The Observer Cut Principle, Self-Reference Inaccessibility, and the NLO Hubble Constant from the R12 Rendering Algebra
Abstract
We derive the next-to-leading-order (NLO) Hubble constant from the rendering algebra
R12 ∼= M12(C) by formalising the role of the observer. Three theorems are proved.
(1) Observer Uniqueness Theorem: the unique nontrivial operator in R12 that is simultaneously perspective-invariant (fixed by every ∗-automorphism), unitary, and Hermitian is B = −I12.
(2) Self-Reference Inaccessibility Theorem (SRIT): for any completely positive trace-preserving (CPTP) map E on M12(C), we have E(B) = B; consequently, the bare internal structure of the observer (contributing 25/27 to the Arrhenius prefactor) is algebraically unresolvable by any physical operation within R12.
(3) Landauer Replacement Theorem:t he only observable effect of B is its information-theoretic signature ln 2, arising from B2 = I (Z2 symmetry, 1 bit) and the Landauer principle. Combining these with the LO result of Paper XLIII
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BibTeX
@misc{lim2026observer,
title = {{The Observer Cut Principle, Self-Reference Inaccessibility, and the NLO Hubble Constant from the R12 Rendering Algebra}},
author = {Han-Jun Lim},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23604033},
url = {https://zenodo.org/records/23604033},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - The Observer Cut Principle, Self-Reference Inaccessibility, and the NLO Hubble Constant from the R12 Rendering Algebra
AU - Han-Jun Lim
PY - 2026
DA - 2026/10/23
PB - Zenodo
DO - 10.5281/zenodo.23604033
UR - https://zenodo.org/records/23604033
AB - We derive the next-to-leading-order (NLO) Hubble constant from the rendering algebra R12 ∼= M12(C) by formalising the role of the observer. Three theorems are proved. (1) Observer Uniqueness Theorem: the unique nontrivial operator in R12 that is simultaneously perspective-invariant (fixed by every ∗-automorphism), unitary, and Hermitian is B = −I12. (2) Self-Reference Inaccessibility Theorem (SRIT): for any completely positive trace-preserving (CPTP) map E on M12(C), we have E(B) = B; consequently, the bare internal structure of the observer (contributing 25/27 to the Arrhenius prefactor) is algebraically unresolvable by any physical operation within R12. (3) Landauer Replacement Theorem:t he only observable effect of B is its information-theoretic signature ln 2, arising from B2 = I (Z2 symmetry, 1 bit) and the Landauer principle. Combining these with the LO result of Paper XLIII
ER -