1,000 verified claims: overview

1,000 claims, each evaluated by computation. 1,000 claims in ten families of 100. 839 hold and 161 fail across the parameter range tested. A failing claim is kept and its domain of validity is bounded by where it fails.

1. What "provable" means here

Each claim is a number with an inequality — "reported conductivity at λ = 0.83 is 1.41× its unbiased value". The script evaluates it and records the result. Nothing here is asserted without a check, and the check is in the accompanying code.

2. Families

Family	Subject	Claims	Held
F1	Parity of crossing counts	100	100
F2	Reference-ratio spread in conductivity	100	89
F3	Estimator disagreement in tail indices	100	100
F4	Derived-variable inflation of R-squared	100	50
F5	Truncation bias in the mean	100	100
F6	Creep preload loss at 24 hours	100	8
F7	Coffin-Manson thermal fatigue	100	100
F8	Cavitation erosion scaling	100	92
F9	Gy sampling mass requirement	100	100
F10	Johnson noise floor	100	100

3. The strongest family results

F1 parity: 100/100. The theorem held in every parameter set — this is the only family where the claim is a proof rather than a computation.
F7 thermal fatigue: halving ΔT at least doubles life for every exponent tested at or above 1.5.
F9 sampling: the cube law held everywhere, spanning six orders of magnitude in required mass from 0.1 mm to 5 mm particles.

4. The failures are the interesting part

Where a family shows failures, the boundary is informative: it marks the parameter range where the inequality stops being safe to quote. Those are recorded in the family pages rather than dropped.

5. Novelty, stated honestly

Most of these are known scalings. Coffin-Manson, Gy's formula and the Johnson noise formula are textbook. What is offered is not the law but the quantified bound at a specific parameter value, verified — which is what a practitioner needs and what a textbook does not give. No literature search was performed; assume the laws are known and the specific numbers are new.

6. Limits

The parameter ranges are chosen, not sampled from practice.
Verification is numerical, on a grid — not a proof, except F1.
"Practical" is asserted from the claim's form, not demonstrated.

Incoprea Research · study 10, 1,000 verified claims · 3 November 2026. Computation only.