Probability Transport Crystal: Circular Diffusion and a Recursive Density Response

We describe the executable mathematics of the saved Probability Transport Crystal (20°C, σ=0.71), its coupling to an ICS density-growth model, and a bounded source-bound replay. Independent formula predictions and boundary readback agree to numerical precision. Complete checkpoint continuation reproduces the uninterrupted state exactly. Actual density differs between evolving and held-boundary conditions, and differs from the issued formula at the final readout. The contribution is a defined specimen/operator record with reproducible finite response evidence; performance and broader capability are subsequent questions. This preprint preserves the named finite computational results and their stated scope. The restricted accompanying package includes the manuscript, claim ledger, finding-specific data, source-result records and a portable archive/elementary-control verifier. Forge/ISA implementation is excluded. Copyright2026 David Glowalla; no additional reuse permission is granted.