The reflections hkl and −h−k−l form a Friedel or Bijvoet pair. Under normal scattering their intensities are expected to match, but significant resonant scattering in a non-centrosymmetric structure can break that equality. Ordinary point-group equivalents and inversion-related Friedel mates therefore must not be merged without checking the scattering model.
This guide develops one focused reader question within the X-ray Crystallography subject guide. It adds a complete mechanism, original worked decisions, changed-context transfer checks and explicit limits. Read it with The Gold Standard of Education | Learning That Transfers into Life and the How X Works.
All numerical examples are invented teaching cases. They are not operational measurements, production records, financial advice, conservation findings or compliance results.
A fictional corrected dataset gives I(231)=1200±35 and I(−2−3−1)=980±32. Their difference is 220 and its simple independent uncertainty is √(35²+32²)≈47.4, about 4.6 standard uncertainties. That is evidence of a difference under the supplied assumptions, but it does not by itself prove absolute structure: absorption, scaling, indexing and other systematic effects must be checked. The IUCr Friedel-pair definition states when pair intensities are equal and how resonant scattering can break Friedel’s law.
Continue with Separating Systematic Absence from an Unobserved Weak Reflection, Separating Site Occupancy from Atomic Displacement in Refinement and the X-ray Crystallography root.
The short answer is to keep the target quantity, observation and reporting rule separate. Name what the system intends to estimate, what was actually observed, how the summary was formed and which conditions make the inference defensible. If one field is missing, keep the ambiguity visible.
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The reflections hkl and −h−k−l form a Friedel or Bijvoet pair. Under normal scattering their intensities are expected to match, but significant resonant scattering in a non-centrosymmetric structure can break that equality. Ordinary point-group equivalents and inversion-related Friedel mates therefore must not be merged without checking the scattering model.
Chapter contents
Frame the question · Chapters 1–5
2. Separate the two target quantities
Work the example · Chapters 6–10
6. Work the central calculation
7. Check units before interpretation
Check the evidence · Chapters 11–14
11. Use controls that can fail differently
12. Carry uncertainty into the claim
Transfer the method · Chapters 15–18
16. Change one consequential condition
Audit and continue · Chapters 19–22
19. State what it cannot establish
20. Repair an overconfident sentence
Ask whether two reflections are related by the crystal point group, by inversion added under Friedel’s law or only by a chosen merging convention.
Write an evidence ledger before calculating: target quantity, object, unit, boundary, observation rule, transformation and decision limit. Mark every input as observed, stipulated, fitted or assumed.
Apply the rule to the central fictional case with unrounded inputs, then label the result with its object, unit and protocol. Name one alternative explanation and the observation that would distinguish it.
For X-ray Crystallography, complete seven fields: target, object, unit, boundary, protocol, result and limit. For “define the reader question”, a plausible number can otherwise hide a changed definition or undocumented condition.
Change one condition that matters while holding the remaining basis fixed. Recalculate or re-inspect the evidence, state what stays comparable and name the stronger conclusion that still does not follow.
Close with two lines. The first states what the evidence establishes under the named conditions. The second states the nearest tempting conclusion that remains unsupported. Ask another reader to identify the condition that would make the first line false.
Evidence check: preserve the raw observation, the transformation, the comparison rule and the failed alternatives in one audit note. A future reader should be able to reproduce the narrow result without guessing which conditions were held constant.
A Friedel pair reverses all three indices. Ordinary equivalents arise from the actual point-group operations in the chosen setting.
Draw the mechanism in order. Separate the underlying state, the measurement, the mathematical summary and the claim. Then name one rival explanation and the additional observation that could distinguish it.
Apply the rule to the central fictional case with unrounded inputs, then label the result with its object, unit and protocol. Name one alternative explanation and the observation that would distinguish it.
For X-ray Crystallography, complete seven fields: target, object, unit, boundary, protocol, result and limit. For “separate the two target quantities”, a plausible number can otherwise hide a changed definition or undocumented condition.
Change one condition that matters while holding the remaining basis fixed. Recalculate or re-inspect the evidence, state what stays comparable and name the stronger conclusion that still does not follow.
Close with two lines. The first states what the evidence establishes under the named conditions. The second states the nearest tempting conclusion that remains unsupported. Ask another reader to identify the condition that would make the first line false.
Evidence check: preserve the raw observation, the transformation, the comparison rule and the failed alternatives in one audit note. A future reader should be able to reproduce the narrow result without guessing which conditions were held constant.
