Scale Calculus: A Domain-General Framework for Spectral Vessel Aggregation

I introduce Scale Calculus, a domain-general mathematical framework built on four axioms (M1–M4) governing spectral vessel aggregation. The central result, T-H1, establishes the Spectral-Coupling Correspondence: α = ln(κ) ⟺ κ = e^α. I derive integer arithmetic, the Fundamental Theorem of Arithmetic, rings, fields, p-adic media, the Adèle ring, the Riemann Hypothesis as prime self-duality, Langlands correspondences, and quantum mechanics as instantiations of vessel aggregation. A forbidden zone κ ∈ (e^{−1}, e^{−1/2}) is identified, populated exclusively by biological and neural systems. Anti-probability vessels and a resigned medium are introduced as candidates for matter-antimatter asymmetry and dark energy respectively. The paper closes with a formal description of the person as a complete vessel and a new section on Directed Resonance Crossing (DRC) — the mechanism by which a complete identity uses self-referential feedback to deliberately modulate its coupling coefficient toward structural boundaries, distinguishing it formally from stochastic resonance, coherence resonance, and autoresonance. Four open problems are stated at the boundary of current mathematics.