The Adelic Physics Program: Epistemological Foundations and Communications Framework

In the paper's words

The QNFO Adelic Physics Program proposes that the physically accessible base field of physics is Q (the rational numbers), not R (the real numbers). Ostrowskis theorem demands all p-adic completions of Q be physically meaningful. This paper provides the epistemological and pedagogical infrastructure.

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

Numbers it reports

1. The Adelic Cross-Domain Program reports that 11 Standard Model mass ratios fit this scheme to approximately 2%, with specific examples including: $m_{\tau } / m_{c} = 136.63$ vs. $3^{7} / 2^{4} = 136.7$ (deviation 0.07%) $m_{\tau } / m_{d} = 20.02$ vs. $2^{2} \cdot 5 = 20$ (exact) Convergent evidence (independent of QNFO): Chen, Liu, and Hung (2024) independently treat the Bruhat-Tits tree as a physical geometry, constructing a p-adic BTZ black hole on $T_{p}$.

   from 6.1 Discrete Substrate of Spacetime

2. The adelic programme is not "new physics" — it is the removal of an unjustified assumption that has constrained physics for 150 years.

   from 11. Conclusion: What Changes

How it is done

1. Ostrowski's theorem — a proven result in number theory — then demands that all p-adic completions of $\mathbb{Q}$ be physically meaningful, transforming the Adelic Physics Program from mathematical speculation into a physical programme.

   from Abstract

2. The physically accessible numbers are rational — every measurement produces a rational number, every computer simulation operates on finite-precision approximations, and every number that has ever appeared in a physics paper ($\pi , e, \sqrt{2}$, the fine-structure constant $\alpha$) is computable — meaning it can be approximated to arbitrary precision by a finite rational procedure.

   from 1. Introduction

3. Physics inherited $\mathbb{R}$ from mathematics, not from experiment.

   from $2.1 \mathbb{R}$ Is Not Forced by Physical Necessity

4. A computable real number is one for which there exists a finite Turing-machine procedure (a D/R procedure in the terminology of Autaxys Ontological Closure) that approximates it with a computable modulus of convergence.

   from 2.2 The Computable Reals Argument

What would falsify it

1. The burden of proof therefore shifts to the advocate of $\mathbb{R}$: demonstrate a physical prediction that requires infinite-precision real numbers and cannot be reproduced by any finite-precision rational computation.

   from $2.1 \mathbb{R}$ Is Not Forced by Physical Necessity

2. To our knowledge, no such prediction exists [untested — open research question] [proposed — this is a methodological stance, not an established fact that $\mathbb{Q}$ is sufficient for all physics].

   from $2.1 \mathbb{R}$ Is Not Forced by Physical Necessity

3. The non-computable reals (Chaitin's $\Omega$, etc.) have never appeared in any physical prediction [established].

   from 2.2 The Computable Reals Argument

Where the claim stops

1. The adelic programme is not "new physics" — it is the removal of an unjustified assumption that has constrained physics for 150 years.

   from 11. Conclusion: What Changes

2. The advocate of $\mathbb{R}$ must now demonstrate a physical prediction that requires infinite-precision real numbers and cannot be reproduced by any finite-precision rational computation.

   from 11. Conclusion: What Changes

3. Until such a prediction is found — and none has been found to date — the working assumption should be that $\mathbb{Q}$ is the physical base field, and that Ostrowski's theorem applies.

   from 11. Conclusion: What Changes

Where to read

1. Abstract236 words · 1 min
2. 1. Introduction585 words · 3 min
3. 2. The Unjustified Assumption637 words · 3 min
4. 3. Number-Theoretic Foundations336 words · 1 min
5. 4. Constructing Numbers from Distinctions348 words · 2 min
6. 5. The Gisin–Del Santo Programme: Independent Convergence424 words · 2 min
7. 6. Bruhat-Tits Trees as Physical Geometry348 words · 2 min
8. 7. Ultrametric Quantum Computation266 words · 1 min
9. 8. The Langlands Bridge240 words · 1 min
10. 9. Domain Translation Errors: A Communications Framework295 words · 1 min
11. 10. Observer-Centered Epistemology274 words · 1 min
12. 11. Conclusion: What Changes223 words · 1 min