2-adic

Algebraic Formulation of the Collatz Operator in Jacobsthal Space: The 3J+J(0,1) Transformation

Uniform spectral gap for the Syracuse (3n+1) mod-2^k transfer operator, proved elementarily for all scales (cert <= 0.8536). The earlier cycle-elimination claim is retracted (3x-1 control) - see README/THEOREM.md. Not a proof of Collatz.

Jacobsthal Slide and Shiftless Orbit in Collatz Trajectory

A finite-data audit of apparent branching in observed Collatz state transitions under position, side, and basin conditioning.

Jacobsthal Spinor Transfer Model from J3 to J2 Space in Collatz Inverse Trees

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.

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.

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.

Reconstruction of the Collatz Mapping via Jacobsthal-Normalized Spinor Representation

Generalization of 3n+1 Collatz Orbits via Jacobsthal Sequences: Visualization using Voronoi Tessellation in 2-adic Logarithmic Spiral Space

The Antlion's Pit in a Morning Glory: Visualizing the Structural Gravity of the 2-adic Collatz Tower

This tool proves that specific exponent patterns cannot correspond to integer Collatz cycles. Unlike testing individual integers, we enumerate the pattern space — proving structural impossibility.