Relational Spherical Calculus (RSC): A Pure Geometric Framework for Gravity, Cosmology, Quantum Mechanics, and Atomic Structure

Authors/Creators Campbell, Christopher Description Relational Spherical Calculus (RSC) proposes that space is not a void containing objects - space is the structure of relationships between objects. Remove the relationships, and there is no space. From two axioms (pure relationality and conservation of information), two foundational refusals (the Planck length refuses zero size; the speed of light refuses zero time), and one master wave equation, the framework derives fundamental constants, quantum measurement laws, galactic dynamics, and the orbital structure of the periodic table - all from geometry, with zero fitted parameters. Precision results derived from pure geometry: Fine structure constant: α⁻¹ = 137.0366 (observed: 137.0360, match: 0.0004%) Proton-electron mass ratio: 1835.7 (observed: 1836.15, match: 0.027%) Cosmic expansion ratio: Rᵤ = (10/3)·c·Tᵤ (match: ~1%) Hubble constant: H₀ = 70.06 km/s/Mpc (within the Hubble tension range) Empirical validation: 175 SPARC galaxies, 3,398 velocity measurements, 2,645 point-by-point wins over Newtonian gravity (77.84%), median error 26.20% vs. Newton's 51.20% - with zero per-galaxy fitting and zero dark matter halos. New in v6.0 (April 2026): The framework advances from Phase II into Phase III with major results across four domains: The fine structure constant is derived to 0.0004% precision via a two-term correction: multiplicative geometric friction during wave transit and additive spatial contraction at measurement. Every mathematical operation is forced by the physics of the correction. Zero fitted parameters. The Born rule of quantum mechanics - the foundational law that probabilities equal amplitude squared - is derived from the framework's void cost mechanics, not assumed as a postulate. The double-slit interference pattern follows from two native principles with no imported quantum axioms. The measurement problem is dissolved: superposition is pre-temporal geometry, collapse is the heartbeat's crystallization event, and entanglement arises from shared holographic encoding. The periodic table's orbital structure is derived from the master wave's energy density ratio. The compressive phase supports exactly four interior standing wave modes, bounded by the singularity refusal principle. These correspond to the four orbital types (s, p, d, f). The framework predicts that g-orbitals are geometrically forbidden - a specific, falsifiable claim that distinguishes RSC from standard quantum mechanics. The SPARC rotation curve engine is validated across the full 175-galaxy database (expanded from 26 in v5.0), confirming out-of-sample predictive power with zero parameter adjustment. This release includes the theoretical framework (v6.0), methodology supplement with reproducible code, and complete SPARC validation data for all 175 galaxies. RSC is offered as a geometric foundation - a place to stand from which the rest of physics can be examined on relational terms. The invitation is open.