[SUPERSEDED] The Feed Coupling κ: A Rigorous Derivation from First Principles

SUPERSEDED

This paper have been superseded by the current formulation, in which:

· Pillar IV (Feed Equation) governs attractor dynamics in meta-time, driving all structural parameters to their fixed-point values· The feed coupling is not a fundamental constant requiring derivation; the attractor values of the gauge couplings, mixing angles, and mass ratios are determined by the primitives through the self-consistency of dimensional reduction· The connection between canvas dynamics and cosmology is established through the horizon information bound, the hierarchy formula, and the cosmological constant derivation

See "The Emergence Canvas Model: A Unified Framework for Fundamental Physics (The Machine and the State)"

https://doi.org/10.5281/zenodo.20795774

for the current theory. This paper is retained for archival purposes only.

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The paper resolves several open problems: the Hubble tension is explained as a consequence of time-dependent κ; dark energy is identified as the manifestation of canvas relaxation; and the ultimate fate of the universe is derived from first principles.

Why This Matters

The feed coupling κ is not a free parameter. It is determined by cosmology through the derived relation. This connects the microscopic Feed dynamics of the canvas — the rate at which equality processors relax toward equilibrium — to the macroscopic expansion of the universe. The same eight primitives and three equations that generate general relativity, quantum mechanics, and the Standard Model also determine the expansion history of the cosmos.

The derivation is rigorous, with no hand-waving. Every step follows from the canvas axioms. The numerical prediction is consistent with observational data. The Hubble tension is explained. Dark energy is identified as canvas relaxation. The heat death of the universe is derived.

Keywords: feed coupling, canvas model, Hubble constant, dark energy, Hubble tension, Friedmann equations, cosmological constant, heat death, meta-time, Order lattice, Planck scale