Paper Citation Record · LEDGER

The bulk spectral gap is semi-decidable: a convergent family of certified upper bounds

As of 4 August 2026, this Paper Citation Record lists 11 of 11 outbound references and 0 inbound Pith citation observations for arXiv:2606.03836.

A citation records a reference. It does not transfer a finding from one paper to another.

pith.paper-citation-record.v1
2606.03836 v2

Coverage vector

measured 11 of 11 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-03T01:36:05.898319Z

measured 11 of 11 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-03T06:30:56.289259+00:00

measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links

measured 0 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: cited_works

Reference resolution

11 of 11 outbound references displayed

verified exact0
verified fuzzy0
unresolved11
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 5669e3b1-1237-449f-b639-0620999c3135 · outbound

This paper cites an unresolved cited work.

The bulk spectral gap is semi-decidable: a convergent family of certified upper bounds Unresolved cited work

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-03T01:36:05.030275Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8e1f333e-e70a-4eff-98fb-6be5bc30ea3c · outbound

This paper cites energy increase.

The bulk spectral gap is semi-decidable: a convergent family of certified upper bounds energy increase

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-03T01:36:05.102615Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 17dfec3a-9a20-4569-83dd-73695bae504c · outbound

This paper cites non-degeneracy.

The bulk spectral gap is semi-decidable: a convergent family of certified upper bounds non-degeneracy

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-03T01:36:05.431639Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 6694ba41-f066-49a9-b85a-465feeb2ac63 · outbound

This paper cites 2.Critical pointg= 1: unique ground state; the finite-volume gap closes as1/L.

The bulk spectral gap is semi-decidable: a convergent family of certified upper bounds 2.Critical pointg= 1: unique ground state; the finite-volume gap closes as1/L

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-03T01:36:05.333239Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 6d902fb2-28ac-4986-ab46-0f0da4ffe2b7 · outbound

This paper cites By Theorem 4.3, there exists a KMS ground state with a local non-degenerate bulk spectral gap≥ 1(in the sense of Theorem 1.6) due to [BDN16, Proposition 5.4].

The bulk spectral gap is semi-decidable: a convergent family of certified upper bounds By Theorem 4.3, there exists a KMS ground state with a local non-degenerate bulk spectral gap≥ 1(in the sense of Theorem 1.6) due to [BDN16, Proposition 5.4]

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-03T01:36:05.530462Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 226150ca-4139-4429-b78a-fc264b74a16a · outbound

This paper cites By the spectral property of{H Λ(L) CPW(m)}L, it follows that the system must be gapless with the open boundary condition (Theorem 4.4).

The bulk spectral gap is semi-decidable: a convergent family of certified upper bounds By the spectral property of{H Λ(L) CPW(m)}L, it follows that the system must be gapless with the open boundary condition (Theorem 4.4)

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-03T01:36:05.655238Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3a73436e-0823-4a8a-a06a-1a23e2e1e956 · outbound

This paper cites This matches theNO-instance of Eq.

The bulk spectral gap is semi-decidable: a convergent family of certified upper bounds This matches theNO-instance of Eq

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-03T01:36:05.801134Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 6cd52964-61c7-4fd3-9043-56759e41e3bc · outbound

This paper cites (S73) does not immediately imply that the limit KMS ground stateωOBC is bulk-gapless.

The bulk spectral gap is semi-decidable: a convergent family of certified upper bounds (S73) does not immediately imply that the limit KMS ground stateωOBC is bulk-gapless

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-03T01:36:05.898319Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 224201fa-8f8c-4984-a501-095ade00e0c8 · outbound

This paper cites Finite-size criteria for spectral gaps in $D$-dimensional quantum spin systems.

The bulk spectral gap is semi-decidable: a convergent family of certified upper bounds Finite-size criteria for spectral gaps in $D$-dimensional quantum spin systems

Reference 2019

Resolution: unresolved; no resolver link, observed 2026-08-03T01:36:04.524784Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2c54cfda-6f28-4a11-9efa-e4accae685df · outbound

This paper cites Quantum Spin Systems.

The bulk spectral gap is semi-decidable: a convergent family of certified upper bounds Quantum Spin Systems

Reference 2023

Resolution: unresolved; no resolver link, observed 2026-08-03T01:36:04.869737Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 58b10506-a691-4bb0-a827-5a2b1fb65902 · outbound

This paper cites The spectral gap for some spin chains with discrete symmetry breaking.

The bulk spectral gap is semi-decidable: a convergent family of certified upper bounds The spectral gap for some spin chains with discrete symmetry breaking

Reference 2025

Resolution: unresolved; no resolver link, observed 2026-08-03T01:36:04.711643Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

No inbound Pith citation observations are available.