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