Passes 3981–3988

Exact baseline retained

The fixed-parent extension problem has exact maximum A4 = 57. The five-fiber coherent algebra has 48 orbital relations and 904 nonzero intersection constants.

Universal adjacent-factor bound

For every port order, the cut identity

B_kB_k^T = 36I − A_k²

and trace constraints force

N_adjacent ≥ 229.

The known order has cut sum 253; an exact searched order reaches 251.

Photon falsifier

The design uses 48 randomized cells and 16 independent regressors. It separates the length-by-log(mode-count) slope from encoder, detector, transverse momentum, spectrum, pulse width, intensity, and drift.

Deleting measured spatial and spectral covariates creates a false gamma ≈ 1.124×10⁻⁹; the full noiseless model removes it.

Exact W33 photon reflection

U = exp(−iπL/2) = −(I+A)/3 + 2J/15

Each row has amplitude −1/5 on the point and its twelve neighbors, and 2/15 on its twenty-seven nonneighbors. The matrix is a real symmetric involution: U²=I.

This is a global parallel 40-mode analog operation—not forty sequential orthogonal updates.

Metrology and geometry echo

The W33 Laplacian gives ideal QFI 48 for a localized probe and 256 for the optimal extremal-sector superposition. The dual-geometry difference generator has full spectral-range QFI 400, while the sum arm is geometry-blind on the nonuniform sector.

Self-similar tensor kernel

For an actual m-fold tensor carrier, only m+1 amplitude shells occur:

multiplicity = C(m,r)13^m−r27^r

amplitude = (−1/5)^m−r(2/15)^r

The control description compresses; Hilbert-space dimension and vacuum light speed do not.