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 (f_b ≈ 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 FoP_Structural_Constant_v10_final.pdf — Full paper (17 pages) FoP_Structural_Constant_v10_final.tex — LaTeX source Figures Fig0_2plus3_concept.pdf — Conceptual illustration of 2⊕3 symmetry (HQ version) Fig1_DOF_decomposition.pdf — Group-theoretic 2⊕3 pattern Fig2_GHZ_extremum.pdf — Even/odd parity structural extrema Fig3_Logos_functional.pdf — Double-well potential structure Fig4_robustness.pdf — Parameter dependence and cosmological comparison Fig5_GHZ_Sc_detailed.pdf — NEW: Structural coherence curves for GHZ states Supplementary Materials FoP_Cover_Letter.txt — Journal cover letter FoP_Submission_Materials.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 → f_b ≈ 0.156 (~3% deviation) Citation @misc{takagi2025structural, 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).