slice-at-large-side

• Computes the central hexagon x + y + z = 3(N-1)/2 of the dim 3 parity designs at large odd side and on words of growing odd sides, from the carry block S_b of notes/spectra.md.
• A word (b_1, .., b_L) lists its letters coarsest first; its count is (S_(b_L) .. S_(b_1))[0, 0] and its ink is the count over the (3N^2 + 1)/4 lattice points of the hexagon.
• words counts the slice by brute force over every lattice point of the plane, by the 3x3 carry automaton and by the 2x2 block, on twelve words for code 23 and four words for each of seven other codes, and checks that no carry leaves abs(c) <= 1.
• letter derives the block as polynomials in b per class of b mod 4 by inclusion-exclusion on boxes, checks them against the digit polynomial at odd b = 3..101 and against the closed forms of spectra, splits S_b/b^2 = A + B/b + B_2/b^2, checks the three-carry limit f(c') q(c + c' + g), matches A to [[3u/4, v/8], [3v/2, u/4]], and prints the Perron roots, the exact rho_b, the first-order coefficient mu and the side expansion log(2 lambda) + (mu - 3/2)/b.
• drift derives the drift exponents 1/4, 1/4 + 1/(2 sqrt(7)) and (2 + sqrt(2))/4 by first-order perturbation of the limit letter and of the limit pair in both orders, then runs four words to length 32000 in floats and prints the local exponent at L -> 2L for L = 4000, 8000, 16000 and one Richardson step.
• constants runs the same four words at 40 digits to L = 16384 and 16385, divides the ink by lambda^L L^gamma, extrapolates by Neville in 1/L at two depths and prints their agreement, then the blink ratio against its derived value sqrt((5 sqrt(2) - 1)/3).
• closed checks S_(4k-1) = (k/2)(k K_1 + K_0), the polynomial identity behind W = (1 - 24z + 96z^2)^(-3/4) (1 - 6z, 12z), the series against the integer product at L = 1..60, and Gamma(3/4)(1 + sqrt(3)) / (3 (sqrt(3) - 1)^(3/4)) against the extrapolated constant, printed to 25 digits.
• designs runs all 255 nonempty codes through their 63 weight classes: the symbolic block per class against the digit polynomial at odd b up to 61, the limit letter against [[3u/4, v/8], [3v/2, u/4]], the real roots of the two sign polynomials and of the case guard s_01 s_10 (s_00 where s_01 vanishes), the codes whose block has a zero diagonal on a class, an exact sign check at every odd base up to 15, the law sgn(o - e) at 3 mod 4 and sgn(e - o) at 1 mod 4, and the automaton row sums of the e = o designs at odd b = 3..41.
• Exact arithmetic everywhere except drift, in floats, and constants, in mpmath at 40 digits. Runtimes: words 0.1s, letter 0.2s, drift 0.2s, constants 1.9s, closed 0.3s, designs 0.7s; all six 3.7s.

RUN

uv run python research/lab/py/slice-at-large-side/large.py
uv run python research/lab/py/slice-at-large-side/large.py words
uv run python research/lab/py/slice-at-large-side/large.py letter
uv run python research/lab/py/slice-at-large-side/large.py drift
uv run python research/lab/py/slice-at-large-side/large.py constants
uv run python research/lab/py/slice-at-large-side/large.py closed
uv run python research/lab/py/slice-at-large-side/large.py designs

WITNESSES

• spectra.md THE SLICE AT LARGE SIDE, The word product, the counts 60, 72, 2412, 2688, 300: verb words, no mismatch.
• spectra.md THE SLICE AT LARGE SIDE, The letter at infinite side, the limits, the Perron roots, the exact roots and the side expansion: verb letter.
• spectra.md THE SLICE AT LARGE SIDE, The drift, the exponents and the local fits: verb drift.
• spectra.md THE SLICE AT LARGE SIDE, The constants, the closed form at sides 3 mod 4: verb closed; the blink and the extrapolated constants: verb constants.
• spectra.md THE SLICE AT LARGE SIDE, Every parity design, the letter of every design, the ties and the sign law: verb designs, no mismatch and no violation.