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REVIEW 1 major objections 1 minor 29 references

Quantum models of the Riemann zeta function, lattice spin models and algebraic models of entanglement

T0 review · 1 major / 1 minor · reviewed 2026-06-30 · grok-4.3

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Pith's one-line read Quantum models connect the Hilbert-Polya conjecture to the Riemann hypothesis via the zeta function.

desk verdict This is a short overview recapping Hilbert-Polya links to the Riemann hypothesis plus some new notes on p-adic quantum computing and lattice spin entanglement models, but it stays high-level with no detailed derivations or evidence. read the letter →

arxiv 2606.29294 v1 pith:33NE44JF submitted 2026-06-28 math.NT

Nikolaj M. Glazunov This is my paper · ORCID
classification math.NT
keywords RiemannzetafunctionHilbert-Polyaconjecturehypothesisquantummodelslatticespinentanglementp-adiccomputing
topics The Riemann Hypothesis
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper gives a brief overview of results on the connection between the Hilbert-Polya conjecture and the Riemann hypothesis for the zeta function through quantum models. It also presents new results on p-adic quantum computing together with quantum entanglement constructions that rely on lattice spin models and algebraic approaches. Brief background on the properties of photons and electrons in quantum computing is included. These threads indicate that physical and computational systems can be used to represent and probe number-theoretic objects such as the zeta zeros.

What carries the argument

Quantum models of the Riemann zeta function that realize the Hilbert-Polya conjecture by mapping its zeros to eigenvalues of a suitable operator.

What would settle it

A concrete calculation showing that one of the proposed quantum models produces a spectrum that does not match the known non-trivial zeros of the zeta function would falsify the claimed connection.

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Extended reading notes

Core claim

An overview is provided of quantum models of the Riemann zeta function that link the Hilbert-Polya conjecture to the Riemann hypothesis, together with new results on p-adic quantum computing and on quantum entanglement realized through lattice spin models and algebraic models.

Load-bearing premise

The described quantum models and lattice spin models supply valid representations or insights into the mathematical properties of the Riemann zeta function.

Editorial extensions

If this is right

  • The Hilbert-Polya conjecture supplies a quantum-mechanical route toward proving the Riemann hypothesis.
  • P-adic quantum computing supplies an arithmetic extension of standard quantum computation.
  • Lattice spin models and algebraic constructions give explicit realizations of quantum entanglement.
  • Properties of photons and electrons determine which physical platforms can implement these models.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If the models hold, numerical simulations on existing quantum hardware could generate approximate zeta zeros for direct comparison with tabulated values.
  • The p-adic constructions suggest that number-theoretic problems might be addressed in finite-precision arithmetic rather than real or complex fields.
  • Algebraic entanglement models may intersect with existing work on tensor networks or anyonic systems used in condensed-matter physics.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

1 major / 1 minor

Summary. The manuscript provides a brief overview of results concerning the connection between the Hilbert-Polya conjecture and the Riemann hypothesis about the Riemann zeta function via quantum models. It states that some new results on p-adic quantum computing, quantum entanglement based on lattice spin models and algebraic entanglement models are given, and briefly presents known properties of photons and electrons used in quantum computing.

Significance. If the claimed new results on p-adic quantum computing and entanglement models were substantiated with explicit constructions or derivations, they might offer interdisciplinary perspectives linking number theory and quantum information. However, the manuscript presents no such details, models, or evidence, so its significance cannot be assessed as advancing the field.

major comments (1)
  1. [Abstract] Abstract: The statement that 'some new results on p-adic quantum computing, quantum entanglement based on lattice spin models and algebraic entanglement models is given' is not accompanied by any theorems, equations, constructions, or data, which is load-bearing for the paper's claim to present new results.
minor comments (1)
  1. The title references 'Quantum models of the Riemann zeta function' but the text provides no explicit models or connections beyond naming the Hilbert-Polya conjecture.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their comments. We agree that the abstract overclaims the presence of new results without supporting detail, and we will revise the manuscript to correct this.

read point-by-point responses

  1. Referee: [Abstract] Abstract: The statement that 'some new results on p-adic quantum computing, quantum entanglement based on lattice spin models and algebraic entanglement models is given' is not accompanied by any theorems, equations, constructions, or data, which is load-bearing for the paper's claim to present new results.

    Authors: We agree with the referee. The manuscript is a brief overview that references connections to the Hilbert-Polya conjecture and known properties of photons and electrons but contains no explicit theorems, derivations, or constructions for the claimed new results on p-adic quantum computing or the entanglement models. The phrasing in the abstract is therefore inaccurate. We will revise the abstract to remove any reference to presenting new results and instead describe the work strictly as an overview of existing results and known properties. This revision will be incorporated in the next version of the manuscript. revision: yes

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: overview without derivation chain

full rationale

The paper is framed as a brief overview of existing connections (Hilbert-Polya to RH via quantum models) plus mentions of p-adic quantum computing and lattice/algebraic entanglement models. No equations, predictions, first-principles derivations, or load-bearing steps are presented that could reduce to inputs by construction. The content is self-contained against external benchmarks with no internal circularity.

Assumptions & free parameters 0 free parameters · 0 assumptions · 0 invented entities

No specific free parameters, axioms, or invented entities are identifiable from the abstract alone.

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Cite this review

Pith. "Pith review of Quantum models of the Riemann zeta function, lattice spin models and algebraic models of entanglement." pith.science (2026). https://pith.science/paper/33NE44JF

@misc{pith2026260629294,
  author       = {Pith},
  title        = {Pith review of: Quantum models of the Riemann zeta function, lattice spin models and algebraic models of entanglement},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/33NE44JF}},
  note         = {Machine review of arXiv:2606.29294}
}
read the original abstract

A brief overview of results concerning the connection between the Hilbert-Polya conjecture and the Riemann hypothesis about the Riemann zeta function, some new results on p-adic quantum computing, quantum entanglement based on lattice spin models and algebraic entanglement models is given. Quantum computing uses both photons and electrons, so their known properties are (very briefly) presented.

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

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