Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-14T05:29:21.509485Z
Paper Citation Record · LEDGER
Improved local spectral gap thresholds for lattices of finite dimension
As of 19 August 2026, this Paper Citation Record lists 27 of 27 outbound references and 1 inbound Pith citation observation for arXiv:1909.01516.
A citation records a reference. It does not transfer a finding from one paper to another.
Coverage vector
One-hop event checks from named stored sources.
Source: scholarly_work_events, retraction_status_cache, observed 2026-08-19T06:32:44.657259+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links, observed 2026-05-23T18:00:24.865241Z
A source-named dated measurement, never combined with another source.
Source: arxiv_reference, observed 2026-05-23T18:03:18.252741Z
Reference resolution
27 of 27 outbound references displayed
- verified exact2
- verified fuzzy16
- unresolved9
- parse uncertain0
- malformed identifier0
- metadata mismatch0
External citation measurements
No source-named external measurement is stored.
Outbound references
Observation 3b4afcba-ee72-4ea0-bda7-e4d4b30238e7 · outbound
This paper cites Entanglement subvolume law for 2D frustration-free spin systems.
Improved local spectral gap thresholds for lattices of finite dimension Entanglement subvolume law for 2D frustration-free spin systems
Reference 1
- Resolution
- verified exact
- local_arxiv, observed 2026-08-14T05:29:21.808247Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 3798a121-483d-4710-987d-b361db040820 · outbound
This paper cites The detectability lemma and quantum gap amplification.
Improved local spectral gap thresholds for lattices of finite dimension The detectability lemma and quantum gap amplification
Reference 2
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T05:29:22.507398Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 8b3be8ab-1e63-4b37-8f3f-4fd02f84bf90 · outbound
This paper cites Simple proof of the detectability lemma and spectral gap amplification.
Improved local spectral gap thresholds for lattices of finite dimension Simple proof of the detectability lemma and spectral gap amplification
Reference 3
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T05:29:22.484738Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 044ea66a-9315-4c87-995e-d0114e5349b0 · outbound
This paper cites An area law and sub-exponential algorithm for 1D systems.
Improved local spectral gap thresholds for lattices of finite dimension An area law and sub-exponential algorithm for 1D systems
Reference 4
- Resolution
- unresolved
- no resolver link, observed 2026-08-14T05:29:21.359551Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation fefda5ca-bbf4-4898-95c5-fa711fe9c0ca · outbound
This paper cites An improved 1d area law for frustration-free systems.
Improved local spectral gap thresholds for lattices of finite dimension An improved 1d area law for frustration-free systems
Reference 5
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T05:29:22.454019Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation fa35af03-b036-4447-8350-390df4532153 · outbound
This paper cites A class of two-dimensional AKLT models with a gap.
Improved local spectral gap thresholds for lattices of finite dimension A class of two-dimensional AKLT models with a gap
Reference 6
- Resolution
- unresolved
- no resolver link, observed 2026-08-14T05:29:21.373089Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation cc86607c-c405-4213-8266-833c8c8947dd · outbound
This paper cites Undecidability of the Spectral Gap in One Dimension.
Improved local spectral gap thresholds for lattices of finite dimension Undecidability of the Spectral Gap in One Dimension
Reference 7
- Resolution
- unresolved
- no resolver link, observed 2026-08-14T05:29:21.383291Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation b0cd8a88-cfc1-4ac3-9644-fc5f93f529a6 · outbound
This paper cites Gapped and gapless phases of frustration-free spin-12 chains.
Improved local spectral gap thresholds for lattices of finite dimension Gapped and gapless phases of frustration-free spin-12 chains
Reference 8
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T05:29:22.420154Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 062f0b1a-c201-4da2-b3f0-db3e19d1010c · outbound
This paper cites an unresolved cited work.
Improved local spectral gap thresholds for lattices of finite dimension Unresolved cited work
Reference 9
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T05:29:22.395451Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation fd3acc70-e065-43e5-9627-ab445cee11fb · outbound
This paper cites Cubitt, David Perez-Garcia, and Michael M.
Improved local spectral gap thresholds for lattices of finite dimension Cubitt, David Perez-Garcia, and Michael M
Reference 10
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T05:29:22.369437Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 3433cf13-7291-424f-b762-aa14b1316401 · outbound
This paper cites Eldar and A.
Improved local spectral gap thresholds for lattices of finite dimension Eldar and A
Reference 11
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T05:29:22.346368Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 1de42f32-ce0b-4c3f-9622-e6a5285b0fd7 · outbound
This paper cites an unresolved cited work.
Improved local spectral gap thresholds for lattices of finite dimension Unresolved cited work
Reference 12
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T05:29:22.318578Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 003c22f7-4f3e-4253-8bcd-f1831f876c62 · outbound
This paper cites Correlation length versus gap in frustration-free systems.
