The Reduced 5k−1(3)/4 Collatz-Type Domain with Two Observed Attractors up to 10^11

This work studies the reduced 5k−1(3)/4 Collatz-type domain on the positive odd integers. For each positive odd integer k, the map applies 5k−r(k), where r(k)=1 when k ≡ 1 (mod 4) and r(k)=3 when k ≡ 3 (mod 4), and then removes all factors of 2 to return to an odd integer. The system has two observed fixed-point attractors: 1 and 3. An exhaustive computational verification was performed for every positive odd starting value below 10^11, comprising 50,000,000,000 starting values. Every tested trajectory reached either 1 or 3; no additional cycles were detected and no 128-bit overflow events occurred. The final basin counts are 32,318,909,987 trajectories reaching 1 and 17,681,090,013 trajectories reaching 3, corresponding to approximately 64.63782% and 35.36218%, respectively. The paper develops the algebraic structure of the reduced map, an exact periodic-orbit identity, inverse branches, two-adic valuation statistics, a probabilistic contraction heuristic, basin statistics, stopping-time and peak records, and complete numerical trajectory examples. The computational results motivate a Two-Attractor Conjecture for the positive odd integers. The exhaustive verification up to 10^11 is a finite computational result and is not claimed as a proof of global convergence. This Zenodo record includes the research article and a reproducibility package containing the C source code, computational results, validation data, checksums, and the LaTeX source of the paper.