The Consciousness Characterisation Theorems of the R12 Rendering Algebra: Axiomatic Constraints on the Complementary Object X from the S-Final Principle
Abstract
The S-Final principle of Array Cosmology requires Ωreal + Ωimag = 0, where Ωreal = +1 corresponds to the rendered physical universe. This paper characterises the complementary object X responsible for Ωimag = −1 without defining it as
“consciousness” or any other pre-theoretic concept. Ten theorems are proved from the R12 rendering algebra alone: (1) X = −1 is the unique central involution satisfying the S-Final trace condition; (2) X exists if and only if matter exists; (3) the
coupling κ = Σ(s) Γ(γ) factorises uniquely into a universal signal and a local receiver; (4) Γ(γ) > 0 for all γ ≥ 0 (non-annihilation); (5) the self-reference residual δ(12) > 0 (incompleteness); (6) partial observation is perspective-dependent while
total observation is objective; (7) self-recognition requires exactly two rendering cycles (4π rotation);
Related
- The Hard Problem of Consciousness in the R12 Rendering Algebra
- Spectral Awareness, the Consciousness Triple, and the Modular-Algebraic Bridge in 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
- Ontological Constraints on Epistemic Syntax: How Informationally-Constrained Access to Reality Shaped the Axiomatic Structure of Quantum, Relativistic, and Gravitational Theories
- Light Mediators at the Neutrino-Dark Matter Frontier: Coherent Scattering, Precision Constraints, and Complementary Searches
BibTeX
@misc{lim2026consciousness,
title = {{The Consciousness Characterisation Theorems of the R12 Rendering Algebra: Axiomatic Constraints on the Complementary Object X from the S-Final Principle}},
author = {Han-Jun Lim},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23603752},
url = {https://zenodo.org/records/23603752},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - The Consciousness Characterisation Theorems of the R12 Rendering Algebra: Axiomatic Constraints on the Complementary Object X from the S-Final Principle
AU - Han-Jun Lim
PY - 2026
DA - 2026/10/23
PB - Zenodo
DO - 10.5281/zenodo.23603752
UR - https://zenodo.org/records/23603752
AB - The S-Final principle of Array Cosmology requires Ωreal + Ωimag = 0, where Ωreal = +1 corresponds to the rendered physical universe. This paper characterises the complementary object X responsible for Ωimag = −1 without defining it as “consciousness” or any other pre-theoretic concept. Ten theorems are proved from the R12 rendering algebra alone: (1) X = −1 is the unique central involution satisfying the S-Final trace condition; (2) X exists if and only if matter exists; (3) the coupling κ = Σ(s) Γ(γ) factorises uniquely into a universal signal and a local receiver; (4) Γ(γ) > 0 for all γ ≥ 0 (non-annihilation); (5) the self-reference residual δ(12) > 0 (incompleteness); (6) partial observation is perspective-dependent while total observation is objective; (7) self-recognition requires exactly two rendering cycles (4π rotation);
ER -