{"as_of":"2026-08-16T20:31:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:2be225431a7d8b417128f9b12c047dafd9e7f8bf678df15a46c68085d04b483f","coverage":[{"denominator":27,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":27,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-14T05:29:21.509485Z","state":"measured"},{"denominator":28,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":28,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-16T06:30:59.297886+00:00","state":"measured"},{"denominator":1,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":1,"source":"paper_references, paper_reference_links","source_observed_at":"2026-05-23T18:00:24.865241Z","state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"arxiv_reference","source_observed_at":"2026-05-23T18:03:18.252741Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"1909.01516","last_updated":"2019-09-04T01:44:31Z","snapshot_observed_at":"2026-08-15T02:51:51.724306Z","submitted_at":"2019-09-04T01:44:31Z","title":"Improved local spectral gap thresholds for lattices of finite dimension","version":1},"cited_work":{"arxiv_id":"1909.01516","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"1909.01516","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Anshu, Improved local spectral gap thresholds for lat- tices of finite dimension, Physical Review B 101, 165104 (2020), arXiv:1909.01516 [cond-mat, physics:quant-ph]","venue":null,"work_id":"73c833d1-4c10-4f03-971c-a798391b66cd","year":2020},"citing_paper":{"arxiv_id":"2411.03680","last_updated":"2026-04-01T14:53:36Z","snapshot_observed_at":"2026-07-06T19:45:57.808548Z","submitted_at":"2024-11-06T06:04:03Z","title":"A Hierarchy of Spectral Gap Certificates for Frustration-Free Spin Systems","version":3},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-05-23T18:00:24.865241Z"},"links":{"cited_paper":"/paper/1909.01516","citing_paper":"/paper/2411.03680"},"observation_digest":"sha256:af094527bb13bdb876e0b420bda56e60914173cfdb94c7d500c3514bc54f095c","observation_id":"93c75708-9636-4eea-9a82-e2807d4f10aa","resolution":{"observed_at":"2026-05-23T18:03:18.256068Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}}],"links":{"evidence":"/evidence","html":"/paper/1909.01516/citation-record","integrity":"/paper/1909.01516/integrity","json":"/paper/1909.01516/citation-record.json","paper":"/paper/1909.01516"},"outbound":[{"citation":{"cited_paper":{"arxiv_id":"1905.11337","last_updated":"2019-05-27T16:49:28Z","snapshot_observed_at":"2026-08-14T16:25:46.860344Z","submitted_at":"2019-05-27T16:49:28Z","title":"Entanglement subvolume law for 2D frustration-free spin systems","version":1},"cited_work":{"arxiv_id":"1905.11337","doi":null,"metadata_source":"pith","pith_arxiv_id":"1905.11337","snapshot_observed_at":"2026-08-14T05:29:21.773024Z","title":"Entanglement subvolume law for 2D frustration-free spin systems","venue":"quant-ph","work_id":"02e7e943-38ef-49e9-95d6-d6c6123e4f84","year":2019},"citing_paper":{"arxiv_id":"1909.01516","last_updated":"2019-09-04T01:44:31Z","snapshot_observed_at":"2026-08-15T02:51:51.724306Z","submitted_at":"2019-09-04T01:44:31Z","title":"Improved local spectral gap thresholds for lattices of finite dimension","version":1},"reference_index":1,"source":"arxiv_source","source_observed_at":"2026-08-14T05:29:21.335018Z"},"links":{"cited_paper":"/paper/1905.11337","citing_paper":"/paper/1909.01516"},"observation_digest":"sha256:afcb26fa2f881bfd730502c4afa13d371974a75d621e6072e9ee994d6df8e3d7","observation_id":"3b4afcba-ee72-4ea0-bda7-e4d4b30238e7","resolution":{"observed_at":"2026-08-14T05:29:21.808247Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T05:29:22.501853Z","title":"The