dimension-one-ladder

• Regenerates the coprime terms of the three base-three mask designs, the moment ladder of the ternary gasket, and the occupied-ray census.
• Terms: A(level) for the carpet, sponge and Vicsek plus by Mobius over the quotient box with a subset-lattice inner count, checked against brute force and the kept terms/ files.
• Ladder: exact carry matrices for the even moments E_2K(G_a), a direct convolution as second builder, factored characteristic polynomials, the strongly connected component of the zero state and the energy cap, a Sturm bracket for lambda_10, the rungs beta_0^(2K) to 2K = 20, the Fourier identities and master bound on every prime 5..199, the dyadic tail and the order-10 main range.
• Census: every ray of the gasket at one level by exact enumeration, per-octave counts, Z, and the multiplier distribution at level 13.

RUN

• CARGO_BUILD_JOBS=4 cargo run --release -p dimension-one-ladder runs the carpet and plus to level 18, the sponge to level 16, the census at level 13..16, about two minutes on eight cores.
• ... -p dimension-one-ladder -- terms carpet 20 or census 13 14 picks one job; the kept rows reach level 20 for the two planar designs and level 18 for the sponge, and print from terms/ labelled stored only.
• uv run python research/lab/rs/dimension-one-ladder/ladder.py runs the ladder in about a second.

WITNESSES

• coprime.md:82 and research/claims/:27 the carpet gap halving per level to -3.52e-07 at level 20, the sponge gap -3.45e-05 at level 18.
• coprime.md:126 lambda_6 = 57 + 6 sqrt 46 = 97.693980, lambda_8 = 456 + 3 sqrt 11017 = 770.885694, energies matched on the integer.
• coprime.md:128-129 the ladder with the fourth-term exponents 0.883757, 0.687305, 0.545409, 0.443659; coprime.md:133-136 the rows 0.434233, 0.443624, 0.446717, 0.4475978 with kappa_2K = 1.535026, 1.829430, 1.949148, 1.985806.
• coprime.md:139 and research/claims/:169 the energy cap: components 1, 7, 7, 19 of 1, 9, 9, 25 states, ratios E_2K(G_a)/lambda_2K^a at a = 6 of 1, 0.942327, 0.790590, 0.643725.
• coprime.md:140-142 and research/claims/:170 the master bound at order 2K, the seam 3a against the level, the constant 2/(1 - 3^(-Lambda_2K/2K)) <= 5.1843, worst ratio 0.7839 at (11, 2) for the order-10 block alone over 833 cases and 0.8755 at (13, 4) for the min over all orders, zero violations either way, worst main-range sum over cap 0.8630.
• coprime.md:143-144 and research/claims/:171 the E_10 row, the factored M_10 polynomial, the Sturm bracket lambda_10 < 6664.1136626, kappa_10 > 1.985805792698, beta_0^(10) > 0.447597813453.
• coprime.md:146-147 rows 12..20 to 0.447930346, 6.42e-7 under the wall 0.447930987882; research/claims/:353 the Perron roots 59307.487289 .. 387432198.159.
• research/claims/:114 the pincer window (0.4475978, 0.6402122]; research/claims/:172 and :292 the tenth rung, whose M_10 this study rebuilds by a second builder.
• coprime.md:168 and research/claims/:165 the level 13 census 1,044,842 / 1,044,840, 699,508 singles at 17% of Z, 339,530 in [2,5] at 55%, ten shifts at 14%, sum M = 1,577,940, max M = 376.
• coprime.md:169 and research/claims/:349 totals 3,151,658, 9,491,966, 28,545,342, peak occ(8,level)/3^8 = 2.217, 2.492, 2.740, band exponents 0.5249 / 0.6052, 0.5677, 0.5348 / 0.6096, 0.5765; coprime.md:159 Z = 4,003,372 .. 99,800,950 at level 13..16.