Prime-Gap Absolute-Difference Dynamics: A Frozen Prime-Composite Permutation Experiment and a Finite Collapse Certificate

This paper studies a finite absolute-difference experiment built from the gap sequences of the first 100,000 primes and an equal-length sequence of consecutive composite integers. The investigation began with a stronger qualitative hypothesis—that the composite-derived construction would collapse toward zero while the prime-derived construction preserved 1—which failed and is retained as part of the experimental history. Under the subsequently frozen primary protocol, aggregate zero density over the first 20% of difference depth produced an authentic composite-minus-prime effect of +0.0038769665387030083. Against 200 controls formed by independently and uniformly permuting the exact prime-gap and composite-gap multisets, none reached the authentic effect, giving a one-sided empirical value of 1/201 = 0.0049751 using the standard +1 correction. Post-primary mechanism diagnostics indicate that the prime-side behavior is strongly associated with positional parity/mod-3 structure rather than additional mod-6 information. For the authentic first-100,000-prime input, all values greater than 2 disappear by depth 96. A backward ancestry certificate reduces the row-80 large-amplitude survivors to a 993-node survival skeleton across rows 0–80, originating from 33 initial >2 ancestors in five localized channels. The paper distinguishes proved elementary properties of the absolute-difference operator from authenticated finite computation, permutation evidence, post-primary mechanism diagnostics, and open questions. No universal theorem about prime gaps or proof of Gilbreath's conjecture is claimed.