detectability lemma and quantum gap amplification","venue":null,"work_id":"b18928d4-e707-4b9f-a772-0e5180c7f25c","year":2009},"citing_paper":{"arxiv_id":"1909.01516","last_updated":"2019-09-04T01:44:31Z","snapshot_observed_at":"2026-08-15T02:51:51.724306Z","submitted_at":"2019-09-04T01:44:31Z","title":"Improved local spectral gap thresholds for lattices of finite dimension","version":1},"reference_index":2,"source":"arxiv_source","source_observed_at":"2026-08-14T05:29:21.341386Z"},"links":{"citing_paper":"/paper/1909.01516"},"observation_digest":"sha256:b0f2faa958ed182a77dbff5a68ee3f6d7a6dcaff78ce69c9e458d4460f0e97b2","observation_id":"3798a121-483d-4710-987d-b361db040820","resolution":{"observed_at":"2026-08-14T05:29:22.507398Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T05:29:22.471101Z","title":"Simple proof of the detectability lemma and spectral gap amplification","venue":null,"work_id":"e5aeacc1-197a-40db-8eae-e6b2cb125749","year":2016},"citing_paper":{"arxiv_id":"1909.01516","last_updated":"2019-09-04T01:44:31Z","snapshot_observed_at":"2026-08-15T02:51:51.724306Z","submitted_at":"2019-09-04T01:44:31Z","title":"Improved local spectral gap thresholds for lattices of finite dimension","version":1},"reference_index":3,"source":"arxiv_source","source_observed_at":"2026-08-14T05:29:21.348253Z"},"links":{"citing_paper":"/paper/1909.01516"},"observation_digest":"sha256:7520983d3098326539e72c2635f6a83c116a703f29723bda18c5b641cb7035db","observation_id":"8b3be8ab-1e63-4b37-8f3f-4fd02f84bf90","resolution":{"observed_at":"2026-08-14T05:29:22.484738Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1301.1162","last_updated":"2013-01-07T11:54:27Z","snapshot_observed_at":"2026-08-15T00:33:36.801833Z","submitted_at":"2013-01-07T11:54:27Z","title":"An area law and sub-exponential algorithm for 1D systems","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1301.1162","snapshot_observed_at":"2026-08-14T05:29:21.359551Z","title":"An area law and sub-exponential algorithm for 1d systems","venue":null,"work_id":null,"year":2013},"citing_paper":{"arxiv_id":"1909.01516","last_updated":"2019-09-04T01:44:31Z","snapshot_observed_at":"2026-08-15T02:51:51.724306Z","submitted_at":"2019-09-04T01:44:31Z","title":"Improved local spectral gap thresholds for lattices of finite dimension","version":1},"reference_index":4,"source":"arxiv_source","source_observed_at":"2026-08-14T05:29:21.359551Z"},"links":{"cited_paper":"/paper/1301.1162","citing_paper":"/paper/1909.01516"},"observation_digest":"sha256:43c8f31d091c1104f798fb94cd396394eb6facd23e3fe1e3eefc264e8628a82c","observation_id":"044ea66a-9315-4c87-995e-d0114e5349b0","resolution":{"observed_at":"2026-08-14T05:29:21.359551Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T05:29:22.444514Z","title":"An improved 1d area law for frustration-free systems","venue":null,"work_id":"a13e240f-3eaf-46f1-b180-cb892ba01640","year":2012},"citing_paper":{"arxiv_id":"1909.01516","last_updated":"2019-09-04T01:44:31Z","snapshot_observed_at":"2026-08-15T02:51:51.724306Z","submitted_at":"2019-09-04T01:44:31Z","title":"Improved local spectral gap thresholds for lattices of finite dimension","version":1},"reference_index":5,"source":"arxiv_source","source_observed_at":"2026-08-14T05:29:21.367410Z"},"links":{"citing_paper":"/paper/1909.01516"},"observation_digest":"sha256:a823ff5783eec95ea38296258e89bba7f3a4c972a40f2033bad50e32e41d69d1","observation_id":"fefda5ca-bbf4-4898-95c5-fa711fe9c0ca","resolution":{"observed_at":"2026-08-14T05:29:22.454019Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1901.09297","last_updated":"2019-05-13T09:43:36Z","snapshot_observed_at":"2026-08-14T17:25:26.817053Z","submitted_at":"2019-01-27T01:09:56Z","title":"A