10 concise reference notes for reasoning. These are public reference material, not private user records or a transfer of language-model weights.

Observation and inference

An observation records what was measured or directly encountered. An inference interprets observations using a model or assumptions. Keep the two separate so another person can inspect the evidence without first accepting the explanation.

Authored reference note; not externally verified product advice · ref-001

Necessary and sufficient conditions

A necessary condition must hold for a result to occur. A sufficient condition guarantees the result within the stated model. From A implies B and B alone, A does not follow: another cause may explain B.

Authored reference note; not externally verified product advice · ref-002

Unknown is not false

Missing information does not automatically establish a negative claim. Ask whether the expected evidence would have been observable if the claim were true. Label missing, unmeasured, unsupported and disproven conclusions differently.

Authored reference note; not externally verified product advice · ref-003

Counterexamples

One valid counterexample defeats a universal claim. To test a rule, search for inputs where its assumptions hold but its conclusion fails. Confirming examples can increase confidence but do not establish every possible case.

Authored reference note; not externally verified product advice · ref-004

Alternative explanations

List several plausible explanations before committing to one. For each, state a prediction that differs from its competitors. Prefer the next observation that separates those predictions instead of repeatedly collecting the same confirming evidence.

Authored reference note; not externally verified product advice · ref-005

Scope of a conclusion

Attach conditions, population, time period and measurement definitions to conclusions. A result established for a small test environment need not hold under production concurrency or different data. Narrow claims are easier to verify and update.

Authored reference note; not externally verified product advice · ref-006

Confidence and precision

Numerical precision is not the same as accuracy or justified confidence. A result with many decimal places can rest on poor assumptions. Report input uncertainty, method limits and sensitivity before interpreting precise outputs as trustworthy.

Authored reference note; not externally verified product advice · ref-007

Contradictory evidence

Preserve incompatible observations and inspect their definitions, timestamps, ownership and sources. Do not silently overwrite a contradiction to make the answer simpler. Different scopes can explain an apparent contradiction without making either observation false.

Authored reference note; not externally verified product advice · ref-008

Decision-relevant questions

Ask for missing information only when it can affect the recommended action, calculation or acceptance test. Questions should reduce uncertainty rather than merely make a report longer. Separate useful clarification from information that is interesting but irrelevant.

Authored reference note; not externally verified product advice · ref-009

Falsifiable assumptions

Write important assumptions in a form that could be checked. Specify which observation would change the conclusion. An explanation that accommodates every possible outcome without changing cannot be discriminated by that test.

Authored reference note; not externally verified product advice · ref-010

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