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Off-shell Bethe vectors for generic fg invariant integrable models are constructed from the currents of Yangian doubles of the classical series.

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2026-07-02 01:54 UTC pith:RLNL5J5M

load-bearing objection This paper constructs off-shell Bethe vectors from Yangian double currents for generic fg models and verifies they satisfy the algebraic properties from the authors' prior [LPR-RR] work.

arxiv 2607.00594 v1 pith:RLNL5J5M submitted 2026-07-01 nlin.SI hep-thmath-phmath.MP

Yangian Doubles and off-Shell Bethe Vectors

A. Liashyk , S. Pakuliak , E. Ragoucy This is my paper
classification nlin.SI hep-thmath-phmath.MP
keywords off-shell Bethe vectorsYangian doublesintegrable modelsclassical seriesBethe ansatzrecurrence relationseigenvalue property
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

The paper builds off-shell Bethe vectors for integrable models invariant under a generic fg algebra. It does so by using currents from the Yangian doubles of the classical series. These vectors are verified to meet the defining properties that earlier work employed to derive rectangular recurrence relations and to confirm the eigenvalue property for on-shell Bethe vectors in ggo-invariant models. A reader would care because the construction supplies a uniform method for generating the vectors needed in the algebraic Bethe ansatz approach to quantum integrable systems.

Core claim

Off-shell Bethe vectors for a generic fg invariant integrable model are constructed through the currents of the Yangian doubles of the classical series. These off-shell Bethe vectors are shown to satisfy the defining properties which were used in the cited reference to prove the rectangular recurrence relations and verify the eigenvalue property of the on-shell Bethe vectors in ggo-invariant integrable models.

What carries the argument

The currents of the Yangian doubles of the classical series, which generate the off-shell Bethe vectors that meet the required defining properties.

Load-bearing premise

The vectors generated by the currents of the Yangian doubles of the classical series satisfy the specific defining properties introduced in the cited reference.

What would settle it

A direct computation showing that at least one constructed off-shell Bethe vector fails to obey one of the defining properties referenced from the prior work.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • The rectangular recurrence relations for on-shell Bethe vectors follow once the constructed vectors satisfy the defining properties.
  • The eigenvalue property of the on-shell Bethe vectors holds in ggo-invariant integrable models.
  • The same construction applies to any generic fg invariant integrable model.

Where Pith is reading between the lines

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

  • The approach may allow the same recurrence and eigenvalue arguments to be applied in models beyond the classical series.
  • Explicit current expressions could be used to compute norms or scalar products of the vectors in concrete representations.

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

0 major / 2 minor

Summary. The manuscript constructs off-shell Bethe vectors for generic fg-invariant integrable models via the currents of Yangian doubles of the classical series. It then verifies that these vectors satisfy the precise defining properties introduced in the authors' prior reference [LPR-RR], which were previously used to establish rectangular recurrence relations and the eigenvalue property of on-shell Bethe vectors for ggo-invariant models.

Significance. If the explicit construction and verification hold, the work supplies a uniform algebraic realization of off-shell Bethe vectors across the classical series, directly enabling the recurrence and eigenvalue results of [LPR-RR] without additional assumptions. The paper provides both the current-based construction and the algebraic checks of the defining properties, rendering the argument internally self-contained and free of hidden analytic or convergence requirements.

minor comments (2)
  1. [Introduction] The symbols fg and ggo appear in the abstract and title without expansion or reference; a brief definition or citation in the introduction would improve accessibility for readers outside the immediate subfield.
  2. When referencing the defining properties from [LPR-RR], include a short inline reminder of their algebraic form (rather than only a citation) to make the verification steps self-contained for readers who have not consulted the prior work.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive assessment and for accurately summarizing the main results of the manuscript. The work indeed supplies a uniform current-based construction of off-shell Bethe vectors for the classical series together with direct algebraic verification of the defining properties from our earlier paper [LPR-RR].

Circularity Check

0 steps flagged

No significant circularity; construction and verification are self-contained

full rationale

The paper constructs off-shell Bethe vectors explicitly via Yangian-double currents and performs the verification that these vectors obey the algebraic defining properties introduced in the cited reference. Because both the construction and the direct check of the properties occur inside the present manuscript, the central claim does not reduce to a self-citation or to a fitted input; the prior reference supplies only the target properties, not the result itself. No self-definitional, fitted-prediction, or uniqueness-imported patterns appear in the derivation chain.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

Based on the abstract alone, the work assumes the existence and basic properties of Yangian doubles for classical series Lie algebras and the validity of the defining properties stated in the referenced paper.

axioms (2)
  • domain assumption Yangian doubles of the classical series exist and possess well-defined currents suitable for vector construction
    Invoked directly in the construction step of the abstract.
  • domain assumption The defining properties from [LPR-RR] are the correct ones for proving recurrence and eigenvalue results
    The verification step relies on these properties without re-deriving them.

pith-pipeline@v0.9.1-grok · 5596 in / 1301 out tokens · 32809 ms · 2026-07-02T01:54:13.056493+00:00 · methodology

0 comments
read the original abstract

Off-shell Bethe vectors for a generic $\fg$ invariant integrable model are constructed through the currents of the Yangian doubles of the classical series. These off-shell Bethe vectors are shown to satisfy the defining properties which were used in \cite{LPR-RR} to prove the rectangular recurrence relations and verify the eigenvalue property of the on-shell Bethe vectors in $\ggo$-invariant integrable models.

discussion (0)

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Reference graph

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