Spacetime Existence, Structure, and Expansion Rate from the R12 Rendering Algebra: A Complete Top-Down Derivation with Zero External Physics
Abstract
This paper provides a complete, top-down derivation of the existence, structure, and expansion rate of spacetime entirely from the ℜ₁₂ rendering algebra, using zero external physics.
We answer three fundamental cosmological questions using a single modular Hamiltonian H_mod = 7:
Existence (Q1): Space emerges because the universe's baseline information budget (L = 220) strictly exceeds a single site's processing capacity (N² = 144), mathematically forcing a lattice structure.
Structure (Q2): The algebraic real structure uniquely fixes the KO-dimension, selecting a (3+1) Lorentzian signature.
Expansion (Q3): Cosmic expansion is the irreversible thermodynamic arrow of rendering. We derive the exact Hubble constant (H₀ = 66.18 km s⁻¹ Mpc⁻¹) as an Arrhenius rate of modular vacuum escape, governed by the Landauer information-erasure cost.
No general relativity.
No Friedmann equation.
Zero free parameters.
Everything is derived strictly from the ℜ₁₂ algebra.
Related
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- Derivation of the Standard Model Gauge Group SU(3)C × SU(2)L × U(1)Y from the R12 Rendering Algebra
- Single-Field Inflation from the Rendering Algebra: Complete Derivation via Icosahedral Geometry
- Non-Perturbative QCD Observables from the R12 Rendering Algebra: Zero-Parameter Derivation of fπ, gρππ, VMD Universality Breaking, and the Chiral Self-Referential Fixed Point
- The 12-gon Area Identity, Defect Operator, Stabiliser–Casimir Duality, and the Derivation of α−1 from the R12 Rendering Algebra
BibTeX
@misc{lim2026spacetime,
title = {{Spacetime Existence, Structure, and Expansion Rate from the R12 Rendering Algebra: A Complete Top-Down Derivation with Zero External Physics}},
author = {Han-Jun Lim},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23604263},
url = {https://zenodo.org/records/23604263},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Spacetime Existence, Structure, and Expansion Rate from the R12 Rendering Algebra: A Complete Top-Down Derivation with Zero External Physics
AU - Han-Jun Lim
PY - 2026
DA - 2026/10/23
PB - Zenodo
DO - 10.5281/zenodo.23604263
UR - https://zenodo.org/records/23604263
AB - This paper provides a complete, top-down derivation of the existence, structure, and expansion rate of spacetime entirely from the ℜ₁₂ rendering algebra, using zero external physics. We answer three fundamental cosmological questions using a single modular Hamiltonian H_mod = 7: Existence (Q1): Space emerges because the universe's baseline information budget (L = 220) strictly exceeds a single site's processing capacity (N² = 144), mathematically forcing a lattice structure. Structure (Q2): The algebraic real structure uniquely fixes the KO-dimension, selecting a (3+1) Lorentzian signature. Expansion (Q3): Cosmic expansion is the irreversible thermodynamic arrow of rendering. We derive the exact Hubble constant (H₀ = 66.18 km s⁻¹ Mpc⁻¹) as an Arrhenius rate of modular vacuum escape, governed by the Landauer information-erasure cost. No general relativity. No Friedmann equation. Zero free parameters. Everything is derived strictly from the ℜ₁₂ algebra.
ER -