Name wavelength, anomalous scatterers, centrosymmetry assumption, indexing setting and whether Friedel mates were merged.
Keep the comparison fair by holding the specimen, interval, protocol and denominator constant. If one changes, state that the new number answers a different question even when the label looks familiar.
Apply the rule to the central fictional case with unrounded inputs, then label the result with its object, unit and protocol. Name one alternative explanation and the observation that would distinguish it.
For X-ray Crystallography, complete seven fields: target, object, unit, boundary, protocol, result and limit. For “name the observation rule”, a plausible number can otherwise hide a changed definition or undocumented condition.
Change one condition that matters while holding the remaining basis fixed. Recalculate or re-inspect the evidence, state what stays comparable and name the stronger conclusion that still does not follow.
Close with two lines. The first states what the evidence establishes under the named conditions. The second states the nearest tempting conclusion that remains unsupported. Ask another reader to identify the condition that would make the first line false.
Evidence check: preserve the raw observation, the transformation, the comparison rule and the failed alternatives in one audit note. A future reader should be able to reproduce the narrow result without guessing which conditions were held constant.
Preserve raw intensities, uncertainties, scale batches, absorption correction, detector geometry and symmetry operations.
Use two checks that can fail differently: reconstruct a total, test a limiting case, repeat the result from definitions or inspect a shared control. Two calculations that reuse one assumption are only one check.
Apply the rule to the central fictional case with unrounded inputs, then label the result with its object, unit and protocol. Name one alternative explanation and the observation that would distinguish it.
For X-ray Crystallography, complete seven fields: target, object, unit, boundary, protocol, result and limit. For “protect the denominator and boundary”, a plausible number can otherwise hide a changed definition or undocumented condition.
Change one condition that matters while holding the remaining basis fixed. Recalculate or re-inspect the evidence, state what stays comparable and name the stronger conclusion that still does not follow.
Close with two lines. The first states what the evidence establishes under the named conditions. The second states the nearest tempting conclusion that remains unsupported. Ask another reader to identify the condition that would make the first line false.
Evidence check: preserve the raw observation, the transformation, the comparison rule and the failed alternatives in one audit note. A future reader should be able to reproduce the narrow result without guessing which conditions were held constant.
Build the 231 and −2−3−1 pair with 1200±35 and 980±32 after stipulated corrections.
Separate measurement from decision. A correct number can still be too local, uncertain or method-dependent for the intended action. Report it with its conditions and say what stronger evidence would be needed.
Apply the rule to the central fictional case with unrounded inputs, then label the result with its object, unit and protocol. Name one alternative explanation and the observation that would distinguish it.
For X-ray Crystallography, complete seven fields: target, object, unit, boundary, protocol, result and limit. For “build the fictional evidence ledger”, a plausible number can otherwise hide a changed definition or undocumented condition.
Change one condition that matters while holding the remaining basis fixed. Recalculate or re-inspect the evidence, state what stays comparable and name the stronger conclusion that still does not follow.
Close with two lines. The first states what the evidence establishes under the named conditions. The second states the nearest tempting conclusion that remains unsupported. Ask another reader to identify the condition that would make the first line false.
Evidence check: preserve the raw observation, the transformation, the comparison rule and the failed alternatives in one audit note. A future reader should be able to reproduce the narrow result without guessing which conditions were held constant.
The difference is 220±47.4 under independent errors, about 4.6 standard uncertainties.
| Reflection | Intensity | Standard uncertainty |
|---|---|---|
| 231 | 1200 | 35 |
| −2−3−1 | 980 | 32 |
| difference | 220 | 47.4 |
Preserve identity and order. Equal totals can hide different mechanisms when records come from different specimens, resources, homes or viewing geometries. Aggregate only after the question no longer depends on that identity.
Apply the rule to the central fictional case with unrounded inputs, then label the result with its object, unit and protocol. Name one alternative explanation and the observation that would distinguish it.
For X-ray Crystallography, complete seven fields: target, object, unit, boundary, protocol, result and limit. For “work the central calculation”, a plausible number can otherwise hide a changed definition or undocumented condition.
Change one condition that matters while holding the remaining basis fixed. Recalculate or re-inspect the evidence, state what stays comparable and name the stronger conclusion that still does not follow.
Close with two lines. The first states what the evidence establishes under the named conditions. The second states the nearest tempting conclusion that remains unsupported. Ask another reader to identify the condition that would make the first line false.
