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
Fibonacci polynomial coordinates: E_4(x) = 2 B_0 + 5 B_1 - 3 B_2 - 2 B_3 + B_4
Fibonacci recurrence defects: 5, -65, 1441, -51845
Reversible sequence transfer: 1, -1, 5, -61, 1385 -> 1, 1, 2, 3, 5
Paper IX Fibonacci packets: step 3 gives u[k+2] = 4*u[k+1] + u[k]
Fibonacci precision ladder: F_37 = 24157817; tail valuations 3, 6, 9, exact
Euler/Fibonacci calculus: full round trip is I_4; integral = 5/4
Quartic address gains: normalized 1, 1, 4, 2; original 1, 1, 5, 3
Dyadic inverse: address 2, target 13 mod 64 -> index 21
Finite mode inverse mod 5: weights 1, 1, -1, -1, 1
Logarithmic Euler coordinates: 1, 0, -1, 3, -6, 0, 90, -630, 2520
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
