A Ternary (4k±1)/3 Collatz-Type Map: Exact 3-Adic Symbolic Dynamics, Density-One First Descent, Algebraic Cycle Analysis, and Exhaustive Verification up to 10^11

This record contains Version 3 of the research package for a ternary Collatz-type map defined on the positive integers by three residue classes modulo 3: k -> k/3 when k is congruent to 0 mod 3 k -> (4k-1)/3 when k is congruent to 1 mod 3 k -> (4k+1)/3 when k is congruent to 2 mod 3 The work combines exact algebraic and 3-adic analysis with a fresh exhaustive computational verification through 10^11. The theoretical part develops the accelerated map on integers not divisible by 3, exact inverse branches, the associated 3-adic valuation law, exact multi-step identities, finite-horizon descent criteria, density transfer, and a density-one first-descent theorem. It also establishes that universal first descent is equivalent to global convergence for this map, excludes all nontrivial positive accelerated cycles of period at most six, and derives strong lower bounds on any hypothetical remaining positive cycle by combining algebraic cycle localization with the finite verification. The computational part independently verifies every admissible starting value from 1 through 10^11. A fresh full scan was performed on the base interval through 10^9, followed by a certificate scan on 10^9 < n <= 10^11. In total, 66,666,666,667 admissible starting values were certified, with: 0 unresolved cases 0 arithmetic overflows 0 invariant failures 0 unknown cycles For every admissible starting value 1 < n <= 10^11, a strict first descent was observed. Across the complete verified range, the first descent occurred on the same accelerated edge as the first crossing of the valuation barrier. No discrepancy cases were found. Selected global computational records: Maximum reduced first-descent time: 382 steps, starting at n = 58,528,894,046 Maximum original-map first-descent time: 483 steps, starting at n = 58,528,894,046 Largest reduced peak: 772,688,843,721,858,022,441 Largest original-map peak: 1,030,251,791,629,144,029,921, starting at n = 72,496,238,260 Maximum observed 3-adic valuation: 25 Longest consecutive run with valuation a = 1: 63 The computational archive includes the scanner source code, all chunk-level results, aggregate summaries, audit outputs, trajectory replay certificates, theory certificates, validation material, reproducibility documentation, and SHA-256 manifests. The exhaustive verification through 10^11 is a finite computational result. It does not by itself constitute a proof of global convergence for all positive integers.