Life, Information, and the Rendering Ladder: The Cost of Nothingness, the Scale Cascade, the Rendering Depth Bound, and the Biomolecular Window in Array Cosmology
Abstract
Building on the consciousness framework of Paper XVI, we derive five additional
structural results from the Array Cosmology axioms {12, π, γ1, ln 2, φ}. First, the
Absolute Potentiality Λ∗ is identified with the σ = 1/2 state of the rendering function F(s), and its collapse to the physical universe is shown to follow from the least-action principle: the maintenance cost of perfect symmetry (∼ 1/Z → ∞)
exceeds the cost of existence (∼ Z), so “nothingness is more expensive than being.”
Second, the computational complexity separation P ̸= NP is derived as a direct
consequence of Z ̸= 0: zero rendering friction would eliminate the cost asymmetry between generation and verification, collapsing all potentiality into simultaneity and annihilating spacetime.
Related
- Array Cosmology : The Rendering Algebra
- The Modular Root in Array Cosmology: Forcing of the Rendering Stage H/PSL2(Z) and the Canonical Reading of the Four Axioms
- ζ(Nc) Color Cohesion, CKM Casimir Cascade, and the Complete M3(C) Sector of the R12 Rendering Algebra
- Consciousness in Array Cosmology: The Fractal Coupling Function, the Born-Rule Correction, and the Rung Tower of the R12 Rendering Algebra
- Universal Dimensional Scaling in Information-Geometric Rendering: Substrate-Independent Metric Conservation Across Holographic, Biological, and Engineered Manifolds
BibTeX
@misc{lim2026life,
title = {{Life, Information, and the Rendering Ladder: The Cost of Nothingness, the Scale Cascade, the Rendering Depth Bound, and the Biomolecular Window in Array Cosmology}},
author = {Han-Jun Lim},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23603923},
url = {https://zenodo.org/records/23603923},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Life, Information, and the Rendering Ladder: The Cost of Nothingness, the Scale Cascade, the Rendering Depth Bound, and the Biomolecular Window in Array Cosmology
AU - Han-Jun Lim
PY - 2026
DA - 2026/10/23
PB - Zenodo
DO - 10.5281/zenodo.23603923
UR - https://zenodo.org/records/23603923
AB - Building on the consciousness framework of Paper XVI, we derive five additional structural results from the Array Cosmology axioms {12, π, γ1, ln 2, φ}. First, the Absolute Potentiality Λ∗ is identified with the σ = 1/2 state of the rendering function F(s), and its collapse to the physical universe is shown to follow from the least-action principle: the maintenance cost of perfect symmetry (∼ 1/Z → ∞) exceeds the cost of existence (∼ Z), so “nothingness is more expensive than being.” Second, the computational complexity separation P ̸= NP is derived as a direct consequence of Z ̸= 0: zero rendering friction would eliminate the cost asymmetry between generation and verification, collapsing all potentiality into simultaneity and annihilating spacetime.
ER -