Axiom Reduction and the Higher Categorical Foundation of Adelic Langlands Correspondence FAC 1 Identification and the Monster Scope Boundary
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2026
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| _version_ | 1866901538178334720 |
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| author | Lim, Han-Jun |
| author_facet | Lim, Han-Jun |
| contents | <p>Abstract</p> <p>The Array Cosmology (AC) programme derives Standard Model parameters, cosmological observables, and consciousness structure from four axioms A4 = {12,π,ln2, φ} with zero free parameters. This paper establishes four interlocking structural results.<br>First, the axiom count reduces from four to two structural requirements on the rendering algebra R12 = M12(C): (α) multiple prime sectors, (β) binary involutive structure. Specifically, N = 12 is the unique positive integer satisfying (α) at least two distinct prime divisors and (β) φ(pvp(n)) = 2 at every prime (Theorem 2.1); φ = (1+√5)/2 arises through the chain 12 → M12 → A5 →icosahedron(Theorem 3.1); R12 = M3 ⊗ M4 with Nc = 3, k = 4 is forced by Wedderburn decomposition plus confinement (Theorem 5.1); 12 is the unique source of the AC derivation graph (Theorem 6.2); ln2 reduces to ln|SpecB| for B2 = I (Theorem 7.4). Second, the higher categorical structure of R12 is made explicit. Applying Lurie’s Cobordism Hypothesis, R12 produces a canonical fully extended 2D framed TFT ZR12 with ZR12,M12(S1) ∼ =C15 (Theorem 8.2); dimR12 = 144 admits a four-fold structural coincidence (Theorem 8.3).</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19663852 |
| institution | Zenodo |
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| publishDate | 2026 |
| publisher | Zenodo |
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| spellingShingle | Axiom Reduction and the Higher Categorical Foundation of Adelic Langlands Correspondence FAC 1 Identification and the Monster Scope Boundary Lim, Han-Jun Array Cosmology 배열우주론 R12 Rendering Algebra Rendering Defect Hanjun Lim Adelic Langlands F1 <p>Abstract</p> <p>The Array Cosmology (AC) programme derives Standard Model parameters, cosmological observables, and consciousness structure from four axioms A4 = {12,π,ln2, φ} with zero free parameters. This paper establishes four interlocking structural results.<br>First, the axiom count reduces from four to two structural requirements on the rendering algebra R12 = M12(C): (α) multiple prime sectors, (β) binary involutive structure. Specifically, N = 12 is the unique positive integer satisfying (α) at least two distinct prime divisors and (β) φ(pvp(n)) = 2 at every prime (Theorem 2.1); φ = (1+√5)/2 arises through the chain 12 → M12 → A5 →icosahedron(Theorem 3.1); R12 = M3 ⊗ M4 with Nc = 3, k = 4 is forced by Wedderburn decomposition plus confinement (Theorem 5.1); 12 is the unique source of the AC derivation graph (Theorem 6.2); ln2 reduces to ln|SpecB| for B2 = I (Theorem 7.4). Second, the higher categorical structure of R12 is made explicit. Applying Lurie’s Cobordism Hypothesis, R12 produces a canonical fully extended 2D framed TFT ZR12 with ZR12,M12(S1) ∼ =C15 (Theorem 8.2); dimR12 = 144 admits a four-fold structural coincidence (Theorem 8.3).</p> |
| title | Axiom Reduction and the Higher Categorical Foundation of Adelic Langlands Correspondence FAC 1 Identification and the Monster Scope Boundary |
| topic | Array Cosmology 배열우주론 R12 Rendering Algebra Rendering Defect Hanjun Lim Adelic Langlands F1 |
| url | https://doi.org/10.5281/zenodo.19663852 |