2-adic

Tuppence Programming Language

Arithmetic system of 2-adic numbers in scheme language

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.

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

Jacobsthal Slide and Shiftless Orbit in Collatz Trajectory

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

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

Reconstruction of the Collatz Mapping via Jacobsthal-Normalized Spinor Representation

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

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

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.

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.

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.

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

Implementation of a simple 2-adic cellular automaton.

Exact finite-level mixing geometry for accelerated Collatz dynamics modulo powers of two. This repository does not claim a proof of the Collatz conjecture.