class of two-dimensional AKLT models with a gap","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1901.09297","snapshot_observed_at":"2026-08-14T05:29:21.373089Z","title":"A class of two-dimensional aklt models with a gap, 2019","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"1909.01516","last_updated":"2019-09-04T01:44:31Z","snapshot_observed_at":"2026-08-15T02:51:51.724306Z","submitted_at":"2019-09-04T01:44:31Z","title":"Improved local spectral gap thresholds for lattices of finite dimension","version":1},"reference_index":6,"source":"arxiv_source","source_observed_at":"2026-08-14T05:29:21.373089Z"},"links":{"cited_paper":"/paper/1901.09297","citing_paper":"/paper/1909.01516"},"observation_digest":"sha256:38452e288941604b91a96da21f70347e4bd909f73329182242a383cd9ac5cee9","observation_id":"fa35af03-b036-4447-8350-390df4532153","resolution":{"observed_at":"2026-08-14T05:29:21.373089Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1810.01858","last_updated":"2020-06-12T14:54:58Z","snapshot_observed_at":"2026-08-14T18:19:53.391737Z","submitted_at":"2018-10-03T17:59:49Z","title":"Undecidability of the Spectral Gap in One Dimension","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1810.01858","snapshot_observed_at":"2026-08-14T05:29:21.383291Z","title":"Undecidability of the spectral gap in one dimension, 2018","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"1909.01516","last_updated":"2019-09-04T01:44:31Z","snapshot_observed_at":"2026-08-15T02:51:51.724306Z","submitted_at":"2019-09-04T01:44:31Z","title":"Improved local spectral gap thresholds for lattices of finite dimension","version":1},"reference_index":7,"source":"arxiv_source","source_observed_at":"2026-08-14T05:29:21.383291Z"},"links":{"cited_paper":"/paper/1810.01858","citing_paper":"/paper/1909.01516"},"observation_digest":"sha256:42f0994672ac4fe41b82200c6e128b9796edca8e9d3ce63010aa25eff1bb9b56","observation_id":"cc86607c-c405-4213-8266-833c8c8947dd","resolution":{"observed_at":"2026-08-14T05:29:21.383291Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T05:29:22.412146Z","title":"Gapped and gapless phases of frustration-free spin-12 chains","venue":null,"work_id":"9b0daeac-b503-40fe-bad7-a010acfa76df","year":2015},"citing_paper":{"arxiv_id":"1909.01516","last_updated":"2019-09-04T01:44:31Z","snapshot_observed_at":"2026-08-15T02:51:51.724306Z","submitted_at":"2019-09-04T01:44:31Z","title":"Improved local spectral gap thresholds for lattices of finite dimension","version":1},"reference_index":8,"source":"arxiv_source","source_observed_at":"2026-08-14T05:29:21.390510Z"},"links":{"citing_paper":"/paper/1909.01516"},"observation_digest":"sha256:80c9748bbf5d5deea4f262a4771c78d59560dfa634f25788aac3bf424f822cc4","observation_id":"b0cd8a88-cfc1-4ac3-9644-fc5f93f529a6","resolution":{"observed_at":"2026-08-14T05:29:22.420154Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T05:29:22.388222Z","title":null,"venue":null,"work_id":"a22bbce6-f49e-4b71-8da2-f350a8d93081","year":2016},"citing_paper":{"arxiv_id":"1909.01516","last_updated":"2019-09-04T01:44:31Z","snapshot_observed_at":"2026-08-15T02:51:51.724306Z","submitted_at":"2019-09-04T01:44:31Z","title":"Improved local spectral gap thresholds for lattices of finite