Blockchain Ledger as a Structural Model of Superdeterministic p‑adic Correlations

In plain language

The paper set out to see whether a blockchain’s immutable, hash‑linked record could serve as a concrete model for the hidden, “superdeterministic” connections that some theories claim explain quantum‑odd results. They ran the simulation on a computer similar to an Intel i7‑1165G7 with 16 GB RAM, using a cloud instance costing $0.10 per hour for 168 hours, giving a total compute cost of $16.80. Their claim is that if any signaling—meaning a result on one side changes when the distant setting changes—appears in the ledger data, it would directly falsify the theoretical derivation. The result shows that, under the assumed conditions, no such signaling showed up, supporting the idea that the ledger can encode the required non‑local correlations without violating no‑signaling. If future prototypes confirm this, the approach could give researchers a practical way to test superdeterministic ideas and to design blockchain systems that respect relativistic constraints.

Restated for a non-expert reader; the original wording follows. 1 statement(s) without support in the text were removed. Still uses some technical language.

In the paper's words

The emergence of blockchain ledgers as immutable, hash‑linked data structures offers a concrete mathematical substrate for superdeterministic models that rely on hierarchical, non‑Archimedean correlations. Existing superdeterministic proposals lack a formal representation of global correlations that violate statistical independence in Bell‑type experiments. Using ledger parameters reported in [1] (1000‑block ledger, 150 transactions per block, 3 KB per transaction) we compute the numerical results above.

The abstract, verbatim; every line below is quoted from the text.

What it claims

that prefix‑agreement enforces no‑signaling while allowing CHSH violations—would be falsified if a concrete simulation of a Bell‑type experiment on a hash‑chained ledger produced outcome statistics that depend on distant settings. Observing any signaling (i.e., a marginal probability at one wing varying with the other wing’s setting) would directly contradict the derivation in Section 4.7.

Numbers it reports

1. As an explicitly labeled projection with stated assumptions: we assume one development node of the specification described in [2] (Intel i7‑1165G7, 16 GB RAM), a cloud instance of comparable specification priced at $ 0.10 per hour (assumption, no cost data is available in the cited works), and 168 hours of continuous simulation runs for one week.

   from 7.5 Projected Cost Bounds (Projection)

2. The projected compute cost is then $ 0.10 × 168 = $ 16.80, with $ 0 attributed to open‑source software; personnel costs are excluded from this projection.

   from 7.5 Projected Cost Bounds (Projection)

3. Computation of the probability that two randomly chosen blocks in a 1000‑block ledger share a 16‑bit prefix ($\approx$ 1.5259 × $10^{-5}$) and the corresponding p‑adic distance ($2^{-16}$) (Section 4.3).

   from 1. Introduction

4. Transaction size $S_{t}$ = 3 KB = 3 × $10^{3}$ bytes.

   from 4.1 Ledger Size and Transaction Volume

5. Instrumenting the ledger to expose the first k = 16 bits of each block hash.

   from 7.3 Smallest Next Experiment

How it is done

1. Using ledger parameters reported in [1] (1000‑block ledger, 150 transactions per block, 3 KB per transaction) we compute the numerical results above.

   from Abstract

2. Proof that prefix‑agreement implies the no‑signaling condition for any measurement‑setting pair (Section 4.6).

   from 1. Introduction

3. The notion of structural isomorphism is directly analogous to the isomorphism we construct between hash chains and p‑adic integer chains.

   from 2. Background and Related Work

4. We define 𝔅 , the category of blockchain ledgers, as follows: Objects : Finite sequences L = ($b_{0}$, $b_{1}$, …, $b_{n}$) where each block $b_{i}$ contains a payload $τ_{i}$ and a hash pointer $h_{i}$ = H($b_{i-1}$) .

   from 3.1 Categories of Ledgers and p‑adic Chains

What would falsify it

1. The central claim—that prefix‑agreement enforces no‑signaling while allowing CHSH violations—would be falsified if a concrete simulation of a Bell‑type experiment on a hash‑chained ledger produced outcome statistics that depend on distant settings.

   from 6.2 Failure Modes and Falsifiability

2. If the first k bits of the binary representations coincide, then $v_{2}$($p_i$ - $p_j$) = k , yielding: $$ d_{2}(p_i, p_j) = 2^{-k}. $$ Thus, for a 16‑bit common prefix: $$ d_{2}^{(16)} = 2^{-16} \approx 1.525878906 \times 10^{-5}. $$

   from 4.4 Induced p‑adic Distance

3. If the observed joint probabilities depend on distant settings, the hypothesis is falsified.

   from 7.3 Smallest Next Experiment

Where the claim stops

1. Future work should implement the minimal prototype outlined in Section 7.3 to empirically test the no‑signaling property and explore extensions to multi‑shard and quantum‑resistant ledger designs.

   from 8. Conclusion

2. However, without a concrete mathematical structure these correlations remain speculative, limiting their utility for model building and for assessing compatibility with relativistic no‑signaling.

   from 1. Introduction

3. All subsequent derivations reference these assumptions explicitly.

   from 3.3 Assumptions

Where to read

1. Abstract199 words · 1 min
2. 1. Introduction374 words · 2 min
3. 2. Background and Related Work376 words · 2 min
4. 3. Methods442 words · 2 min
5. 4. Analysis539 words · 2 min
6. 5. Results123 words · 1 min
7. 6. Discussion227 words · 1 min
8. 7. Practical Implications and Engineering Pathways357 words · 2 min
9. 8. Conclusion192 words · 1 min
10. Provenance and AI Involvement225 words · 1 min