "reference": {"value": 11186, "unit": "m/s", "source": "source URL", "checked": "YYYY-MM-DD"},
  "max_order_gap": 1,
  "uncertainty": 50,
  "reference_uncertainty": 20,
  "max_z": 2,
  "conservation": {
    "left": [100.0, 5.0],
    "right": [103.0, 2.0],
    "relative_tolerance": 0.001
  }
}

Field	Meaning	Default
value	candidate value (required)	—
quantity, unit, conditions, source, notes	descriptive text; not checked	—
bounds	hard limits, min and/or max (for example min: 0 for a mass)	—
expected_range	min and max of a justified range, optional source and checked	—
reference	comparison value, optional unit, source, checked; enables the order-of-magnitude check	—
max_order_gap	largest allowed abs(log10(value / reference)); needs reference	1
uncertainty, reference_uncertainty	standard uncertainties (k=1) of the candidate and the reference, in the unit of value; need reference	—
max_z	largest allowed z = abs(value − reference) / sqrt(uncertainty² + reference_uncertainty²); the script prints z	2
conservation	left and right arrays of balance terms, optional relative_tolerance	1e-6

Omit checks for which no honest input exists. Unknown or misspelled fields are input errors, so a check is never skipped silently. Exit code 0 means no mechanical check failed, 1 means at least one failed, and 2 means invalid input. --selftest runs the script's regression cases.

4. Diagnose failures

For each failed check, give:

• the observed discrepancy;
• the physical principle or assumption it threatens;
• likely causes, ranked when possible (unit conversion, sign convention, exponent, omitted exchange term, invalid approximation, wrong regime, bad data);
• the cheapest discriminating next check.

Do not repair the result silently. Preserve the original candidate and show any corrected alternative separately.

Output format

## Candidate
- Quantity: ...
- Result: ...
- Conditions: ...

## Checks
| Check | Status | Evidence |
|---|---|---|
| Units/dimensions | pass/fail/not run | ... |
| Sign/domain | pass/fail/not run | ... |
| Order of magnitude | pass/fail/not run | ratio ..., order gap ... |
| Limiting behavior | pass/fail/not run | ... |
| Conservation/balance | pass/fail/not run | residual ... |
| Uncertainty compatibility | pass/fail/not run | z ..., threshold ... |

## Verdict
plausible | questionable | implausible | insufficient evidence

## Next action
- ...

Verdict rules:

• implausible: at least one clear physical contradiction or failed hard constraint;
• questionable: a material discrepancy remains but could be explained by missing context or uncertainty;
• plausible: all applicable checks pass and at least two independent physical anchors were run;
• insufficient evidence: fewer than two independent anchors can be run.

Never translate plausible into “correct.”

Boundaries and handoffs

• Use dimensional-analysis-checker for detailed term-by-term dimensional auditing.
• Use limiting-case-validator for symbolic limits, asymptotic expansions, or systematic enumeration of limits.
• Use fermi-estimation-coach to construct an estimate when no defensible scale exists yet.
• Use derivation-step-checker when the question is which algebraic or physical-law step failed.
• This skill must not fabricate a reference value, silently convert incompatible units, or claim experimental validation from an internal consistency check.

References

• references/reference-values.md — provenance and comparison rules for reference values (check 3)
• ../_shared/physics-evidence-contract.md — §4 academic-integrity boundary shared by all physics skills

变更记录 / Changelog

版本	日期	变更	类型
0.1.1	2026-09-26	不确定度相容改用 z 值（差值除以合成标准不确定度，输入按 k=1 的标准不确定度，默认阈值 max_z=2），原 ±u 区间重叠判据在约 1.4σ 就判失败（references 同步）；输入格式补 expected_range、max_order_gap、max_z；未知或拼错的键改为输入错误；脚本加 --selftest；泛称"derivation checker"改为点名 derivation-step-checker；补 _shared 证据契约 §4 引用；示例命令改用 python3（macOS 自带的只有 python3）	patch
0.1.0	2026-09-05	初始版本	minor