parity-vectors

Coordinate audit for the Paradoxical Sequence benchmark: separates Rozier–Terracol pure reproduction, our trace_escape sampled-universe baseline, and the RT550 odd-accelerated remaining_K overlay.

Why the Collatz (3x+1) conjecture resists proof: the map as a random walk, an optimizer and a Diophantine problem; proofs that fixed horizon monotone Lyapunov certificates and finite residue sieves cannot settle it and the cycle inequality cannot exclude all cycles; a momentum method from log2 3.

Finite-sample observational chapter mapping Collatz waiting-hall events as a state space organized by exit_distance, with miss-front, k-structure corridor, and position-shape selector audits.

A finite-sample observational atlas of accelerated Collatz trajectories, extending the waiting-hall analysis into boundary-front geometry, trajectory grammar, empirical flow, and numeric path anatomy.

Exploratory analysis of feature co-change bundles across four finite Collatz basins, including B004 dissection, cross-basin census, and internal variation checks.