@article{Novgorodtsev2026,
  author    = {{Aleksei Novgorodtsev}},
  title     = {{Algebraic Proof of the Collatz Conjecture and Universal Classification of 2-Adic Dynamical Systems}},
  publisher = {{Zenodo}},
  year      = {{2026}},
  doi       = {{https://doi.org/10.5281/zenodo.18659804}},
  url       = {{https://zenodo.org/records/18659804}},
  abstract  = {{Complete Algebraic Proof of the Collatz Conjecture
First rigorous proof using elementary modular arithmetic and deterministic counting arguments. No probabilistic, spectral, or measure-theoretic assumptions required for logical closure.

Key Innovation: Resolution of Tao's ensemble-to-trajectory barrier via the Fresh 3-Bit Constraint — a purely algebraic mechanism showing that each return to a fixed exit class consumes 3 fresh bits, creating deterministic rank exhaustion at precision K: at most ⌊(K−6)/3⌋ consecutive returns possible.

Six Independent Obstructions: E[v]=2.0 exact, parity veto, irrationality exclusion, sprint lock (ρ≤1/3), rank exhaustion, marathon lock — ensuring universal convergence.

Verification: All n < 2^71 converge (Barina, 2025). All constants derived analytically.

2. Universal 2-Adic Classification Framework
Information-theoretic unification of integer sequences through single invariant:

δ_eff = log₂(λ) − E_eff[v]

Sign determines fate: δ_eff < 0 → convergence; δ_eff > 0 → divergence/cycles.

Unifies: Collatz family T_m, Fibonacci (δ_eff=−0.416), Pell (δ_eff=+0.322), Tribonacci (δ_eff=−0.043)

Discovery: Rational critical exponents (5/12, 1/5, 4/9, 16/25) governing power-law scaling across T_m family — evidence for discrete renormalization group in 2-adic dynamics.

m=3 Extremality: Classical Collatz uniquely achieves simultaneous extrema in all confining parameters (maximum sprint lock, minimum return drainage, unique negative-drift odd integer).}},
  note      = {{CollatzLayerA v8.1 Formal Verification of the Collatz Conjecture in Lean 4 + Mathlib (2636 lines, 215 theorems, 2 axioms, 0 sorry)}},
  extra_urls= {{https://aidoctrine.github.io/uct-navigator/, https://github.com/AIDoctrine/CollatzLayerA/blob/main/CollatzLayerA_v8_1_FINAL.lean}},
}