executable evidence companion Paper A + Paper B, one claim spine Jeffery Huckstead · Cerebral Graphix

The Finite-Observer Ledger

Exact semidiscrete boundary scattering, and the accounting discipline that caught its own timestep bug.

The boundary sets the impedance. The mode sets the frequency. The exact discrete symbol is two lines of algebra. Below: play with the actual closed forms from Paper A, then see how Paper B's ledger caught — and closed, to 0.41% — a factor-of-two discrepancy the reduced model could not explain.

r(k) = (cos(kh/2) − α)/(cos(kh/2) + α) δ_odd ≈ −κ·R(1−R²) extremum at |R| = 1/√3 96.407% of the discrepancy removed
Paper A PDF Paper B PDF Zenodo 21336985