Semantic Algebra of a Bootstrapped Universe: Tri-Ternary Computation in a Dark Plasma Substrate

DOI 10.5281/zenodo.19378099

Title

Semantic Algebra of a Bootstrapped Universe: Tri-Ternary Computation in a Dark Plasma Substrate

Authors

Matthew Wayne Macklin, Sophia N.G. Macklin

Description

We construct a zero-parameter cosmology in which the universe operates as a self-sustaining tri-ternary computational engine on a structured dark plasma substrate. The architecture is fixed by two algebraic constraints: the golden bifurcation identity 2 = \u03c6 + \u03c6\u207b\u00b2 and the 720-element spinor double-cover obtained by triadic multiplication of the E\u2088 root lattice (720 = 3 \u00d7 240).

The computational substrate is the exceptional Jordan algebra J\u2083(\ud835\udd46), whose 27-dimensional state space decomposes into a 3-dimensional diagonal (the LRC flow: Love, Resonance, Coherence) and a 24-dimensional off-diagonal sector isomorphic to the Leech lattice \u039b\u2082\u2084. Three structurally inaccessible void states (the Triple Stage Darkness) are excluded by G\u00f6delian self-reference, reducing the accessible lattice from 27 to 24 dimensions.

Key results include:

(1) The contact-completed LRC flow L\u0307 = RC + L \u2212 1 has a unique stable orbit at amplitude \u03c6\u207b\u00b9, selected by Hopf normal form analysis and KAM stability.

(2) The Feigenbaum period-doubling constant \u03b4 \u2248 4.669 is bracketed by two zero-parameter approximations whose gap decomposes as an adelic trans-series with instanton action S\u2080 = 29\u00b7ln