Consilience Between Physics and Number Theory

Status: Phase 0 — Project Initialization Started: 2026-07-26 Author: QNFO Research Agent License: QNFO Unified License Agreement (QNFO-ULA) — https://legal.qnfo.org/

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Overview

This research project synthesizes consilience — the convergence of independent lines of evidence — between two seemingly disconnected domains:

• Physics: Quantum mechanics, quantum field theory, zitterbewegung, quantum error correction, the Standard Model mass spectrum
• Mathematics: Ostrowski's theorem, Tate's thesis, the Riemann zeta function, Bruhat-Tits buildings, the adele ring, p-adic numbers

The central claim is that Ostrowski's theorem — which classifies the only non-trivial completions of ℚ as ℝ and ℚₚ — is a universal template for understanding how formal systems partition "distance" or "similarity." Physics currently operates exclusively at the ∞-place (Archimedean completion); a democratic treatment of all completions reveals deeper unities.

Quick Start

# Clone the repo
git clone <repo-url>
cd consilience-physics-numtheory

# Read the plan
cat PROJECT-PLAN.md

# Browse artifacts
ls artifacts/
ls notebooks/

Project Structure

consilience-physics-numtheory/
├── README.md              # This file
├── PROJECT-PLAN.md        # Charter, WBS, milestones, risk register
├── .gitignore             # Excludes ephemeral scripts, secrets, build artifacts
├── paper.md               # Synthesis paper (Phase 5)
├── paper.pdf              # Rendered PDF (Phase 5)
├── docs/                  # Source documents, prior work, reference materials
├── artifacts/             # Phase deliverables (lit reviews, gate memos, test results)
├── notebooks/             # Working notes, thesis development, calculation notebooks
└── releases/              # Versioned Zenodo-ready bundles

Phases

Phase	Tag	Status
0 — Project Init	v0.1-phase0	IN PROGRESS
1 — Due Diligence	v0.2-phase1-dd	Pending
2 — Literature Search	v0.3-phase2-lit	Pending
3 — Deep Research (Theses)	v0.5-phase3-deep	Pending
4 — Expansion (Meta-Framework)	v0.6-phase4-expand	Pending
5 — Publication	v1.0	Pending
6 — Core Distribution	v1.1-distribute	Pending

Key Documents

• PROJECT-PLAN.md — Full project plan with charter, WBS, milestones, risks
• artifacts/phase1-gap-analysis.md — What exists in QNFO corpus vs. what's novel (Phase 1)
• artifacts/phase2-classification.md — Classified literature review (Phase 2)
• artifacts/phase3-red-team.md — Adversarial review of all theses (Phase 3)
• artifacts/phase3-calibration-register.md — Dated prediction registry (Phase 3)

Convergent Theses (in development)

#	Thesis	Certainty
1	Riemann ζ(s) encodes the spectrum of a quantum system over ℚ	4/5
2	Zitterbewegung = ℝ/ℚ₂ topological mixing	3/5
3	Ostrowski's theorem as a selection rule for physical theories	5/5
4	Bruhat-Tits trees as discrete spacetime substrate	2/5
5	Substrate IS the algorithm — number-theoretic QEC	2/5
6	Transcendental numbers as projection artifacts	2/5
7	Tate's thesis as template for adelic QM	4/5
8	Langlands program as adelic physics without the physics	3/5
9	Primes as elementary particles of structure	2/5

External Literature

The canonical external anchor is the p-adic and adelic quantum mechanics programme developed by B. Dragovich, G. Djordjevic, Lj. Nesic, and I.V. Volovich (1987–present). Key supporting work:

• Dragovich (2003): Review of p-adic and adelic QM
• Zúñiga-Galindo (2015): p-Adic Dirac equation with Planck-scale Lorentz violation
• Chen-Liu-Hung (2024): Bending the Bruhat-Tits tree (p-adic BTZ black hole)
• Bost-Connes (1995): Quantum statistical system with ζ(β) as partition function
• Huang-Stoica-Zhong (2024): Quadratic reciprocity from adelic CFT

License

QNFO Unified License Agreement (QNFO-ULA) — https://legal.qnfo.org/