Evidence check: preserve the raw observation, the transformation, the comparison rule and the failed alternatives in one audit note. A future reader should be able to reproduce the narrow result without guessing which conditions were held constant.
Indices are dimensionless; intensities and uncertainties share the dataset’s scale. The 4.6 ratio is not an absolute-structure parameter.
Run a changed-context transfer check. Change one consequential condition while holding the remaining basis fixed, calculate again and explain why the result moves or stays stable.
Apply the rule to the central fictional case with unrounded inputs, then label the result with its object, unit and protocol. Name one alternative explanation and the observation that would distinguish it.
For X-ray Crystallography, complete seven fields: target, object, unit, boundary, protocol, result and limit. For “check units before interpretation”, a plausible number can otherwise hide a changed definition or undocumented condition.
Change one condition that matters while holding the remaining basis fixed. Recalculate or re-inspect the evidence, state what stays comparable and name the stronger conclusion that still does not follow.
Close with two lines. The first states what the evidence establishes under the named conditions. The second states the nearest tempting conclusion that remains unsupported. Ask another reader to identify the condition that would make the first line false.
Evidence check: preserve the raw observation, the transformation, the comparison rule and the failed alternatives in one audit note. A future reader should be able to reproduce the narrow result without guessing which conditions were held constant.
Resonant-scattering strength depends on wavelength and composition. A conclusion cannot be transplanted to a different experiment.
Put the boundary of inference beside the answer. Name the system, representation and interval to which the result applies, then name the nearest tempting conclusion the evidence does not establish.
Apply the rule to the central fictional case with unrounded inputs, then label the result with its object, unit and protocol. Name one alternative explanation and the observation that would distinguish it.
For X-ray Crystallography, complete seven fields: target, object, unit, boundary, protocol, result and limit. For “keep method settings visible”, a plausible number can otherwise hide a changed definition or undocumented condition.
Change one condition that matters while holding the remaining basis fixed. Recalculate or re-inspect the evidence, state what stays comparable and name the stronger conclusion that still does not follow.
Close with two lines. The first states what the evidence establishes under the named conditions. The second states the nearest tempting conclusion that remains unsupported. Ask another reader to identify the condition that would make the first line false.
Evidence check: preserve the raw observation, the transformation, the comparison rule and the failed alternatives in one audit note. A future reader should be able to reproduce the narrow result without guessing which conditions were held constant.
A usable anomalous signal needs consistent differences across many pairs, not one dramatic example.
Use uncertainty as structure. Vary the input most capable of changing the conclusion over a defensible range and show whether the ranking or interpretation changes.
Apply the rule to the central fictional case with unrounded inputs, then label the result with its object, unit and protocol. Name one alternative explanation and the observation that would distinguish it.
For X-ray Crystallography, complete seven fields: target, object, unit, boundary, protocol, result and limit. For “locate the usable range”, a plausible number can otherwise hide a changed definition or undocumented condition.
Change one condition that matters while holding the remaining basis fixed. Recalculate or re-inspect the evidence, state what stays comparable and name the stronger conclusion that still does not follow.
Close with two lines. The first states what the evidence establishes under the named conditions. The second states the nearest tempting conclusion that remains unsupported. Ask another reader to identify the condition that would make the first line false.
Evidence check: preserve the raw observation, the transformation, the comparison rule and the failed alternatives in one audit note. A future reader should be able to reproduce the narrow result without guessing which conditions were held constant.
Merging Friedel mates too early can erase the very differences needed for absolute-structure analysis.
Finish with a reproducible evidence package: source records, definitions, exclusions, calculations, validation result and revision rule.
Apply the rule to the central fictional case with unrounded inputs, then label the result with its object, unit and protocol. Name one alternative explanation and the observation that would distinguish it.
For X-ray Crystallography, complete seven fields: target, object, unit, boundary, protocol, result and limit. For “recognise saturation and censoring”, a plausible number can otherwise hide a changed definition or undocumented condition.
Change one condition that matters while holding the remaining basis fixed. Recalculate or re-inspect the evidence, state what stays comparable and name the stronger conclusion that still does not follow.
Close with two lines. The first states what the evidence establishes under the named conditions. The second states the nearest tempting conclusion that remains unsupported. Ask another reader to identify the condition that would make the first line false.