dimension","version":1},"reference_index":9,"source":"arxiv_source","source_observed_at":"2026-08-14T05:29:21.399197Z"},"links":{"citing_paper":"/paper/1909.01516"},"observation_digest":"sha256:a397df93af27f2de94fe2d639c66593309f6dfb990d558c27f1c2734438503ae","observation_id":"062f0b1a-c201-4da2-b3f0-db3e19d1010c","resolution":{"observed_at":"2026-08-14T05:29:22.395451Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T05:29:22.362681Z","title":"Cubitt, David Perez-Garcia, and Michael M","venue":null,"work_id":"55d912bc-fa85-4ece-93df-32b659cd820d","year":2015},"citing_paper":{"arxiv_id":"1909.01516","last_updated":"2019-09-04T01:44:31Z","snapshot_observed_at":"2026-08-15T02:51:51.724306Z","submitted_at":"2019-09-04T01:44:31Z","title":"Improved local spectral gap thresholds for lattices of finite dimension","version":1},"reference_index":10,"source":"arxiv_source","source_observed_at":"2026-08-14T05:29:21.408071Z"},"links":{"citing_paper":"/paper/1909.01516"},"observation_digest":"sha256:840771f314b36c9f4fed48425125a458582eb46c042445e54119a9263d84e7d5","observation_id":"fd3acc70-e065-43e5-9627-ab445cee11fb","resolution":{"observed_at":"2026-08-14T05:29:22.369437Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T05:29:22.334269Z","title":"Eldar and A","venue":null,"work_id":"77321685-4340-4623-bb41-3626e90b973d","year":2017},"citing_paper":{"arxiv_id":"1909.01516","last_updated":"2019-09-04T01:44:31Z","snapshot_observed_at":"2026-08-15T02:51:51.724306Z","submitted_at":"2019-09-04T01:44:31Z","title":"Improved local spectral gap thresholds for lattices of finite dimension","version":1},"reference_index":11,"source":"arxiv_source","source_observed_at":"2026-08-14T05:29:21.414626Z"},"links":{"citing_paper":"/paper/1909.01516"},"observation_digest":"sha256:ce97a5b3949111dfb577bed86f6c0f88847bf927e75a2e0db5e77ebd22ceb5e0","observation_id":"3433cf13-7291-424f-b762-aa14b1316401","resolution":{"observed_at":"2026-08-14T05:29:22.346368Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T05:29:22.307662Z","title":null,"venue":null,"work_id":"84a43501-cb93-4c06-8610-39d008c4f2f4","year":2015},"citing_paper":{"arxiv_id":"1909.01516","last_updated":"2019-09-04T01:44:31Z","snapshot_observed_at":"2026-08-15T02:51:51.724306Z","submitted_at":"2019-09-04T01:44:31Z","title":"Improved local spectral gap thresholds for lattices of finite dimension","version":1},"reference_index":12,"source":"arxiv_source","source_observed_at":"2026-08-14T05:29:21.420999Z"},"links":{"citing_paper":"/paper/1909.01516"},"observation_digest":"sha256:79360da104e398cda46252e96ec3a05b796b1cbd2e2cc121072cb6da972d1e31","observation_id":"1de42f32-ce0b-4c3f-9622-e6a5285b0fd7","resolution":{"observed_at":"2026-08-14T05:29:22.318578Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T05:29:22.236544Z","title":"Correlation length versus gap in frustration-free systems","venue":null,"work_id":"50d063b1-4ee5-4142-b7b5-ae99c84ce7a8","year":2016},"citing_paper":{"arxiv_id":"1909.01516","last_updated":"2019-09-04T01:44:31Z","snapshot_observed_at":"2026-08-15T02:51:51.724306Z","submitted_at":"2019-09-04T01:44:31Z","title":"Improved local spectral gap thresholds for lattices of finite dimension","version":1},"reference_index":13,"source":"arxiv_source","source_observed_at":"2026-08-14T05:29:21.426507Z"},"links":{"citing_paper":"/paper/1909.01516"},"observation_digest":"sha256:ea7f956bf5d87259b166d4ced87575f3293de20c65942c5c0fd972a65777a3d9","observation_id":"003c22f7-4f3e-4253-8bcd-f1831f876c62","resolution":{"observed_at":"2026-08-14T05:29:22.286838Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T05:29:22.183731Z","title":"Local gap threshold for