COS45 Application — Local 2-adic Reserve and Recharge Constraints in Odd Collatz Dynamics (v1.6 7)
Louis Morissette
Abstract
This document presents an application of the COS45 framework to the analysis of odd Collatz dynamics. It belongs to the APPLICATION layer and applies the geometric detectability framework to observable quantities derived from 2-adic valuation and local reserve/recharge constraints. No new mathematics is introduced. The analysis follows the COS45 structure:EXACT → OBSERVABLE → DECISION → APPLICATION Observable quantities (δ) are constructed from 2-adic properties of odd iterates. The detectability margin is evaluated through η = δ − τ. In this application, τ = 0 is assumed, leading to η = δ. Admissibility therefore requires δ > 0, T = 1, and R ≥ R_min. All results are contingent on the admissibility conditions defined in the COS45 framework. No general claim is made about the global behavior of the Collatz problem. Statements labeled as [PERSPECTIVE] are explicitly non-decision and carry no admissibility claim. This document does not prove convergence, does not establish universal behavior, and does not extend the mathematical structure of the Collatz problem. Its role is to illustrate how COS45 can be applied to a discrete dynamical system under explicit structural constraints. Version (v1.6) refines the separation between observable structure, admissibility, and non-decision perspectives. No change to underlying definitions.