Consilience Between Physics and Number Theory: Convergent Theses from Ostrowski's Theorem to Adelic Quantum Mechanics

In the paper's words

We synthesize convergent evidence from physics (quantum mechanics, quantum field theory, zitterbewegung, quantum error correction, the Standard Model mass spectrum) and number theory (Ostrowski's theorem, Tate's thesis, the Riemann zeta function, Bruhat-Tits buildings, the adele ring) into a unified consilience framework. The central organizing principle is Ostrowski's theorem — the classification of all non-trivial completions of the rational numbers as the Archimedean completion ℝ and the p-adic completions ℚₚ. We develop nine convergent theses, each with calibrated certainty ratings and explicit falsifiability conditions.

The abstract, verbatim, and its opening sentence is the claim. Every line below is quoted from the text.

Numbers it reports

1. The ~2% mass ratio tolerance is too loose for particle physics.

   from 5.2 Empirical Gaps

2. The product 𝒯_2 × 𝒯_3 × 𝒯_5 is a 3-dimensional ultrametric space.

   from 2.4 Bruhat-Tits Trees

3. The product tree 𝒯_2 × 𝒯_3 × 𝒯_5, with its diagonal embedding into the Pythagorean semigroup {$2^{a} \cdot 3^{b} \cdot 5^{c}$}, maps tree geometry to physical mass ratios.

   from Thesis 4: Bruhat-Tits Trees Are the Discrete Substrate of Spacetime

4. The Adelic Cross-Domain Program reports that 11 Standard Model mass ratios fit this scheme to ~2%, with specific examples including $m_{\tau }/m_{c} = 136.63$ vs. $3^{7}/2^{4} = 136.7$ (deviation 0.07%) and $m_{\tau }/m_{d} = 20.02$ vs. $2^{2}\cdot 5 = 20$ (exact).

   from Thesis 4: Bruhat-Tits Trees Are the Discrete Substrate of Spacetime

5. The 2% tolerance is loose by particle physics standards (the Standard Model predicts g-2 to 10 decimal places).

   from Thesis 4: Bruhat-Tits Trees Are the Discrete Substrate of Spacetime

6. Falsifiability: "This would be disconfirmed if Majorana qubit coherence time shows no immunity to Archimedean noise beyond standard QEC performance (P5-C7 protocol, 1–3 year timeline)."

   from Thesis 5: The Substrate IS the Algorithm — Number-Theoretic Quantum Error Correction

How it is done

1. We synthesize convergent evidence from physics (quantum mechanics, quantum field theory, zitterbewegung, quantum error correction, the Standard Model mass spectrum) and number theory (Ostrowski's theorem, Tate's thesis, the Riemann zeta function, Bruhat-Tits buildings, the adele ring) into a unified consilience framework.

   from Abstract

2. This paper examines a specific candidate for consilience: the convergence between physics (quantum mechanics, quantum field theory, the Standard Model) and number theory (Ostrowski's theorem, Tate's thesis, the Riemann zeta function, Bruhat-Tits buildings).

   from 1. Introduction

3. The theorem is proven — it is not a conjecture or an interpretation.

   from 2.1 Ostrowski's Theorem (1916)

4. The programme has proven that adelic quantum mechanics is form-invariant under interchange of $\mathbb{R}$ and $\mathbb{Q}_{p}$ — a mathematical theorem, not a conjecture.

   from 2.3 The Adele Ring $\mathbb{A}_\mathbb{Q}$

What would falsify it

1. We develop nine convergent theses, each with calibrated certainty ratings and explicit falsifiability conditions.

   from Abstract

2. The framework is falsifiable via the experimental decision matrix of the QNFO Grand Synthesis.

   from Abstract

3. Section 6 concludes with the falsifiability decision matrix.

   from 1. Introduction

Where the claim stops

1. Falsifiability: "This would be disconfirmed if $\zeta (s)$ cannot be represented as Tr(e^{-βH}) for any self-adjoint H." Status: NOT disconfirmed.

   from Thesis 1: The Riemann Zeta Function Encodes the Spectrum of a Quantum System Over $\mathbb{Q}$

2. Falsifiability: "This would be disconfirmed if new precision mass measurements diverge from Pythagorean ratios beyond the declared tolerance with no trend toward convergence, and if a genuine pre-measurement prediction of a new mass fails."

   from Thesis 4: Bruhat-Tits Trees Are the Discrete Substrate of Spacetime

3. Certainty: [speculative] — computationally modeled for the ZBW $\mathbb{Z}_{2}$ invariant; experimental claim C7 (Majorana qubit immune to Archimedean noise) unverified. [not yet falsifiable] for generalizations to non-physics domains (biology, neural codes).

   from Thesis 5: The Substrate IS the Algorithm — Number-Theoretic Quantum Error Correction

Where to read

1. Abstract263 words · 1 min
2. 1. Introduction371 words · 2 min
3. 2. The Mathematical Spine480 words · 2 min
4. 3. The Seven Core Convergent Theses1,272 words · 6 min
5. 4. Expansion: Beyond the Seven Theses179 words · 1 min
6. 5. Critical Self-Assessment339 words · 1 min
7. 6. Conclusion: The Shape of the Convergence256 words · 1 min
8. Declarations192 words · 1 min