The Adelic Physics Program: A Grand Synthesis

In the paper's words

This paper consolidates the 6-paper adelic physics chain into a unified research program, from Zitterbewegung as a p-adic observable through Majorana correlators, Bruhat-Tits readout protocols, p-adic anyon braiding, and Ostrowski-based quantum error correction.

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

Numbers it reports

No sentence of this paper reports a figure with a unit or a quantity word, so none is shown.

How it is done

1. Ostrowski's theorem — which classifies all non-trivial completions of the rational numbers as $\mathbb{R}$ and $\mathbb{Q}_p$ for each prime $p$ — is the hidden organizing principle behind quantum measurement, quantum error correction, and the structure of spacetime at the Compton scale.

   from Abstract

2. It is a new physical claim with specific, falsifiable predictions across theory, computation, and experiment: Theory (P1, P2): ZBW is a p-adic observable; the ZBW current correlator is a $\mathbb{Z}_2$ topological invariant QFT (P2): The invariant distinguishes Dirac from Majorana fermions at the field-theoretic level Experiment (P3): Three protocols (spin noise, EELS/RIXS, Gromov $\delta$) can measure the invariant Connection (P4): The invariant encodes p-adic anyon fusion rules; ZBW spectroscopy = p-adic anyon interferometry Protection (P5): The invariant provides intrinsic QEC via Ostrowski's theorem Infrastructure (P6): Deployed computational engine for ultrametric analysis

   from 2. The Central Thesis

3. P1: THEORY P2: QFT P3: EXPERIMENT "ZBW is p-adic" "Correlator = Z₂" "How to measure" Bruhat-Tits trees (δ=0) Momentum-dep. diagnostic 3 falsifiable protocols ↓ ↓ ↓ P4: SYNTHESIS-1 P5: PROTECTION P6: INFRASTRUCTURE "ZBW ↔ p-Adic Anyons" "Ostrowski-based QEC" "Ultrametric Engine" Bridges ZBW to anyons Intrinsic protection Deployed Worker ↓ ↓ ↓ P7: GRAND SYNTHESIS (this paper) "Physics is adelic — the Archimedean is the ∞-readout"

   from 3. The Six-Paper Chain

4. The adelic approach provides a complete alternative to the standard QEC paradigm: Component Standard Approach Adelic Approach Qubit encoding Physical qubits + stabilizer codes Majorana ZBW mode (p-adic fixed point) Error protection Active syndrome measurement Ostrowski incommensurability (passive) Gate operations Unitary gates + fault tolerance p-adic anyon braiding ($O(1)$ apartment shifts) Readout Projective measurement ZBW spectroscopy ($\mathcal{O}_{\text{ZBW}}$) Scaling Polynomial overhead in code distance $O(1)$ — single Majorana mode

   from 6.2 For Quantum Computing

What would falsify it

1. This synthesis paper connects all six companion publications into a coherent research program with specific, falsifiable predictions.

   from Abstract

2. It is a new physical claim with specific, falsifiable predictions across theory, computation, and experiment: Theory (P1, P2): ZBW is a p-adic observable; the ZBW current correlator is a $\mathbb{Z}_2$ topological invariant QFT (P2): The invariant distinguishes Dirac from Majorana fermions at the field-theoretic level Experiment (P3): Three protocols (spin noise, EELS/RIXS, Gromov $\delta$) can measure the invariant Connection (P4): The invariant encodes p-adic anyon fusion rules; ZBW spectroscopy = p-adic anyon interferometry Protection (P5): The invariant provides intrinsic QEC via Ostrowski's theorem Infrastructure (P6): Deployed computational engine for ultrametric analysis

   from 2. The Central Thesis

3. P1: THEORY P2: QFT P3: EXPERIMENT "ZBW is p-adic" "Correlator = Z₂" "How to measure" Bruhat-Tits trees (δ=0) Momentum-dep. diagnostic 3 falsifiable protocols ↓ ↓ ↓ P4: SYNTHESIS-1 P5: PROTECTION P6: INFRASTRUCTURE "ZBW ↔ p-Adic Anyons" "Ostrowski-based QEC" "Ultrametric Engine" Bridges ZBW to anyons Intrinsic protection Deployed Worker ↓ ↓ ↓ P7: GRAND SYNTHESIS (this paper) "Physics is adelic — the Archimedean is the ∞-readout"

   from 3. The Six-Paper Chain

Where the claim stops

1. The Bruhat-Tits tree is the native geometry of the Compton scale, and the Archimedean continuum is an emergent, large-scale approximation.

   from 6.3 For Fundamental Physics

Where to read

1. Abstract144 words · 1 min
2. 2. The Central Thesis141 words · 1 min
3. 3. The Six-Paper Chain168 words · 1 min
4. 4. The Adelic Dirac Equation135 words · 1 min
5. 5. Falsifiability — The Complete Matrix167 words · 1 min
6. 6. Implications216 words · 1 min
7. 7. The Research Program63 words · 1 min
8. 8. Conclusions176 words · 1 min
9. Changelog9 words · 1 min