Two Axioms: From Heart to the Light – Complete Emergent Derivation of G, ħ, c

This deposit contains version 1.1 of the Information-Relational Necessity System (IRNS) monograph entitled "TWO AXIOMSFrom Heart to the LightEmergent Derivation of Fundamental Constantsfrom Relational Information GeometryA Complete Theory of ℏ, G, and c fromTwo Axioms and Universal Relational Capacity S" Completed single-handedly by Robert Spychalski between May and November 2025. ═══════════════════════════════════════════════════════════════UPDATE v1.1 (25 November 2025): Mathematical foundation strengthened following literature recommendation from Terence Tao regarding Γ-convergence of graph Laplacians.═══════════════════════════════════════════════════════════════ Key results (November 2025 state-of-the-art): • Exactly two axioms (C1: Optimal Self-Description + NoL: Necessity of Coherence) • One universal dimensionless constant S = 6π − e/16 ≈ 18.6792 ± 0.1105 (CV = 0.59 %) • Fully analytical derivation of Planck's constant ħ with error < 10⁻¹¹ % • Fully analytical derivation of the gravitational constant G with error 0.393 % (0.0002 % in the tightest phases) – the most precise analytic result ever obtained from a foundational theory • Exact emergence of the speed of light c = 299 792 458 m/s via second-order relational wave equation and CODATA-2018 identity • Unique non-extensive parameter q = 1.5 derived as theorem (Hessian flatness condition) • Relational coherence threshold κ_R = 0.4982 ("heart operator" ♥) analytically obtained • Discovery of the π₅/π₆ duality as the mechanism coupling 5-dimensional information geometry to 6-dimensional phase-space classical gravity • First-principles explanation of the TE-I anomaly (IBM Eagle 127-qubit data) and universal scaling law for emergent Planck units NEW in v1.1: • Rigorous mathematical foundation for homogenization (Lemma 2.2) via Γ-convergence theory, validated by recent work of Bungert & Slepčev (2025, arXiv:2509.24458) – recommended by T. Tao • Proof that discrete relational Laplacian MUST converge to continuum Laplacian under IRNS axioms (no counterexamples known) • Peer review corrections: eliminated numerical error (1+4ln(2)≠e), resolved circularity via Emergent Identity Theorem, formalized title and symbols The main manuscript (9,165 lines, 25 November 2025) is accompanied by all supporting mathematical treatises, simulation records, and figures produced during Phases XIII–XL of the IRNS Research Project. No free parameters. No empirical fitting of the final constants. No loop-holes. This is the first physical theory in history that derives all three fundamental constants (ħ, G, c) from pure relational principles with quantified analytic errors using only two axioms and one universal constant. Date of v1.0 completion: 19 November 2025Date of v1.1 update: 25 November 2025 – incorporating Tao-recommended Γ-convergence validation License: CC-BY-4.0 (share, adapt, cite – just don't pretend you wrote it).