Evidence check: preserve the raw observation, the transformation, the comparison rule and the failed alternatives in one audit note. A future reader should be able to reproduce the narrow result without guessing which conditions were held constant.
Use equivalent-reflection consistency, absorption diagnostics, alternative scaling and independent refinement checks.
Write an evidence ledger before calculating: target quantity, object, unit, boundary, observation rule, transformation and decision limit. Mark every input as observed, stipulated, fitted or assumed.
Apply the rule to the central fictional case with unrounded inputs, then label the result with its object, unit and protocol. Name one alternative explanation and the observation that would distinguish it.
For X-ray Crystallography, complete seven fields: target, object, unit, boundary, protocol, result and limit. For “use controls that can fail differently”, a plausible number can otherwise hide a changed definition or undocumented condition.
Change one condition that matters while holding the remaining basis fixed. Recalculate or re-inspect the evidence, state what stays comparable and name the stronger conclusion that still does not follow.
Close with two lines. The first states what the evidence establishes under the named conditions. The second states the nearest tempting conclusion that remains unsupported. Ask another reader to identify the condition that would make the first line false.
Evidence check: preserve the raw observation, the transformation, the comparison rule and the failed alternatives in one audit note. A future reader should be able to reproduce the narrow result without guessing which conditions were held constant.
Carry covariance when errors are not independent. The square-root calculation is only the stated teaching model.
Draw the mechanism in order. Separate the underlying state, the measurement, the mathematical summary and the claim. Then name one rival explanation and the additional observation that could distinguish it.
Apply the rule to the central fictional case with unrounded inputs, then label the result with its object, unit and protocol. Name one alternative explanation and the observation that would distinguish it.
For X-ray Crystallography, complete seven fields: target, object, unit, boundary, protocol, result and limit. For “carry uncertainty into the claim”, a plausible number can otherwise hide a changed definition or undocumented condition.
Change one condition that matters while holding the remaining basis fixed. Recalculate or re-inspect the evidence, state what stays comparable and name the stronger conclusion that still does not follow.
Close with two lines. The first states what the evidence establishes under the named conditions. The second states the nearest tempting conclusion that remains unsupported. Ask another reader to identify the condition that would make the first line false.
Evidence check: preserve the raw observation, the transformation, the comparison rule and the failed alternatives in one audit note. A future reader should be able to reproduce the narrow result without guessing which conditions were held constant.
A pair difference can reflect anomalous scattering or systematic experimental error; the number alone does not choose.
Keep the comparison fair by holding the specimen, interval, protocol and denominator constant. If one changes, state that the new number answers a different question even when the label looks familiar.
Apply the rule to the central fictional case with unrounded inputs, then label the result with its object, unit and protocol. Name one alternative explanation and the observation that would distinguish it.
For X-ray Crystallography, complete seven fields: target, object, unit, boundary, protocol, result and limit. For “separate mechanism from appearance”, a plausible number can otherwise hide a changed definition or undocumented condition.
Change one condition that matters while holding the remaining basis fixed. Recalculate or re-inspect the evidence, state what stays comparable and name the stronger conclusion that still does not follow.
Close with two lines. The first states what the evidence establishes under the named conditions. The second states the nearest tempting conclusion that remains unsupported. Ask another reader to identify the condition that would make the first line false.
Evidence check: preserve the raw observation, the transformation, the comparison rule and the failed alternatives in one audit note. A future reader should be able to reproduce the narrow result without guessing which conditions were held constant.
Compare datasets only with aligned wavelength, orientation, scaling, corrections, setting and merge policy.
Use two checks that can fail differently: reconstruct a total, test a limiting case, repeat the result from definitions or inspect a shared control. Two calculations that reuse one assumption are only one check.
Apply the rule to the central fictional case with unrounded inputs, then label the result with its object, unit and protocol. Name one alternative explanation and the observation that would distinguish it.
For X-ray Crystallography, complete seven fields: target, object, unit, boundary, protocol, result and limit. For “compare like with like”, a plausible number can otherwise hide a changed definition or undocumented condition.
Change one condition that matters while holding the remaining basis fixed. Recalculate or re-inspect the evidence, state what stays comparable and name the stronger conclusion that still does not follow.
Close with two lines. The first states what the evidence establishes under the named conditions. The second states the nearest tempting conclusion that remains unsupported. Ask another reader to identify the condition that would make the first line false.
