PreprintCC BY 4.0Zenodo
The Modular–Algebraic Bridge Height-12 Forcing, Level–Rank Completion, and the Branching Theorem for the Rendering Character
Abstract
The rendering algebra R12 = M3(C) ⊗ M4(C) of Array Cosmology carries the isotypic energy series Z(τ) = 1+8q3 +15q4 +120q7, with 144 = 122 states organized as End(C12) = (1⊕8)⊗(1⊕15). Thispapersettlesthemodularidentityof Z. First, the height-12 forcing theorem: writing E = C2/2 for the AC energy and h = C2/2(k+h∨) for the affine conformal weight, the finite-index identity E = 12h holds on every sector if and only if k + h∨ = 12 for each factor, which selects the unique level pair (k3,k4) = (9,8) — the co-Coxeter complements of 12 — with central charge c = 16 and exact T-order 12 on the four AC sectors(288 on the fulltheory).
Related
- Spectral Awareness, the Consciousness Triple, and the Modular-Algebraic Bridge in the R12 Rendering Algebra
- The Modular Root in Array Cosmology: Forcing of the Rendering Stage H/PSL2(Z) and the Canonical Reading of the Four Axioms
- Gravitational Wave Ringdown from the Rendering Algebra R12: The Axis Count from the Modular Spectrum, the Extremal Determination of the Rendering Anchor, and the Nine-Event Confrontation
- Orthogonal completion of algebraic systems
- Orthogonal completion of algebraic systems II
BibTeX
@misc{lim2026modularalgebraic,
title = {{The Modular–Algebraic Bridge Height-12 Forcing, Level–Rank Completion, and the Branching Theorem for the Rendering Character}},
author = {Han-Jun Lim},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23603953},
url = {https://zenodo.org/records/23603953},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - The Modular–Algebraic Bridge Height-12 Forcing, Level–Rank Completion, and the Branching Theorem for the Rendering Character
AU - Han-Jun Lim
PY - 2026
DA - 2026/10/23
PB - Zenodo
DO - 10.5281/zenodo.23603953
UR - https://zenodo.org/records/23603953
AB - The rendering algebra R12 = M3(C) ⊗ M4(C) of Array Cosmology carries the isotypic energy series Z(τ) = 1+8q3 +15q4 +120q7, with 144 = 122 states organized as End(C12) = (1⊕8)⊗(1⊕15). Thispapersettlesthemodularidentityof Z. First, the height-12 forcing theorem: writing E = C2/2 for the AC energy and h = C2/2(k+h∨) for the affine conformal weight, the finite-index identity E = 12h holds on every sector if and only if k + h∨ = 12 for each factor, which selects the unique level pair (k3,k4) = (9,8) — the co-Coxeter complements of 12 — with central charge c = 16 and exact T-order 12 on the four AC sectors(288 on the fulltheory).
ER -