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Positive density of Collatz convergence at every rate above 3/log(4/3)

Idris Ali Shaik

Palomar Registrypalomar/PALOMAR-2026-09-23-000002Sep 23, 2026math.NTscore 0

A Lean 4 formalization of eighteen selected Phase 1 statements, led by a single positive lower natural-density constant for the set of positive integers reaching 1 within c log x ordinary Collatz steps, valid for every fixed c > 3/log(4/3). It also covers fixed-target hitting, the exact target criterion, individual-root consequences, vanishing-clock-loss variants, depth-eleven density bounds, exact finite fan allocation, real-moment comparison, target profiles, and bounded actual reference entropy with explicit tail estimates and zero normalized growth. Density witnesses and levels are…

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