Evidence check: preserve the raw observation, the transformation, the comparison rule and the failed alternatives in one audit note. A future reader should be able to reproduce the narrow result without guessing which conditions were held constant.
Test absorption or detector bias by examining symmetry-related pairs across orientation and reciprocal space.
Separate measurement from decision. A correct number can still be too local, uncertain or method-dependent for the intended action. Report it with its conditions and say what stronger evidence would be needed.
Apply the rule to the central fictional case with unrounded inputs, then label the result with its object, unit and protocol. Name one alternative explanation and the observation that would distinguish it.
For X-ray Crystallography, complete seven fields: target, object, unit, boundary, protocol, result and limit. For “test a rival explanation”, a plausible number can otherwise hide a changed definition or undocumented condition.
Change one condition that matters while holding the remaining basis fixed. Recalculate or re-inspect the evidence, state what stays comparable and name the stronger conclusion that still does not follow.
Close with two lines. The first states what the evidence establishes under the named conditions. The second states the nearest tempting conclusion that remains unsupported. Ask another reader to identify the condition that would make the first line false.
Evidence check: preserve the raw observation, the transformation, the comparison rule and the failed alternatives in one audit note. A future reader should be able to reproduce the narrow result without guessing which conditions were held constant.
Change the second intensity to 1170±32. The difference becomes 30±47.4, not persuasive under the same rule.
Preserve identity and order. Equal totals can hide different mechanisms when records come from different specimens, resources, homes or viewing geometries. Aggregate only after the question no longer depends on that identity.
Apply the rule to the central fictional case with unrounded inputs, then label the result with its object, unit and protocol. Name one alternative explanation and the observation that would distinguish it.
For X-ray Crystallography, complete seven fields: target, object, unit, boundary, protocol, result and limit. For “change one consequential condition”, a plausible number can otherwise hide a changed definition or undocumented condition.
Change one condition that matters while holding the remaining basis fixed. Recalculate or re-inspect the evidence, state what stays comparable and name the stronger conclusion that still does not follow.
Close with two lines. The first states what the evidence establishes under the named conditions. The second states the nearest tempting conclusion that remains unsupported. Ask another reader to identify the condition that would make the first line false.
Evidence check: preserve the raw observation, the transformation, the comparison rule and the failed alternatives in one audit note. A future reader should be able to reproduce the narrow result without guessing which conditions were held constant.
The symmetry relation has not changed; only the evidence for a measurable pair difference has changed.
Run a changed-context transfer check. Change one consequential condition while holding the remaining basis fixed, calculate again and explain why the result moves or stays stable.
Apply the rule to the central fictional case with unrounded inputs, then label the result with its object, unit and protocol. Name one alternative explanation and the observation that would distinguish it.
For X-ray Crystallography, complete seven fields: target, object, unit, boundary, protocol, result and limit. For “recalculate the changed case”, a plausible number can otherwise hide a changed definition or undocumented condition.
Change one condition that matters while holding the remaining basis fixed. Recalculate or re-inspect the evidence, state what stays comparable and name the stronger conclusion that still does not follow.
Close with two lines. The first states what the evidence establishes under the named conditions. The second states the nearest tempting conclusion that remains unsupported. Ask another reader to identify the condition that would make the first line false.
Evidence check: preserve the raw observation, the transformation, the comparison rule and the failed alternatives in one audit note. A future reader should be able to reproduce the narrow result without guessing which conditions were held constant.
The example establishes a significant fictional difference under declared independent uncertainties.
Put the boundary of inference beside the answer. Name the system, representation and interval to which the result applies, then name the nearest tempting conclusion the evidence does not establish.
Apply the rule to the central fictional case with unrounded inputs, then label the result with its object, unit and protocol. Name one alternative explanation and the observation that would distinguish it.
For X-ray Crystallography, complete seven fields: target, object, unit, boundary, protocol, result and limit. For “state what the result establishes”, a plausible number can otherwise hide a changed definition or undocumented condition.
Change one condition that matters while holding the remaining basis fixed. Recalculate or re-inspect the evidence, state what stays comparable and name the stronger conclusion that still does not follow.
Close with two lines. The first states what the evidence establishes under the named conditions. The second states the nearest tempting conclusion that remains unsupported. Ask another reader to identify the condition that would make the first line false.
Evidence check: preserve the raw observation, the transformation, the comparison rule and the failed alternatives in one audit note. A future reader should be able to reproduce the narrow result without guessing which conditions were held constant.