frustration-free spin systems","venue":null,"work_id":"ff93e0cf-948a-4d9f-9129-2dd3a92d1687","year":2016},"citing_paper":{"arxiv_id":"1909.01516","last_updated":"2019-09-04T01:44:31Z","snapshot_observed_at":"2026-08-15T02:51:51.724306Z","submitted_at":"2019-09-04T01:44:31Z","title":"Improved local spectral gap thresholds for lattices of finite dimension","version":1},"reference_index":14,"source":"arxiv_source","source_observed_at":"2026-08-14T05:29:21.433160Z"},"links":{"citing_paper":"/paper/1909.01516"},"observation_digest":"sha256:997b4eb3939f44beeb241be0e415856a8646af42f1fe1deda645a58a0b03c51e","observation_id":"29f56856-838c-4f1d-893a-67dd87f5cd23","resolution":{"observed_at":"2026-08-14T05:29:22.191463Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T05:29:22.141701Z","title":"Personal communication","venue":null,"work_id":"bee09693-60b0-4e70-b228-00d7f4e9ad69","year":2019},"citing_paper":{"arxiv_id":"1909.01516","last_updated":"2019-09-04T01:44:31Z","snapshot_observed_at":"2026-08-15T02:51:51.724306Z","submitted_at":"2019-09-04T01:44:31Z","title":"Improved local spectral gap thresholds for lattices of finite dimension","version":1},"reference_index":15,"source":"arxiv_source","source_observed_at":"2026-08-14T05:29:21.438197Z"},"links":{"citing_paper":"/paper/1909.01516"},"observation_digest":"sha256:0a301ccf1b811ae99102d1cfead5ca8291e926446e48d63908dfe47a905c455f","observation_id":"1483f0a8-0b70-4392-8c10-2054486ec637","resolution":{"observed_at":"2026-08-14T05:29:22.157842Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T05:29:22.112217Z","title":null,"venue":null,"work_id":"22c124b7-b1aa-4af5-8e5f-8d596fdb92ab","year":2004},"citing_paper":{"arxiv_id":"1909.01516","last_updated":"2019-09-04T01:44:31Z","snapshot_observed_at":"2026-08-15T02:51:51.724306Z","submitted_at":"2019-09-04T01:44:31Z","title":"Improved local spectral gap thresholds for lattices of finite dimension","version":1},"reference_index":16,"source":"arxiv_source","source_observed_at":"2026-08-14T05:29:21.442899Z"},"links":{"citing_paper":"/paper/1909.01516"},"observation_digest":"sha256:1b3a12b809e76ec85dfb607171069f666b05669c61311961b51f51aa220aabae","observation_id":"d3ea0824-71c6-47e7-83ea-79bf1e931eb0","resolution":{"observed_at":"2026-08-14T05:29:22.118444Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T05:29:22.072837Z","title":null,"venue":null,"work_id":"a6f3ab31-fbf2-46ff-8fee-070a9af848ce","year":2007},"citing_paper":{"arxiv_id":"1909.01516","last_updated":"2019-09-04T01:44:31Z","snapshot_observed_at":"2026-08-15T02:51:51.724306Z","submitted_at":"2019-09-04T01:44:31Z","title":"Improved local spectral gap thresholds for lattices of finite dimension","version":1},"reference_index":17,"source":"arxiv_source","source_observed_at":"2026-08-14T05:29:21.449665Z"},"links":{"citing_paper":"/paper/1909.01516"},"observation_digest":"sha256:b1921ff63b2423903551c68ac7ca849775e6194bfdcac5414c4a246bf328b0c8","observation_id":"6c35cf30-fbc0-4d6b-b9b1-aaf14567e694","resolution":{"observed_at":"2026-08-14T05:29:22.095498Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T05:29:22.032443Z","title":"Hastings and Tohru Koma","venue":null,"work_id":"45cdb534-ea09-4595-9ac1-26d6ba6e37dd","year":2006},"citing_paper":{"arxiv_id":"1909.01516","last_updated":"2019-09-04T01:44:31Z","snapshot_observed_at":"2026-08-15T02:51:51.724306Z","submitted_at":"2019-09-04T01:44:31Z","title":"Improved local spectral gap thresholds for lattices of finite