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RemarkRemark: Literature-sourcedProof: AI-adaptedPipeline-generatedprecheck passjudge pass (gpt-6-luna)
How statement and proof provenance work

The first chip identifies the source of the statement or construction; the second identifies the source of its local proof or verification.

  • Literature-sourced: the exact statement appears in a cited source; only wording and notation differ.
  • AI-adapted: a semantically identical restatement of literature-sourced material, modulo indexing, notation, and boundary cases adopted by the library.
  • AI-generated: a genuinely novel statement formulated by AI, with no source for the claim itself.

These labels describe origin, not correctness: citations and verification chips remain separate evidence.

Scaling limits and non-open boundary models remain source-qualified

Statement

The XXZ and Potts definitions in this batch are exact finite-dimensional open-chain operator families. The cited continuum-limit discussion calls its proposed lattice-to-Virasoro-mode formula conjectural and its derivation heuristic, while noting free-fermion results and numerical support in interacting cases. The source does not establish a theorem covering every spectrum, spectral gap, Bethe state, or boundary algebra; that limit is an inference from the stated scope of the cited discussion. Periodic, blob, and two-boundary Temperley–Lieb variants require their own generators and boundary relations and are outside these open-chain definitions.

Facts & Assumptions

Given: The finite open-chain conventions and the cited continuum-limit source.

[F1]

The XXZ Hamiltonian sums only ei for 1≤i<L, and the Potts Hamiltonian sums only ei for 1≤i<2L; neither definition includes a generator connecting the right endpoint to the left endpoint. (Open XXZ spin-half generators and Hamiltonian convention, Open Potts clock-shift Temperley–Lieb generators)

[F2]

Around equation (49), the authors say “this formula is a conjecture” and that its derivation “is definitely heuristic”; they also report free-fermion convergence and numerical evidence for interacting systems. (Gainutdinov et al., discussion around (49), printed p. 19)

Proof

Given: The model definitions and source statements in [F1]–[F2].

1.1F1givenalgebra

The finite operator formulas in [F1] contain only adjacent generators within the listed open range. A periodic bond would require a separately defined operator acting on sites L and 1 (or the corresponding last and first Potts sites), and no such term occurs in either sum. Thus these formulas define open-chain models only.

2.1F1F2step 1.1given∎

The exact source labels and qualifications in [F2] make the lattice-to-Virasoro-mode correspondence conjectural/heuristic, despite the stated partial evidence. This item therefore makes no universal spectral, Bethe-completeness or boundary-algebra claim; that limit is an inference from the scope of the cited result, not a separate assertion by its authors.

Depends on

Used by

Nothing in the library uses this result yet.

Dependency tree · two levels

3 results within two dependency steps of this one, each drawn at its shortest distance from it. An arrow runs from a result to what uses it, so the chart reads left to right and ends at this result, which carries a heavier outline. Every node is a link to that result. Click elsewhere on the chart to enlarge it.

Sources