Secant numbers: 1, 1, 5, 61, 1385, 50521, 2702765
Quartic reciprocal: 1, 1, 69, 33661, 60376809
Odd-length and dyadic reconstructions: E_8 = 1385
Dyadic E_8 tail valuations: 5, 8, 13, 15, exact
Matrix checks: inverse, composition, factorial normalization, packets, Pascal sampling
Sampling cutoff control: 3 columns give 32; 5 columns give 1376
Base changes: exact cocycle; prime-dependent precision checked
Supercongruence combination: 8 mod 81 and 9 mod 32 give 1385 mod 2592
Signed Euler difference coordinates: 1, -2, 8, -80, 1664
Spacing-two lane: 1, 5, 1385; differences: 1, 4, 1376
Refinement: 2*4 + 1376 = 1384
Prime residual: 2*(-2) + 8 = 4
Newton residual orders: 2, 4, 8, 16, at least 32
PASS: Euler packets, polynomials and residuals
