ULTRAMETRIC PHYSICS: RESEARCH PLAN

This research plan presents a complete framework for ultrametric physics based on fundamental scaling ratios rather than anthropocentric number representations. The core insight: physical reality is described by dimensionless scaling ratios (π, φ, e, α, etc.) that operate on hierarchical discrete structures, independent of any base representation (decimal, binary, etc.) or continuum assumptions.

Key Innovations:

1. Ratio-Based Valuations: Scaling bases q ∈ ℝ⁺ as pure ratios, not “numbers”
2. Base-Invariant Formulations: All mathematics independent of decimal/binary representations
3. Hierarchical Discrete Reality: Bruhat-Tits trees as fundamental substrate
4. Simultaneous Unification: Quantum computation, quantum gravity, consciousness
5. Constrained Methodology: 0.5 FTE PI, LLM-assisted, open dissemination via Zenodo/ResearchGate