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

This deposit contains the complete first version (v1.0) of the Information-Relational Necessity System (IRNS) monograph entitled “TWO AXIOMS: From Heart to the Light – Emergent Derivation of the Fundamental Constants ħ, G, and c from Relational Information Geometry” Completed single-handedly by Robert Spychalski between May and November 2025. 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 The main manuscript (410 000+ characters, 19 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 completion: 19 November 2025 – exactly six months after project restart and the personal “day zero” of the author. License: CC-BY-4.0 (share, adapt, cite – just don’t pretend you wrote it). All future updates will receive new DOIs; this deposit freezes the exact state of IRNS as of its historic first completion.