A Falsifiability‑First Audit Program for the Photon‑Primacy, Helical‑Electron, and Adelic‑Mass Claim Cluster

In the paper's words

The photon‑primacy / helical‑electron / adelic‑mass cluster proposes that particle rest‑energies arise from photonic circulation, that electron spin is literal helical motion at twice the Compton frequency, and that mass ratios encode arithmetic structure on Bruhat–Tits trees. The literature surrounding these ideas is fragmented and lacks a systematic, falsifiability‑driven audit methodology. We present a Falsifiability‑First Audit Program (FFAP) that (i) extracts every explicit claim from the QNFO corpus, (ii) maps each claim onto a concrete experimental observable or logical kill condition, (iii) enumerates the full combinatorial test space, and (iv) derives statistically rigorous significance thresholds that respect multiple‑testing constraints.

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

Numbers it reports

1. Assuming a per‑test Type I error of 5 % the naïve family‑wise error rate exceeds 96 %; a Bonferroni correction yields a per‑test significance level of $\alpha = 7.8 \times 10^{-4}$ .

   from Abstract

2. A feasibility projection for the trapped‑ion ultrametric test shows that, under standard‑quantum‑limit assumptions, a depth‑4 test would demand ≈ $10^{10}$ coherent cycles (≈ 11.6 days), whereas a Heisenberg‑limited protocol would reduce this to ≈ 10 s.

   from Abstract

3. Assuming a readout contrast $\eta = 10^{-3}$ and $\rho = 10^{-2}$, the standard‑quantum‑limit (SQL) number of coherent cycles required is $$ N_{\text{SQL}} \approx \left(\frac{1}{\eta\rho}\right)^{2}= \left(\frac{1}{10^{-5}}\right)^{2}=10^{10}. $$ At a gate rate of $10^{4}$ cycles $s^{-1}$ this corresponds to ≈ 11.6 days of continuous coherent operation, exceeding current coherence budgets.

   from 4.8 Projected Ion‑Trap Discrimination Power (C7)

4. The projection is highly sensitive to the assumed $\rho$; if $\rho = 10^{-3}$ the SQL requirement rises to ≈ 116 days, while the Heisenberg limit remains ≈ 100 s.

   from 4.8 Projected Ion‑Trap Discrimination Power (C7)

5. Naïve FWER 0.9624 Without correction the audit would produce a false positive in ≈ 96 % of runs.

   from 5. Results

6. Projected ion‑trap cycles (SQL) $10^{10}$ cycles ≈ 11.6 days Feasibility envelope; suggests Heisenberg‑limited protocols are required.

   from 5. Results

How it is done

1. A feasibility projection for the trapped‑ion ultrametric test shows that, under standard‑quantum‑limit assumptions, a depth‑4 test would demand ≈ $10^{10}$ coherent cycles (≈ 11.6 days), whereas a Heisenberg‑limited protocol would reduce this to ≈ 10 s.

   from Abstract

2. Yet the community has no systematic protocol for deciding whether a new measurement “kills” a claim.

   from 1. Introduction

3. Turing‑Church Thesis, Constructive Mathematics and Intuitionist Logic [8] argues for constructive proof techniques in computability theory.

   from 2. Background and Related Work

4. A Heisenberg‑limited protocol would reduce the requirement to $$ N_{\text{HL}} \approx \frac{1}{\eta\rho}=10^{5}\;\text{cycles}\approx10\;\text{s}, $$ which is feasible with existing hardware.

   from 4.8 Projected Ion‑Trap Discrimination Power (C7)

What would falsify it

1. A single defensible derivation that predicts a new observable without introducing additional fitted parameters (i.e., $f \leq n$) and survives all KC checks would falsify our grade‑F verdicts for the helical‑electron and adelic‑mass sub‑claims, forcing a revision of the audit’s grading rubric.

   from 6.3 What Would Falsify the Audit’s Meta‑Claim

2. How should the audit handle immunization moves (e.g., redefining “near‑integer” after seeing the data) without sacrificing falsifiability?

   from 6.4 Open Questions

3. The literature surrounding these ideas is fragmented and lacks a systematic, falsifiability‑driven audit methodology.

   from Abstract

Where the claim stops

1. Independence assumption: The FWER calculation assumes statistical independence among the 64 tests.

   from 6.1 Limitations

2. Alternative procedures (Holm‑Šidák, FDR) could be explored in future work.

   from 6.1 Limitations

3. Null model for integer‑log concentration: The uniform‑fractional‑part null used in C6 is a crude approximation; a physically motivated prior could shift the chance‑hit probability by an order of magnitude.

   from 6.1 Limitations

Where to read

1. Abstract312 words · 1 min
2. 1. Introduction295 words · 1 min
3. 2. Background and Related Work373 words · 2 min
4. 3. Methods396 words · 2 min
5. 4. Analysis592 words · 3 min
6. 5. Results166 words · 1 min
7. 6. Discussion420 words · 2 min
8. 7. Conclusion178 words · 1 min
9. Correction Notice105 words · 1 min
10. Appendix B. Claim Attribution309 words · 1 min