# Stacked hexagon moire

- 2026-08-28 [Verified] The Walsh law's `1/n` and `1/n^2` coefficients follow from plane counting: the plane `x + y + z = 6n - 2`, `z` even, `0 <= x,y,z < 4n` at odd scale `n` splits by macro parity into counts that depend only on the weight `k`, `N_k(2h+1) = [t^(3h+1)](1 + 6t + t^2) E_h(t)^(3-k) O_h(t)^k` with `E_h = 1 + t^2 + ... + t^(2h)` and `O_h = t + t^3 + ... + t^(2h-1)` extracts all four exact quadratic quasipolynomials by finite binomial calculation, and ink is linear in the eight counts, so only the constant, `1/n` and `1/n^2` orders survive the normalization; exact by direct enumeration of the plane at every odd `n <= 55`, all eight macro-parity triples, 28 layers, zero discrepancies; the crate rebuilds only the ink, at codes 23 and 11 over `n = 1..11`, where `m_3 = 0` leaves `N_3(n)` unexercised, so the eight-triple split stays the lane's. Witness: walsh-spectrometer, mrlydemo::walsh_spectrum.
- 2026-08-28 [Conjecture] Layer alignment of the hexagon stack is imperfect by construction: the transparent grid fraction of the common box grows from `0.000` at `n = 1` to `0.245` at `n = 55`, so 24.5% of the box differs between the smallest and largest silhouettes, and ray scans on the triangular lattice are aliasing-limited below band half-width `~0.01`.
- 2026-08-28 [Conjecture] The adjacent-pair limit is `-11/135 = -0.0814815` (lab/rs/hexagon-moire measures `-0.08116` at `(199, 201)` and `-0.08150` at `(249, 251)`, with residue oscillation) and the gcd-echo limit is `29/135 = 0.2148148` (lab/rs/hexagon-moire measures `+0.21473` at `(67, 201)` and `+0.21476` at `(99, 297)`); both are numerology-grade fits and each needs its lattice integral. Witness: lab/rs/hexagon-moire. Superseded: `-11/135` and `29/135` are exact by the phase-map integral, see the layer-pair row under Diagonal slice stack in SETTLED.
- 2026-08-28 [Conjecture] The carpet star's exact decay rate, the coefficient on `(ln L)/L`, is open: one frame measures `-1/8` and another `-0.18`.
- 2026-09-06 [Conjecture] The exact doubling constant of the stack is `253/2160`, matching the two independent branch extrapolations to `2.6e-6` and `2.2e-6` where `19/162` fails at `1.57e-4`; a derivation is missing. Witness: lab/rs/hexagon-moire. Superseded: the constant is exactly `253/2160` by the phase-map integral, see the layer-pair row under Diagonal slice stack in SETTLED.