Why does the output look like our Universe?
derivation map
Every continuous one-parameter automorphism group of the finite private algebra acts by blockwise unitary conjugation, generated by one Hamiltonian per block.
For a k-block partition the record channel is exactly the uniform average of the 2^k independently signed block reflections. Cross-block coherence cancels only when all of them are included.
For the layered read law the crossing count per layer is (π/4) n² a⁴ |Σ| in the refinement limit. The finite golden family reproduces it: the ratio to the box-corrected value is within 0.026 of one for q ≥ 21.
The model has no continuum horizon, no collapse and no emitted flux. The area law is a counting statement about a plane section, and the information ledger is finite.
seam-count receipt
Unordered crossing reads per layer across the mid-plane, against the infinite-plane and box-corrected values.
| q | count | π q⁴/4 | vs plane | box value | vs box |
|---|---|---|---|---|---|
| 5 | 323 | 490.9 | 0.658 | 352.2 | 0.917 |
| 8 | 2,164 | 3,217 | 0.673 | 2,487.3 | 0.870 |
| 13 | 17,754 | 22,431.8 | 0.791 | 18,390.1 | 0.965 |
| 21 | 129,830 | 152,745 | 0.850 | 130,882.5 | 0.992 |
| 34 | 907,080 | 1,049,555.8 | 0.864 | 930,602 | 0.975 |
| 55 | 6,496,004 | 7,186,884.1 | 0.904 | 6,542,684.6 | 0.993 |
Move the second slider to the full 2^k patterns and the cross-block weight falls to zero. That is the information the public record does not carry, while the underlying evolution stays unitary. Counts and theorems are quoted from Black-hole information ledger (r2042).
Follow the complete readout from finite causal records into a smooth spacetime image, effective gravity, microscopic interactions, a black-hole lens and an observer-centred sky diagnostic.
The model has no horizon, no collapse and no emitted flux. The area law counts reads across a plane section.
source and scope
What is drawn: Exact crossing counts at q = 5 to 55 against the π q⁴/4 and box-corrected values.
package shared-physics-2026-09-10 · manifest sha256 ec364cad65eede46c7367badf480632e8e39899eedb3abfc883a651789149ff4