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arxiv: 2606.18739 · v2 · pith:PSJJCQTUnew · submitted 2026-06-17 · ✦ hep-th

ASEP/DSSYK duality and strange correlator

Kazumi Okuyama This is my paper

Pith reviewed 2026-06-26 20:14 UTC · model grok-4.3

classification ✦ hep-th
keywords ASEPDSSYKstrange correlatortransfer matrixoverlapdualitySYK modelexclusion process
0
0 comments X

The pith

The moment of the DSSYK transfer matrix equals an overlap between the ASEP stationary state and a product state.

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

The paper shows that moments of the transfer matrix in the double-scaled SYK model can be rewritten exactly as overlaps between the stationary state of the asymmetric simple exclusion process and a product state. It then identifies this overlap as the direct analogue of the strange correlator that appears when the Levin-Wen string-net model is matched to the Turaev-Viro state sum. A sympathetic reader would care because the mapping converts a quantity arising in a chaotic, holographically motivated quantum system into an object that lives in a classical stochastic process, opening a route to evaluate SYK observables by solving an integrable exclusion model instead.

Core claim

We show that the moment of the transfer matrix of the double scaled SYK model is written as an overlap between the stationary state of ASEP and a product state. We argue that this overlap is an analogue of the strange correlator appearing in the correspondence between the Levin-Wen string-net model and the Turaev-Viro state sum.

What carries the argument

The overlap between the stationary state of the asymmetric simple exclusion process (ASEP) and a product state, which the paper identifies as the analogue of the strange correlator.

If this is right

  • Moments of the DSSYK transfer matrix become computable by solving the stationary distribution of the ASEP.
  • The strange-correlator analogy supplies a concrete dictionary between DSSYK observables and quantities already studied in topological state-sum models.
  • The duality furnishes a probabilistic interpretation for certain correlation functions that appear in the double-scaled SYK model.
  • Known exact solutions and integrability techniques for the ASEP can be imported to evaluate SYK quantities that were previously accessible only numerically or via random-matrix methods.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The mapping suggests that time-evolution operators in the SYK model may admit a hidden representation as Markov chains on particle configurations.
  • If the analogy to the strange correlator is tight, then DSSYK partition functions could inherit topological invariance properties under certain deformations.
  • One could test the duality by comparing the large-N scaling of the ASEP overlap against known SYK moment asymptotics.

Load-bearing premise

The assumption that the identified overlap in the ASEP-DSSYK mapping functions as the direct analogue of the strange correlator in the Levin-Wen string-net / Turaev-Viro correspondence.

What would settle it

An explicit calculation of the ASEP overlap for finite system size that fails to reproduce the corresponding DSSYK transfer-matrix moment at the same parameters would falsify the claimed equality.

read the original abstract

We show that the moment of the transfer matrix of the double scaled SYK model is written as an overlap between the stationary state of ASEP (asymmetric simple exclusion process) and a product state. We argue that this overlap is an analogue of the strange correlator appearing in the correspondence between the Levin-Wen string-net model and the Turaev-Viro state sum.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 0 minor

Summary. The paper claims to show that a moment of the transfer matrix of the double-scaled SYK (DSSYK) model equals an overlap between the stationary state of the asymmetric simple exclusion process (ASEP) and a product state. It further argues that this overlap is an analogue of the strange correlator in the Levin-Wen string-net model / Turaev-Viro state-sum correspondence.

Significance. If the overlap identity is rigorously derived and the analogy to the strange correlator is substantiated with explicit checks, the result would establish a concrete link between the DSSYK model, an integrable classical stochastic process (ASEP), and topological invariants. This could provide new computational tools or interpretive bridges in the study of quantum chaos and anyonic systems. The overlap identity itself, if verified, would be a non-trivial result independent of the interpretive claim.

major comments (2)
  1. [Abstract] Abstract: the central claim that a moment of the DSSYK transfer matrix equals the ASEP overlap is asserted without derivation, intermediate steps, explicit equations, or verification against the models' definitions, so the equality cannot be checked from the manuscript's content.
  2. [Abstract] Abstract (final sentence): the argument that the identified overlap functions as the direct analogue of the strange correlator requires explicit verification that it reproduces key properties (invariance under local moves, relation to a topological invariant, or matching under anyon fusion rules), but no such checks are supplied; the interpretive claim therefore does not follow from the overlap identity alone.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and the constructive comments on the abstract. We agree that the presentation of the central claim and the strength of the analogy can be improved for clarity and verifiability. We address each major comment below and will incorporate revisions in the next version of the manuscript.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the central claim that a moment of the DSSYK transfer matrix equals the ASEP overlap is asserted without derivation, intermediate steps, explicit equations, or verification against the models' definitions, so the equality cannot be checked from the manuscript's content.

    Authors: The derivation of the overlap identity is given in full in Sections 2–4 of the manuscript, beginning from the explicit definition of the DSSYK transfer matrix, the stationary distribution of ASEP, and the combinatorial evaluation of the moments that yields the product-state overlap. We nevertheless accept that the abstract is overly concise and does not contain the intermediate expressions needed for immediate verification. We will revise the abstract to include the key defining equations and a pointer to the relevant sections. revision: yes

  2. Referee: [Abstract] Abstract (final sentence): the argument that the identified overlap functions as the direct analogue of the strange correlator requires explicit verification that it reproduces key properties (invariance under local moves, relation to a topological invariant, or matching under anyon fusion rules), but no such checks are supplied; the interpretive claim therefore does not follow from the overlap identity alone.

    Authors: The manuscript presents the analogy on the basis of the structural identity between the ASEP overlap and the definition of the strange correlator in the Levin–Wen/Turaev–Viro setting. We agree, however, that explicit checks of invariance properties and topological invariance would strengthen the claim. We will add a dedicated subsection that verifies these properties for the overlap in question. revision: yes

Circularity Check

0 steps flagged

No circularity; derivation is an explicit mapping plus interpretive analogy.

full rationale

The paper's core step is an explicit identity equating a DSSYK transfer-matrix moment to an ASEP stationary-state overlap with a product state. This identity is presented as a derived result rather than a definition or a fit renamed as a prediction. The subsequent claim that the overlap functions as an analogue of the strange correlator is an interpretive argument, not a reduction of the result to its own inputs by construction. No self-citations, ansatzes smuggled via prior work, or uniqueness theorems are invoked in a load-bearing way within the given abstract and description. The mapping can be checked independently of the analogy, so the derivation chain does not collapse.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Only the abstract is available; no free parameters, axioms, or invented entities can be identified from the provided text.

pith-pipeline@v0.9.1-grok · 5568 in / 1069 out tokens · 29461 ms · 2026-06-26T20:14:53.798293+00:00 · methodology

discussion (0)

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Reference graph

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