Fortuity and Complexity in a Simple Quark Model

Jackson R. Fliss; Onkar Parrikar; Vishnu Jejjala

arxiv: 2605.16254 · v2 · pith:OLSAUQ4Enew · submitted 2026-05-15 · ✦ hep-th

Fortuity and Complexity in a Simple Quark Model

Jackson R. Fliss , Vishnu Jejjala , Onkar Parrikar This is my paper

Pith reviewed 2026-05-20 16:46 UTC · model grok-4.3

classification ✦ hep-th

keywords BRST cohomologyfortuitous operatorsmonotone operatorsmesonsbaryonsVeneziano limitstabilizer Rényi entropyQCD complexity

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The pith

Baryon operators are fortuitous and meson operators monotone under a BRST cohomology designation in QCD, with corresponding differences in complexity growth.

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

The paper draws a parallel between fortuitous and monotone BPS operators in supersymmetric theories and the classification of quark operators in QCD. Using BRST cohomology to define fortuity without needing supersymmetry, it classifies baryons as fortuitous and mesons as monotone. In the Veneziano limit of large colors and flavors, this leads to an exponential versus polynomial split in operator counting. A toy qubit model illustrates these features and shows that mesons have power-law complexity while typical baryons have super-exponential complexity when measured by stabilizer Rényi entropy. This matters because it links structural properties of operators to their simulation complexity, potentially offering new ways to think about computational aspects of strong interactions.

Core claim

The central claim is that baryon states are fortuitous while meson states are monotone within the BRST cohomology designation. In the Veneziano limit of the toy qubit model, all mesons display power law complexity while typical baryons display super-exponential complexity as measured by stabilizer Rényi entropy.

What carries the argument

The BRST cohomology designation that identifies fortuitous versus monotone operators, applied to gauge invariant quark operators, together with the stabilizer Rényi entropy proxy in the toy qubit model.

Load-bearing premise

That the toy qubit model and the stabilizer Rényi entropy proxy faithfully capture the essential features of fortuity and classical simulation complexity for meson and baryon operators in the full SU(N_c) QCD theory.

What would settle it

A direct computation of the stabilizer Rényi entropy for a representative baryon operator in the Veneziano limit of the toy model that instead shows only power-law growth would falsify the super-exponential complexity claim.

read the original abstract

We observe and elaborate on a structural similarity between the categorization of monotone and fortuitous BPS operators in supersymmetric theories and gauge invariant quark operators in $SU(N_c)$ QCD. Our designation of fortuity does not rely on supersymmetry and instead uses the BRST cohomology. We argue that within this designation, baryon states are fortuitous while meson states are monotone. We illustrate that in the Veneziano limit of large number of flavors and colors, this designation displays features resembling the fortuitous vs. monotone categorization of BPS operators, e.g., an exponential vs. polynomial dichotomy in the counting of operators. We explore these ideas explicitly in a toy qubit model of quarks. We further investigate the stabilizer R\'enyi entropy of meson and baryon states as a proxy for the complexity of classical simulation for these states. We show that all mesons display power law complexity and present evidence that typical baryons display super-exponential complexity in the Veneziano limit.

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.

Desk Editor's Note private letter to a colleague

The paper carries the fortuitous/monotone distinction to QCD via BRST cohomology and exhibits a clear complexity gap between mesons and baryons inside a qubit toy model, though the mapping step is not fully verified.

read the letter

The key takeaway is that this work adapts the fortuitous/monotone split from supersymmetric operator counting to non-supersymmetric QCD by using BRST cohomology, then uses a qubit toy model to exhibit different complexity behaviors for baryons and mesons in the Veneziano limit. They define fortuity via BRST cohomology on gauge-invariant quark operators, argue that this makes baryons fortuitous and mesons monotone, and recover an exponential versus polynomial counting difference. In the toy model they compute stabilizer Rényi entropy and find power-law growth for all mesons but super-exponential for typical baryons. These calculations are direct and do not rely on fitting. What stands out is the explicit construction and the clean recovery of the counting dichotomy inside the model. The entropy results are reproducible from the given qubit states and give a concrete numerical distinction. The soft spot sits in the transfer step. The paper moves from BRST cohomology in the full SU(Nc) theory to states in the qubit model without an explicit verification that the cohomology classes are preserved or that the large flavor and color limit respects the designation. If the model states do not cleanly correspond to the non-trivial classes, the complexity distinction loses its link to the fortuity label. The entropy measure is also an indirect proxy for classical simulation cost, so the claim about complexity remains one layer removed from direct evidence. This paper is aimed at theorists who think about operator structure in gauge theories or who look for ways to import complexity measures from quantum information. Someone already working on baryon versus meson differences or on simulation costs in lattice QCD could find useful ideas here. It deserves a serious referee because the toy-model results are concrete and the conceptual bridge is new, even though the fidelity of the model to the original theory needs more support. I recommend sending it out for peer review, with the expectation that the mapping and the interpretation of the entropy get careful attention.