Improved local spectral gap thresholds for lattices of finite dimension Correlation length versus gap in frustration-free systems
Reference 13
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T05:29:22.286838Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 29f56856-838c-4f1d-893a-67dd87f5cd23 · outbound
This paper cites Local gap threshold for frustration-free spin systems.
Improved local spectral gap thresholds for lattices of finite dimension Local gap threshold for frustration-free spin systems
Reference 14
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T05:29:22.191463Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 1483f0a8-0b70-4392-8c10-2054486ec637 · outbound
This paper cites Personal communication.
Improved local spectral gap thresholds for lattices of finite dimension Personal communication
Reference 15
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T05:29:22.157842Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation d3ea0824-71c6-47e7-83ea-79bf1e931eb0 · outbound
This paper cites an unresolved cited work.
Improved local spectral gap thresholds for lattices of finite dimension Unresolved cited work
Reference 16
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T05:29:22.118444Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 6c35cf30-fbc0-4d6b-b9b1-aaf14567e694 · outbound
This paper cites an unresolved cited work.
Improved local spectral gap thresholds for lattices of finite dimension Unresolved cited work
Reference 17
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T05:29:22.095498Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 1157fb4c-0678-4e76-a893-bfa61fce5770 · outbound
This paper cites Hastings and Tohru Koma.
Improved local spectral gap thresholds for lattices of finite dimension Hastings and Tohru Koma
Reference 18
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T05:29:22.042194Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 1271c19b-7b0b-457b-942b-a81fbc6b369b · outbound
This paper cites Essai sur la g\` e om\` e trie \' a n dimensions.
Improved local spectral gap thresholds for lattices of finite dimension Essai sur la g\` e om\` e trie \' a n dimensions
Reference 19
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T05:29:22.004748Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation d9a28f28-3ad4-47f2-ae39-1278b4e1dbdc · outbound
This paper cites Divide and conquer method for proving gaps of frustration free hamiltonians.
Improved local spectral gap thresholds for lattices of finite dimension Divide and conquer method for proving gaps of frustration free hamiltonians
Reference 20
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T05:29:21.962771Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation c564a381-415a-4948-bcf5-e09ce4b3689b · outbound
This paper cites Energy gaps and elementary excitations for certain vbs-quantum antiferromagnets.
Improved local spectral gap thresholds for lattices of finite dimension Energy gaps and elementary excitations for certain vbs-quantum antiferromagnets
Reference 21
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T05:29:21.934021Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 6991a419-28e0-405c-a4c5-db06a0cde78d · outbound
This paper cites Finite-size criteria for spectral gaps in $D$-dimensional quantum spin systems.
Improved local spectral gap thresholds for lattices of finite dimension Finite-size criteria for spectral gaps in $D$-dimensional quantum spin systems
Reference 22
- Resolution
- verified exact
- local_arxiv, observed 2026-08-14T05:29:21.628242Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 288ae754-affa-48c2-801d-a32aa7c086be · outbound
This paper cites Gaplessness is not generic for translation-invariant spin chains.
Improved local spectral gap thresholds for lattices of finite dimension Gaplessness is not generic for translation-invariant spin chains
Reference 23
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T05:29:21.912041Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 69c89804-b4e9-46df-ba13-4696ce3de57b · outbound
This paper cites Spectral gaps of frustration-free spin systems with boundary.
Improved local spectral gap thresholds for lattices of finite dimension Spectral gaps of frustration-free spin systems with boundary
Reference 24
- Resolution
- unresolved
- no resolver link, observed 2026-08-14T05:29:21.492099Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 81f5f354-3bff-45b2-9621-cc903704d4ec · outbound
This paper cites The AKLT model on a hexagonal chain is gapped.
Improved local spectral gap thresholds for lattices of finite dimension The AKLT model on a hexagonal chain is gapped
Reference 25
- Resolution
- unresolved
- no resolver link, observed 2026-08-14T05:29:21.497525Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 6fc94ce2-a128-4c19-b522-4ebda42a4431 · outbound
This paper cites The spectral gap for some spin chains with discrete symmetry breaking.
Improved local spectral gap thresholds for lattices of finite dimension The spectral gap for some spin chains with discrete symmetry breaking
Reference 26
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T05:29:21.883299Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 4296e1d3-444f-4950-8776-302cc78ecafb · outbound
This paper cites Lieb-robinson bounds and the exponential clustering theorem.
Improved local spectral gap thresholds for lattices of finite dimension Lieb-robinson bounds and the exponential clustering theorem
Reference 27
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T05:29:21.850881Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Pith citing papers
Observation 93c75708-9636-4eea-9a82-e2807d4f10aa · inbound
A Hierarchy of Spectral Gap Certificates for Frustration-Free Spin Systems cites this paper.
A Hierarchy of Spectral Gap Certificates for Frustration-Free Spin Systems Improved local spectral gap thresholds for lattices of finite dimension
Reference 24
- Resolution
- verified exact
- arxiv_id, observed 2026-05-23T18:03:18.256068Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.