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Computational finding

FPRD-QA-COL-C02

Deterministic-selector census

Exact statement

At depths one through four, all selectors have 2-adic sections; integral counts are 3,5,6,13,5,6,1 and positive counts are 1,0,0,01,0,0,0.

StatusReproduced
External reviewNo documented external or specialist review of this Quotient Arsenal result is recorded.

Context

Parity words are exact affine charts. Their seams, response quotients, integral cokernels, and 2-adic inverse limits show precisely where finite compatibility differs from membership in the ordinary nonnegative integers.

Proof or evidence

The exact census covers 4, 16, 256, and 65,536 selectors.

Collatz guard-chamber review and independent audit →

Verification notes

The affine word, residue-cylinder, seam, response, integral, positive, 2-adic, selector, rotation, and fixed-weight arguments were reconstructed. An independent implementation checked 131,070 parity words, 98,304 seams, 98,305 swaps, 8,800 primitive necklaces, and all selectors through depth four, including the 001 and all-ones hostile examples.

Limitations

  • No asymptotic law is inferred.

Open work

Study cross-depth compatibility rather than another marginal count.