Geometric Origin of Electromagnetic Waves: F-Perturbation Propagation, Photon Ontology, and the Unified Mechanism of Radiation

Electromagnetic waves are among the most thoroughly characterized phenomena in physics, yet several ontological questions remain structurally unanswered: What is the medium? Why are E and B exactly simultaneous? What is the photon? Why does acceleration produce radiation? This paper — PP-07 in the META Physics preprint series — derives the geometric ORIGIN of electromagnetic waves from the uniform rotation of the four-dimensional ball B⁴ (R) and the geometric structure of its three-dimensional boundary S³ (R). Eight principal results are established with zero free parameters. (I) The medium of electromagnetic waves is identified as the continuum of zero-dimensional points on S³ (R), undetectable from WS₃ because it generates spacetime rather than inhabiting it. (II) Each zero-dimensional point possesses an ATI effective radius (ρ₁, ρ₂) — Hopf allocation parameters — governing wave amplitude (ρ₂) and frequency (δΩ). (III) The 0s–0i phase alternation resolves the zero-crossing existential problem: energy alternates between surface port (WS₃-observable) and inner port (ES-interior), with sin²φ + cos²φ = 1. (IV) E-B "simultaneity" is derived, not assumed: the electromagnetic field strength tensor F = dωV is a single 2-form on S³ (R) ; E and B are its WS₃ decomposition components. (V) The photon is not a substance — not in the PGS list B⁰,. . . , B⁵. It is the quantum-viewpoint observation of F-perturbation propagation. "Wave-particle duality" is a category error resolved by the quantum/continuum viewpoint distinction. (VI) Antenna radiation, quantum transition emission, and pair-annihilation radiation are unified as three triggering conditions of one geometric mechanism: ρ₂ variation → F-perturbation → cascading propagation on S³ (R). (VII) The Poynting vector unit decomposition W/m² = kg·s⁻³ reveals the ES structure: spatial dimension exactly cancelled, leaving stacking number (kg) and triple quaternion rotation (s⁻³) — the same structural components that constitute gravity. (VIII) Gamma-ray pair production is derived as topological winding-pair generation: n = 0 → (n = +1) + (n = −1), with energy threshold E ≥ 2mₑ c² as the minimum stacking number for two |n| = 1 configurations. E = mc² is the state change of the same stacking number from propagating (energy) to localized (mass). Thirty established results are derived across 13 sections. The electromagnetic wave — from its medium and propagation speed, through photon ontology and quantum transitions, to pair production — is a unified geometric consequence of the B⁴ (R) rotation structure on S³ (R). Mathematical formalization and documentation: Claude (Anthropic, Claude Opus 4. 6). The core insights, physical intuitions, and axiom system originate from the author's 30 years of independent research.