E17 Finite illustrations and computational checks
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The figures in the article use small matrices chosen to make each mechanism visible. They are not evidence for claims outside the proved finite setting. The accompanying verification script recomputes the following identities with independently generated data.
Packet block convolution, the block differential system, and the Laplace resolvent formula.
The Duhamel and resolvent defect identities.
Exact and perturbed Markov lumping.
Conditional expectation, tower laws, martingale packet energy, and Hermite multipliers.
Bayesian reconstruction, sufficiency, local distortion, and information decomposition.
The evidence variance identity along a Bayesian flow.
The Balakrishnan formula and the fractional defect estimate.
Nodal Green reconstruction and the Poisson error bound.
Discrete Feynman Kac path enumeration.
The Schur Feshbach resolvent and memory transform.
Jordan memory modes, modal truncation, and the Volterra stability estimate.
Feynman Kac killing, survival transforms, moments, and competing risk masses.
| Identity | Typical residual |
|---|---|
| Packet block convolution | below \(3\times10^{-14}\) |
| Duhamel defect | below \(3\times10^{-12}\) |
| Markov lumping | below \(3\times10^{-14}\) |
| Bayesian reconstruction | below \(3\times10^{-15}\) |
| Fractional spectral law | below \(3\times10^{-12}\) |
| Nodal Green identity | below \(3\times10^{-13}\) |
| Feynman Kac enumeration | below \(3\times10^{-14}\) |
| Schur Feshbach resolvent | below \(3\times10^{-12}\) |
| Memory Laplace identity | below \(3\times10^{-11}\) |
| Survival moment formulas | below \(3\times10^{-11}\) |