The Naulthène Model: From axiom to predictions — Δα/α = Φ/c² derived from a sub-Planckian aggregation framework (Version 3.2)

This document presents a theoretical framework called the “Naulthène Model” which derives the prediction Δα/α = Φ/c² (variation of the fine-structure constant proportional to the local gravitational potential) from a single axiom: the existence of sub-Planckian, massless entities with an intrinsic tendency to aggregate.The derivation follows a chain of five logical steps: (1) aggregation produces a network of connections, (2) this network constitutes emergent spacetime geometry (consistent with Causal Dynamical Triangulation), (3) the local density of synchronized connections (Q·K) determines the fine-structure constant α, (4) this identification is derived via a Bekenstein-Hawking entropy counting argument applied to the network, combined with Verlinde’s entropic gravity, and (5) gravitational fields modify the local density, hence α.The framework produces three independent testable predictions: (P1) Δα/α ≈ 2.5 × 10⁻⁴ on Sirius B, (P2) an anti-correlation Δμ/μ = −Δα/α in quasar absorption spectra, and (P3) an oscillation of α synchronized with gravitational waves (Δα/α ≈ h), which is, to our knowledge, an original prediction.Notably, the prediction P1 is compatible with existing measurements on white dwarf G191-B2B by Hu, Webb et al. (2021, MNRAS 500, 1466), which report Δα/α = (4.21–6.36) × 10⁻⁵ at a gravitational potential Φ/c² ≈ 5 × 10⁻⁵.This work was developed by a non-academic researcher using AI-assisted formalization (Claude/Anthropic) to translate physical intuitions into mathematical physics. The document prioritizes intellectual honesty: open problems, weak points, and speculative steps are explicitly identified throughout.