A Practical Coverage-Based Framework for the Collatz Conjecture

This paper introduces a practical, coverage-based framework for analyzing the Collatz conjecture. The framework is built upon two empirical invariants observed up to M = 10^10 1. SPC - Let S(M) denote the number of seeds in the interval [1, M]. The Constant (SPC) is defined as SPC = lim (M → ∞) S(M) / M Empirical computations show that this limit stabilizes around the constant: 1 - e^(−2) C = ──────────── ≈ 0.4323323584= SPC 22. SPP - A periodic structure of seed gaps bounded by 3, with a repeating 1–2–3 pattern and finite runs of 3s. Together, these invariants support a stable coverage mechanism ensuring that every integer up to M is covered by Collatz trajectories of numbers. We argue that, if SPC and SPP persist for all M, then divergence and nontrivial cycles are excluded, providing a practical but non-formal proof of the Collatz conjecture.