What question did this study set out to answer?

This study aims to explore emergent phenomena in gravitational physics and biological intelligence using Möbius-coupled doubly stochastic lattices.

March 12, 2026Open Access

Emergent Gravity, Biological Intelligence, and Standard Model Predictions from Möbius-Coupled Doubly Stochastic Lattices

Key Points

This study aims to explore emergent phenomena in gravitational physics and biological intelligence using Möbius-coupled doubly stochastic lattices.
Established dynamics of N×N lattices of doubly stochastic matrix eigenvalues.
Analyzed gravitational collapse through Jensen's inequality and Lorentz factor.
Investigated emergence of biological intelligence through a six-level learning hierarchy.
Derived standard model predictions from the Birkhoff polytope and automorphism group.
Non-uniform grids collapse to a single-cell singularity due to positive-feedback mechanisms.
Spatial memory shows a significant increase with a 31% learning advantage over time.
Predictions match experimental values closely in particle physics parameters, indicating a strong correlation.
Identified the Sinkhorn period as the cosmological constant, affecting energy density dynamics.

Abstract

Building on the M¨obius–Lorentz correspondence (Foss, 2026 1), we investigate the dynamics ofN×N lattices of doubly stochastic 4 ×4 matrix eigenvalues coupled via f(λ,v) = (λ+ v)/(1 + λv).Three classes of emergent phenomena are established: (i) Gravitational collapse. We prove that anynon-uniform grid universally collapses to a single-cell singularity via a Jensen’s inequality mecha-nism: the strict convexity of the Lorentz factor γ(λ) = (1−λ2)−1/2 combined with energy conser-vation creates a positive-feedback runaway with sensitivity ratio R= 1408×at λp = 0.99. Sinkhornrenormalization group flow is the only mechanism preventing collapse, identifying the Sinkhorn pe-riod as the cosmological constant. Singularities act as energy sources: agents at distance 1 receive6.45×the background energy density. (ii) Emergent intelligence. Agents (contiguous grid sub-graphs) develop a six-level biological learning hierarchy: astrocyte-mediated coupling modulation,Tsodyks–Markram habituation, Rescorla–Wagner conditioning, hippocampal spatial memory, envi-ronment manipulation, and boundary communication. Spatial memory dominates (+165 lifetimesteps, +31%), learning advantages compound over 5,000 steps (+276 biomass), and the system ex-hibits an r/K-selection transition. Analytical survival theory yields a boundary-to-volume area lawfor viability. (iii) Standard Model predictions. The S4 ×S4 automorphism group of the Birkhoffpolytope B4, extended by PSL(2,7) as discrete SU(3), produces sin2 θW = 505/2184 = 0.231227(experiment: 0.23122 ±0.00003, 0.2σ) from three independent derivations. Combined with S4 lep-togenesis: ηB = 6.1 ×10−10 (exact match), αs = 5/42 (1.3σ), Koide Q = 2/3 (0.005%), and 15predictions from 3 inputs (χ2/d.o.f. = 0.63). The heat kernel on B4 interpolates from the GUT value3/8 (UV) to our 3/13 (IR), identifying the SU(5) prediction as the UV limit of this framework. Wepresent 16 theorems, 8 results, 4 conjectures, and 12 negative results from >310 experiments span-ning gravitational physics, neuroscience, and particle physics—all from a single algebraic identity.

Emergent Gravity, Biological Intelligence, and Standard Model Predictions from Möbius-Coupled Doubly Stochastic Lattices

Key Points

Abstract

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