ODR Thesis: The Compton Count as the Only Primitive

In the paper's words

ODR framework: Compton count as the only primitive physical invariant.

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

Numbers it reports

1. Such an observation has not been reported in approximately 90 years of condensed matter physics. [speculative; null test held for ~90yr]

   from 2.3 The Quasiparticle Extension

2. Physicists have used $\mathbb{R}$ for approximately 400 years, implicitly treating the Archimedean completion as the "real" number system.

   from 3.1 Ostrowski's Theorem

3. Systematic review of PDG and solid-state databases would test this negative prediction — it has held for approximately 90 years since Landau's Fermi liquid theory.

   from 5.3 P5: Quasiparticle Invariance Null Test

4. A single counterexample (identical $m^*$ in two chemically distinct lattices) would disconfirm the claim. [speculative] Testability: P2 is testable within 2-5 years with existing Fermi-LAT data or the Cherenkov Telescope Array (CTA).

   from 5.3 P5: Quasiparticle Invariance Null Test

5. RQ4 candidate P2 (Lorentz-violation dispersion from tree discreteness, testable with Fermi-LAT GRB data within 2-5 years) is the fulcrum: if confirmed, it elevates RQ1-3 from Philosophy to Physics.

   from 7. Synthesis and Conclusion

6. The silo costs are staggering: Domain Structure Name Year Connection Silo Cost Key Paper Number Theory Ostrowski completions 1916 2026 (ODR) 110 yr Ostrowski, Acta Math 1916 Quantum Foundations Zitterbewegung/Compton 1928 2026 (ODR) 98 yr Dirac, Proc.

   from 6.1 The Five Trees

How it is done

1. Ostrowski's theorem (1916) proves that the only non-trivial absolute values on $\mathbb{Q}$ are the Archimedean absolute value (the usual real norm) and the $p$-adic absolute values for each prime $p$ [established — mathematics].

   from 3.1 Ostrowski's Theorem

2. The thesis proposes that Lorentz invariance is an emergent Archimedean symmetry, recovered at large separation scales where the tree's discrete structure is smoothed into the real continuum. [speculative — no proof exists] The p-adic AdS/CFT program faces the same issue: the BT tree's isometry group is $\operatorname{PGL}(2, \mathbb{Q}_p)$, not the Poincaré group.

   from 4.3 Lorentz Invariance

3. The 110-year gap between Ostrowski's theorem (1916) and its application to particle ontology (2026) represents a century of physics done on $\mathbb{R}$ when the natural number system for particle identities was $\mathbb{Q}$ with its $p$-adic completions.

   from 6.2 Why Does This Matter?

4. 41:271-284 (1916). [established — mathematics] Kaletha, T., Prasad, G., Bruhat–Tits Theory: A New Approach .

   from Bibliography

What would falsify it

1. This is not a flaw — it is the precise geometric account of why condensed matter physicists distinguish elementary from emergent excitations. [speculative] Falsifiability: RQ1 would be disconfirmed if a quasiparticle were found with an effective mass identical across multiple chemically distinct host lattices — a single counterexample would demonstrate context-independence in a rational function.

   from 2.3 The Quasiparticle Extension

2. This precedent supports the claim that Lorentz breaking is UV-only and undetectable at accessible energies. [speculative] Falsifiability: RQ3 would be disconfirmed if Lorentz violation were detected at energies below the Planck scale AND shown to have no tree-geometry structure — i.e., if the symmetry breaking were smooth and continuous rather than prime-structured.

   from 4.3 Lorentz Invariance

3. Without at least one falsifiable prediction that distinguishes ODR from standard QFT, the thesis is Philosophy rather than Physics.

   from 5.1 The Enabling Constraint

Where the claim stops

1. For the electron, the cyclic frequency is approximately $1.236 \times 10^{20}$ Hz.

   from 2.1 Definition

2. Such an observation has not been reported in approximately 90 years of condensed matter physics. [speculative; null test held for ~90yr]

   from 2.3 The Quasiparticle Extension

3. Physicists have used $\mathbb{R}$ for approximately 400 years, implicitly treating the Archimedean completion as the "real" number system.

   from 3.1 Ostrowski's Theorem

Where to read

1. Abstract227 words · 1 min
2. 1. Introduction247 words · 1 min
3. 2. RQ1: The Compton Count as the Only Primitive391 words · 2 min
4. 3. RQ2: $\mathbb{Q}$ as the Physical Number System381 words · 2 min
5. 4. RQ3: The Bruhat–Tits Tree as Coordinate System455 words · 2 min
6. 5. RQ4: Testable Predictions261 words · 1 min
7. 6. RQ5: The Silo Failure Diagnosis375 words · 2 min
8. 7. Synthesis and Conclusion262 words · 1 min
9. Declarations82 words · 1 min