Slope holonomy is not the fixed-point obstruction

Exact statement

Linear-part holonomy may be nontrivial on a realized cycle even though exact state differences telescope; the affine translation and its cokernel are indispensable.

StatusRefuted exactly

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 realized $1\to2\to1$ cycle is the explicit control.

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 novelty or specialist-review claim is made; the statement is limited to the displayed presentation and hypotheses.

Open work

Use the full affine block rather than its multiplier alone.