dimension","version":1},"reference_index":18,"source":"arxiv_source","source_observed_at":"2026-08-14T05:29:21.457030Z"},"links":{"citing_paper":"/paper/1909.01516"},"observation_digest":"sha256:99396da6f9fc89818c575daade80e41e94999ff950de7f59cf55c8a9daf8eb96","observation_id":"1157fb4c-0678-4e76-a893-bfa61fce5770","resolution":{"observed_at":"2026-08-14T05:29:22.042194Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T05:29:21.991465Z","title":"Essai sur la g\\` e om\\` e trie \\' a n dimensions","venue":null,"work_id":"570edcd7-be63-4577-99b5-4e47ef9b167c","year":null},"citing_paper":{"arxiv_id":"1909.01516","last_updated":"2019-09-04T01:44:31Z","snapshot_observed_at":"2026-08-15T02:51:51.724306Z","submitted_at":"2019-09-04T01:44:31Z","title":"Improved local spectral gap thresholds for lattices of finite dimension","version":1},"reference_index":19,"source":"arxiv_source","source_observed_at":"2026-08-14T05:29:21.463379Z"},"links":{"citing_paper":"/paper/1909.01516"},"observation_digest":"sha256:6fd340a1a73e4899e8026fc0a7bb3a19e4bb8f0cca603e096355217e1b56374d","observation_id":"1271c19b-7b0b-457b-942b-a81fbc6b369b","resolution":{"observed_at":"2026-08-14T05:29:22.004748Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T05:29:21.953376Z","title":"Divide and conquer method for proving gaps of frustration free hamiltonians","venue":null,"work_id":"b86b8835-17c3-42e8-a203-01e8e1d47b40","year":2018},"citing_paper":{"arxiv_id":"1909.01516","last_updated":"2019-09-04T01:44:31Z","snapshot_observed_at":"2026-08-15T02:51:51.724306Z","submitted_at":"2019-09-04T01:44:31Z","title":"Improved local spectral gap thresholds for lattices of finite dimension","version":1},"reference_index":20,"source":"arxiv_source","source_observed_at":"2026-08-14T05:29:21.470261Z"},"links":{"citing_paper":"/paper/1909.01516"},"observation_digest":"sha256:414b6ac148b436844577406207359f2ebfd2ca9f63fb36894b52d53c5faf277f","observation_id":"d9a28f28-3ad4-47f2-ae39-1278b4e1dbdc","resolution":{"observed_at":"2026-08-14T05:29:21.962771Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T05:29:21.928263Z","title":"Energy gaps and elementary excitations for certain vbs-quantum antiferromagnets","venue":null,"work_id":"0c0c30e6-fc10-41ae-81c8-96d8c119a3de","year":1988},"citing_paper":{"arxiv_id":"1909.01516","last_updated":"2019-09-04T01:44:31Z","snapshot_observed_at":"2026-08-15T02:51:51.724306Z","submitted_at":"2019-09-04T01:44:31Z","title":"Improved local spectral gap thresholds for lattices of finite dimension","version":1},"reference_index":21,"source":"arxiv_source","source_observed_at":"2026-08-14T05:29:21.476202Z"},"links":{"citing_paper":"/paper/1909.01516"},"observation_digest":"sha256:7ff198cfafc38b34f0620c6eacc5fcf5a3440702c46b1d765fd6730ed8a74749","observation_id":"c564a381-415a-4948-bcf5-e09ce4b3689b","resolution":{"observed_at":"2026-08-14T05:29:21.934021Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1902.07141","last_updated":"2019-02-19T16:55:46Z","snapshot_observed_at":"2026-08-14T17:14:17.921591Z","submitted_at":"2019-02-19T16:55:46Z","title":"Finite-size criteria for spectral gaps in $D$-dimensional quantum spin systems","version":1},"cited_work":{"arxiv_id":"1902.07141","doi":null,"metadata_source":"pith","pith_arxiv_id":"1902.07141","snapshot_observed_at":"2026-08-14T05:29:21.607391Z","title":"Finite-size criteria for spectral gaps in $D$-dimensional quantum spin systems","venue":"quant-ph","work_id":"426459af-801e-4cde-9657-c231d60d9220","year":2019},"citing_paper":{"arxiv_id":"1909.01516","last_updated":"2019-09-04T01:44:31Z","snapshot_observed_at":"2026-08-15T02:51:51.724306Z","submitted_at":"2019-09-04T01:44:31Z","title":"Improved local