16 Numerical certificates
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All calculations in this release were run on CPU. No GPU timing or performance claim is made. Floating-point residuals are implementation checks and are not substitutes for the symbolic proofs.
| Certificate | Value |
|---|---|
| Packet-block semigroup composition residual | \(2.554\times10^{-15}\) |
| Operator reconstruction residual | \(0\) |
| Random-walk mass error | \(0\) |
| Exact Markov generator-lumping defect | \(5.551\times10^{-17}\) |
| Exact finite-horizon lumping error | \(2.220\times10^{-16}\) |
| Perturbed ten-step lumping error | \(6.523\times10^{-3}\) |
| Linear defect bound for that example | \(2.000\times10^{-1}\) |
| Bayesian composition residual | \(5.551\times10^{-17}\) |
| Bayesian packet reconstruction residual | \(0\) |
| Bayesian refinement commutation residual | \(1.110\times10^{-16}\) |
| Bayesian defect-factorization residual | \(7.286\times10^{-17}\) |
| Bayesian flow generator residual | \(1.959\times10^{-11}\) |
| Conditional-expectation tower residual | \(0\) |
| Hermite Gram residual | \(9.992\times10^{-15}\) |
| Fractional semigroup residual | \(2.082\times10^{-17}\) |
| Maximum square-root subordination error | \(1.665\times10^{-16}\) |
| Exact fractional-naturality residual | \(0\) |
| Fractional-power defect / gap certificate | \(0.51059 / 0.95079\) |
| Fractional-semigroup defect / certificate | \(0.12969 / 0.44480\) |
| Observed low-mode PDE convergence order | \(1.999854\) |
| Feynman–Kac enumeration residual | \(1.665\times10^{-16}\) |
| Feshbach projected-resolvent residual | \(5.551\times10^{-17}\) |
| Memory Laplace-transform residual | \(6.939\times10^{-18}\) |
| Duhamel refinement identity residual | \(2.108\times10^{-16}\) |
| Survival monotonicity violation | \(0\) |
| Hidden-Markov normalization error | \(1.110\times10^{-16}\) |
Numerical certificate 16.1: Test suite
The September 6 release records the following automated-test result:
The tests cover projector reconstruction, packet-block semigroup composition, exact and approximate Markov lumping, Bayesian composition and flow, the exact Bayesian refinement criterion, information-loss factorization, likelihood-profile partitions, conditional-expectation towers, Hermite orthogonality, fractional semigroups, square-root subordination, fractional intertwining and semigroup-defect bounds, discrete Green kernels, PDE convergence, Feynman–Kac enumeration, Schur–Feshbach elimination, memory kernels, refinement defects, hidden Markov filtering, and survival curves.
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