Variations, kernels and distinguishability
The maintained derivations are in the technical paper and its PDF.
| Result | Paper location |
|---|---|
| Positive action differences accumulate at zero for the constant-force family and nondegenerate smooth variations | Propositions 1–2 |
| The Dirichlet Hessian has a positive normalized bound while its quadratic cost scales with amplitude | Section 3 |
| The free short-time kernel tends to \(\delta\) with a correction proportional to \(\delta''\) | Section 4 |
| The quantum two-arm first-lobe threshold is \(2\hbar\arccos([4p(1-p)]^{1/(2N)})\) | Proposition 3 |
| A free relativistic particle retains arbitrarily small positive action differences inside a strict speed margin | Section 6 |
The operational result assumes the specified quantum states, phase rule, equal priors and joint binary measurements on \(N\) independent copies. At fixed \(1/2<p<1\) its threshold tends to zero as \(N\) grows; at \(p=1\) it stays \(\pi\hbar\) for every finite \(N\).
The claim ledger records assumptions and review status. The next calculation compares oscillator and free-particle spectral gaps (M03).