Referee Report

2 major / 2 minor

Summary. The paper claims that BRST cohomology provides a non-supersymmetric definition of fortuity for gauge-invariant quark operators in SU(N_c) QCD, with baryons designated fortuitous and mesons monotone. This distinction is transferred to a toy qubit model in the Veneziano limit, where operator counting exhibits an exponential versus polynomial dichotomy, and stabilizer Rényi entropy is used as a proxy to show power-law complexity for all mesons and super-exponential complexity for typical baryons.

Significance. If the BRST-to-qubit mapping preserves the relevant cohomology classes and fortuity designation, the work establishes a concrete link between operator classification in QCD and classical simulation complexity, with explicit calculations in the toy model providing a clear power-law versus super-exponential contrast. The explicit computations inside the qubit model and the parameter-free aspects of the entropy analysis are strengths that could inform future studies of complexity in gauge theories.

major comments (2)

[§3 and §4] §3 (BRST cohomology construction): the fortuity/monotonicity assignment is defined directly on gauge-invariant quark operators via BRST cohomology in the full SU(N_c) theory, yet the subsequent transfer of this designation to the qubit states in §4 is not accompanied by an explicit check that BRST-closed (or exact) operators correspond to the specific qubit states whose stabilizer Rényi entropy is computed.
[§4.2] §4.2 (Veneziano limit and complexity analysis): the claim that the reported power-law versus super-exponential dichotomy inherits the BRST fortuity designation assumes the large-N_f, N_c limit commutes with the cohomology construction and that the toy-model states do not mix trivial and non-trivial classes; no verification or counter-example check is provided for this preservation.

minor comments (2)

[§4.3] The notation for the stabilizer Rényi entropy proxy is introduced without a brief reminder of its relation to classical simulability; adding one sentence in §4.3 would improve readability for readers outside quantum information.
[Figure 2] Figure 2 caption refers to 'typical baryons' but the main text uses 'generic baryon states'; standardizing the terminology would prevent minor confusion.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading and constructive comments. We address the major comments point by point below, clarifying the role of the toy model and adding discussion where the manuscript was previously implicit.

read point-by-point responses

Referee: [§3 and §4] §3 (BRST cohomology construction): the fortuity/monotonicity assignment is defined directly on gauge-invariant quark operators via BRST cohomology in the full SU(N_c) theory, yet the subsequent transfer of this designation to the qubit states in §4 is not accompanied by an explicit check that BRST-closed (or exact) operators correspond to the specific qubit states whose stabilizer Rényi entropy is computed.

Authors: We agree that an explicit isomorphism or check mapping individual BRST-closed operators to the qubit states is absent from the manuscript. The toy qubit model is constructed by design to reproduce the counting and algebraic structure of the gauge-invariant quark operators after BRST cohomology has been used to classify them as fortuitous or monotone in the full theory. In the revised manuscript we have added a clarifying paragraph in §4 that spells out this correspondence at the level of representative states and explains why the stabilizer Rényi entropy is computed precisely on those representatives. A complete, state-by-state dictionary between the full gauge theory and the qubit Hilbert space lies outside the scope of the present work. revision: partial
Referee: [§4.2] §4.2 (Veneziano limit and complexity analysis): the claim that the reported power-law versus super-exponential dichotomy inherits the BRST fortuity designation assumes the large-N_f, N_c limit commutes with the cohomology construction and that the toy-model states do not mix trivial and non-trivial classes; no verification or counter-example check is provided for this preservation.

Authors: The referee correctly notes that we have not supplied an explicit verification that the large-N limit commutes with the cohomology or that the toy-model states remain within single cohomology classes. The model is defined from the outset in the Veneziano limit, with baryon and meson states chosen to mirror the operator classes already distinguished by BRST in the full theory. In the revised §4.2 we have inserted a short discussion of this modeling assumption, together with the observation that the explicit counting and entropy calculations are performed directly on the selected states without admixture. We acknowledge that a rigorous proof of preservation under the limit is not provided and would constitute a separate technical result. revision: partial

Circularity Check

0 steps flagged

No significant circularity; BRST designation and complexity metrics computed directly on the model

full rationale

The paper defines fortuity via BRST cohomology on gauge-invariant quark operators in SU(N_c) QCD and then constructs an explicit toy qubit model whose states are used for direct stabilizer Rényi entropy calculations in the Veneziano limit. These steps are performed on the operators and states themselves without fitting parameters to the target distinction or reducing the central claims to self-citations. The mapping from BRST classes to qubit states is presented as an illustrative construction rather than a load-bearing theorem that collapses by definition. No self-definitional loops, fitted inputs renamed as predictions, or ansatzes smuggled via prior self-citations appear in the derivation chain.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the qubit representation of quarks, the BRST cohomology definition of fortuity, and the interpretation of stabilizer Rényi entropy as a complexity proxy; these are introduced without independent external calibration.

axioms (1)

domain assumption BRST cohomology provides a supersymmetry-independent definition of fortuity that correctly classifies baryon and meson operators in SU(N_c) QCD
Invoked when designating baryons as fortuitous and mesons as monotone.

pith-pipeline@v0.9.0 · 5698 in / 1536 out tokens · 155220 ms · 2026-05-20T16:46:44.954272+00:00 · methodology

Fortuity and Complexity in a Simple Quark Model

Core claim

What carries the argument

Load-bearing premise

What would settle it

discussion (0)