A Universal Structural Constant from the Information-Geometric 2⊕3 Symmetry: Mathematical Foundations and Physical Manifestations

Universal Structural Constant λ₃* from Information-Geometric 2⊕3 Symmetry Version 2. 2 (Foundations of Physics Submission Ready - Final) Author: Takayuki TakagiAffiliation: Independent Researcher, Higashimatsuyama, Saitama, JapanDate: November 30, 2025License: CC BY 4. 0 Abstract This work derives a universal structural constant λ₃* = 0. 1520845. . . from information-geometric first principles. The constant emerges as the stable fixed point of a "Logos functional" constructed axiomatically from Shannon entropy and logarithmic structural tension, with coupling α = ln (5/2) determined by the group-theoretic decomposition 5 = 2 ⊕ 3. The same value appears independently as the structural extremum in odd-parity multipartite GHZ quantum states, providing cross-domain verification. We point out a possible connection to the cosmological baryon fraction (fb ≈ 0. 156), noting the ~3% deviation as an open question. Key Results Theorem 3. 1: Existence and uniqueness of λ₃* as stable minimum Proposition 2. 5: Axiomatic uniqueness of the Logos functional Lemma 4. 3: Independence of GHZ extremum from auxiliary parameters Conjecture 6. 1: Cosmological echo hypothesis Files in This Release Main Manuscript FoPStructuralConstantᵥ10final. pdf — Full paper (17 pages) FoPStructuralConstantᵥ10final. tex — LaTeX source Figures Fig0₂plus3concept. pdf — Conceptual illustration of 2⊕3 symmetry (HQ version) Fig1DOFdecomposition. pdf — Group-theoretic 2⊕3 pattern Fig2GHZₑxtremum. pdf — Even/odd parity structural extrema Fig3Logosfunctional. pdf — Double-well potential structure Fig4ᵣobustness. pdf — Parameter dependence and cosmological comparison Fig5GHZScdetailed. pdf — NEW: Structural coherence curves for GHZ states Supplementary Materials FoPCoverLetter. txt — Journal cover letter FoPSubmissionMaterials. txt — Highlights and significance statement README. md — This file Version History Version Date Description 1. 0 Nov 29, 2025 Initial Nature Physics format 2. 0 Nov 30, 2025 FoP submission ready: rigorous proofs, corrected coefficients, refined figures 2. 1 Nov 30, 2025 Added 2⊕3 conceptual figure, 16 pages 2. 2 Nov 30, 2025 Added GHZ Sc curves, HQ concept figure, 17 pages (6 figures) Changes in v2. 2 Added Fig5: GHZ structural coherence curves (Even/Odd dichotomy) Upgraded Fig0: High-quality 2⊕3 concept figure with equations Paper expanded to 17 pages Total 6 figures Changes in v2. 1 Added Fig0: Conceptual illustration of 2⊕3 symmetry (Information Manifold + Structural Manifold) Paper expanded to 16 pages (was 15) Total 5 figures (was 4) Changes in v2. 0 Proposition 2. 5: Full proof of Logos functional uniqueness (replacing sketch) Lemma 4. 3: Mathematical proof of extremum independence Corrected J'' (1/2) coefficient: -3. 33 (was -0. 70) Figure 1 (d): Fixed notation (removed erroneous "= ln (2/5) ") Abstract: Softened cosmological claim ("point out" vs "conjecture") Section 7. 2: Adjusted philosophical language ("reminiscent of" vs "aligns with") Mathematical Framework Logos Functional J (λ; α) = -H (λ) + αL (λ) where: H (λ) = -λ ln λ - (1-λ) ln (1-λ) (Shannon entropy) L (λ) = -ln (λ² + (1-λ) ²) (logarithmic structural tension) α = ln (5/2) ≈ 0. 916 (from 5 = 2 ⊕ 3 decomposition) Fixed Point λ₃* = 0. 1520845211. . . Three Independent Manifestations Logos functional variational principle → λ* = 0. 1520845. . . Odd-parity GHZ structural extremum → λ* ≈ 0. 152044 Cosmological baryon fraction → fb ≈ 0. 156 (~3% deviation) Citation @misctakagi2025structural, author = {Takagi, Takayuki, title = A Universal Structural Constant from the Information-Geometric 2⊕3 Symmetry: Mathematical Foundations and Physical Manifestations, year = 2025, publisher = Zenodo, version = 2. 0, doi = 10. 5281/zenodo. XXXXXXX } Related Work This research is part of the TSTT (Transcendental Structural Tension Theory) and SRTA (Structural Resonance Theory of Anthropic Principle) research program. Contact Takayuki TakagiEmail: lemissio@gmail. com License This work is licensed under a Creative Commons Attribution 4. 0 International License (CC BY 4. 0).