It does not determine a real absolute structure, validate a Flack parameter or prescribe data-collection practice.
Use uncertainty as structure. Vary the input most capable of changing the conclusion over a defensible range and show whether the ranking or interpretation changes.
Apply the rule to the central fictional case with unrounded inputs, then label the result with its object, unit and protocol. Name one alternative explanation and the observation that would distinguish it.
For X-ray Crystallography, complete seven fields: target, object, unit, boundary, protocol, result and limit. For “state what it cannot establish”, a plausible number can otherwise hide a changed definition or undocumented condition.
Change one condition that matters while holding the remaining basis fixed. Recalculate or re-inspect the evidence, state what stays comparable and name the stronger conclusion that still does not follow.
Close with two lines. The first states what the evidence establishes under the named conditions. The second states the nearest tempting conclusion that remains unsupported. Ask another reader to identify the condition that would make the first line false.
Evidence check: preserve the raw observation, the transformation, the comparison rule and the failed alternatives in one audit note. A future reader should be able to reproduce the narrow result without guessing which conditions were held constant.
Replace “Friedel equivalents must be identical” with the scattering conditions and the observed pair evidence.
Finish with a reproducible evidence package: source records, definitions, exclusions, calculations, validation result and revision rule.
Apply the rule to the central fictional case with unrounded inputs, then label the result with its object, unit and protocol. Name one alternative explanation and the observation that would distinguish it.
For X-ray Crystallography, complete seven fields: target, object, unit, boundary, protocol, result and limit. For “repair an overconfident sentence”, a plausible number can otherwise hide a changed definition or undocumented condition.
Change one condition that matters while holding the remaining basis fixed. Recalculate or re-inspect the evidence, state what stays comparable and name the stronger conclusion that still does not follow.
Close with two lines. The first states what the evidence establishes under the named conditions. The second states the nearest tempting conclusion that remains unsupported. Ask another reader to identify the condition that would make the first line false.
Evidence check: preserve the raw observation, the transformation, the comparison rule and the failed alternatives in one audit note. A future reader should be able to reproduce the narrow result without guessing which conditions were held constant.
Are Friedel mates always ordinary equivalents? No. That depends on centrosymmetry and scattering assumptions.
Should they always be merged? No. Preserve them when anomalous information matters.
Does one difference prove chirality? No.
Write an evidence ledger before calculating: target quantity, object, unit, boundary, observation rule, transformation and decision limit. Mark every input as observed, stipulated, fitted or assumed.
Apply the rule to the central fictional case with unrounded inputs, then label the result with its object, unit and protocol. Name one alternative explanation and the observation that would distinguish it.
For X-ray Crystallography, complete seven fields: target, object, unit, boundary, protocol, result and limit. For “answer focused reader questions”, a plausible number can otherwise hide a changed definition or undocumented condition.
Change one condition that matters while holding the remaining basis fixed. Recalculate or re-inspect the evidence, state what stays comparable and name the stronger conclusion that still does not follow.
Close with two lines. The first states what the evidence establishes under the named conditions. The second states the nearest tempting conclusion that remains unsupported. Ask another reader to identify the condition that would make the first line false.
Evidence check: preserve the raw observation, the transformation, the comparison rule and the failed alternatives in one audit note. A future reader should be able to reproduce the narrow result without guessing which conditions were held constant.
Use IUCr definitions, retain unmerged evidence where appropriate and connect pair differences to full refinement and validation.
Draw the mechanism in order. Separate the underlying state, the measurement, the mathematical summary and the claim. Then name one rival explanation and the additional observation that could distinguish it.
Apply the rule to the central fictional case with unrounded inputs, then label the result with its object, unit and protocol. Name one alternative explanation and the observation that would distinguish it.
For X-ray Crystallography, complete seven fields: target, object, unit, boundary, protocol, result and limit. For “continue through verified routes”, a plausible number can otherwise hide a changed definition or undocumented condition.
Change one condition that matters while holding the remaining basis fixed. Recalculate or re-inspect the evidence, state what stays comparable and name the stronger conclusion that still does not follow.
Close with two lines. The first states what the evidence establishes under the named conditions. The second states the nearest tempting conclusion that remains unsupported. Ask another reader to identify the condition that would make the first line false.
Evidence check: preserve the raw observation, the transformation, the comparison rule and the failed alternatives in one audit note. A future reader should be able to reproduce the narrow result without guessing which conditions were held constant.
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