| _version_ | 1866901579303485440 |
|---|---|
| author | Lim, Han-Jun |
| author_facet | Lim, Han-Jun |
| contents | <p>Abstract<br>We formalize the computational rules of the rendering algebra R12 ∼= M3(C) ⊗<br>M4(C) that generate all Array Cosmology predictions. Four computational tools determine the numerical value of any AC observable: (1) a representation assignment theorem classifying observables into six exhaustive types, each with a uniquely determined Landauer denominator; (2) a Casimir–dimension duality distinguishing<br>the confined sector (Casimir eigenvalue) from the unconfined sector (dimension ratio); (3) a Landauer linearity principle proving that single-erasure observables are exactly linear in the rendering friction Z; and (4) a representation-theoretic derivation of the lepton mass coefficient f(1) = 5 from dim(su(4))/ dim(∧2C4) = 5/2.<br>Four structural verification tools establish the internal consistency of the framework: (5) the product structure Z = (π−3) ln 2 derived from sequential conditional probability; (6) the uniqueness of the M3 ⊗ M4 decomposition from the two-factor<br>theorem; (7) a completeness check showing all </p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19323563 |
| institution | Zenodo |
| language | |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Computational Rules and Structural Verification of the R12 Rendering Algebra Lim, Han-Jun Array Cosmology 배열우주론 R12 Rendering Algebra Rendering Defect Zero-Parameter Derivation Z_noise Topo-Thermodynamic Framework 5 Axioms Array Cosmology Hanjun Lim 임한준 <p>Abstract<br>We formalize the computational rules of the rendering algebra R12 ∼= M3(C) ⊗<br>M4(C) that generate all Array Cosmology predictions. Four computational tools determine the numerical value of any AC observable: (1) a representation assignment theorem classifying observables into six exhaustive types, each with a uniquely determined Landauer denominator; (2) a Casimir–dimension duality distinguishing<br>the confined sector (Casimir eigenvalue) from the unconfined sector (dimension ratio); (3) a Landauer linearity principle proving that single-erasure observables are exactly linear in the rendering friction Z; and (4) a representation-theoretic derivation of the lepton mass coefficient f(1) = 5 from dim(su(4))/ dim(∧2C4) = 5/2.<br>Four structural verification tools establish the internal consistency of the framework: (5) the product structure Z = (π−3) ln 2 derived from sequential conditional probability; (6) the uniqueness of the M3 ⊗ M4 decomposition from the two-factor<br>theorem; (7) a completeness check showing all </p> |
| title | Computational Rules and Structural Verification of the R12 Rendering Algebra |
| topic | Array Cosmology 배열우주론 R12 Rendering Algebra Rendering Defect Zero-Parameter Derivation Z_noise Topo-Thermodynamic Framework 5 Axioms Array Cosmology Hanjun Lim 임한준 |
| url | https://doi.org/10.5281/zenodo.19323563 |