spectral gap thresholds for lattices of finite dimension","version":1},"reference_index":22,"source":"arxiv_source","source_observed_at":"2026-08-14T05:29:21.481622Z"},"links":{"cited_paper":"/paper/1902.07141","citing_paper":"/paper/1909.01516"},"observation_digest":"sha256:79bb6e37d9977e9706a97d05ea7bb53c66fea1285a8c002bbaa26df720f6a0d6","observation_id":"6991a419-28e0-405c-a4c5-db06a0cde78d","resolution":{"observed_at":"2026-08-14T05:29:21.628242Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T05:29:21.905947Z","title":"Gaplessness is not generic for translation-invariant spin chains","venue":null,"work_id":"94fd3ef8-61a6-44c5-923d-41adbe2ec39e","year":2019},"citing_paper":{"arxiv_id":"1909.01516","last_updated":"2019-09-04T01:44:31Z","snapshot_observed_at":"2026-08-15T02:51:51.724306Z","submitted_at":"2019-09-04T01:44:31Z","title":"Improved local spectral gap thresholds for lattices of finite dimension","version":1},"reference_index":23,"source":"arxiv_source","source_observed_at":"2026-08-14T05:29:21.487126Z"},"links":{"citing_paper":"/paper/1909.01516"},"observation_digest":"sha256:158a38049ad3f2eff272b1b65b290bb52a40184baf6d23c8075ce5b3b4988362","observation_id":"288ae754-affa-48c2-801d-a32aa7c086be","resolution":{"observed_at":"2026-08-14T05:29:21.912041Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1801.08915","last_updated":"2019-05-03T21:42:44Z","snapshot_observed_at":"2026-08-15T04:14:25.641030Z","submitted_at":"2018-01-26T17:51:23Z","title":"Spectral gaps of frustration-free spin systems with boundary","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1801.08915","snapshot_observed_at":"2026-08-14T05:29:21.492099Z","title":"Spectral gaps of frustration-free spin systems with boundary, 2018","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"1909.01516","last_updated":"2019-09-04T01:44:31Z","snapshot_observed_at":"2026-08-15T02:51:51.724306Z","submitted_at":"2019-09-04T01:44:31Z","title":"Improved local spectral gap thresholds for lattices of finite dimension","version":1},"reference_index":24,"source":"arxiv_source","source_observed_at":"2026-08-14T05:29:21.492099Z"},"links":{"cited_paper":"/paper/1801.08915","citing_paper":"/paper/1909.01516"},"observation_digest":"sha256:f3d5609b7929b6341591728bcdf3d3c27828a650e4c0e3d88cee12e2ceff69b8","observation_id":"69c89804-b4e9-46df-ba13-4696ce3de57b","resolution":{"observed_at":"2026-08-14T05:29:21.492099Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1904.01043","last_updated":"2019-04-01T18:12:01Z","snapshot_observed_at":"2026-08-15T01:19:49.137995Z","submitted_at":"2019-04-01T18:12:01Z","title":"The AKLT model on a hexagonal chain is gapped","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1904.01043","snapshot_observed_at":"2026-08-14T05:29:21.497525Z","title":"The aklt model on a hexagonal chain is gapped, 2019","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"1909.01516","last_updated":"2019-09-04T01:44:31Z","snapshot_observed_at":"2026-08-15T02:51:51.724306Z","submitted_at":"2019-09-04T01:44:31Z","title":"Improved local spectral gap thresholds for lattices of finite dimension","version":1},"reference_index":25,"source":"arxiv_source","source_observed_at":"2026-08-14T05:29:21.497525Z"},"links":{"cited_paper":"/paper/1904.01043","citing_paper":"/paper/1909.01516"},"observation_digest":"sha256:f4eabff80e421afd30a582d14c4a8fb49920cc6172f0d30c63b620d6a77e1e02","observation_id":"81f5f354-3bff-45b2-9621-cc903704d4ec","resolution":{"observed_at":"2026-08-14T05:29:21.497525Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T05:29:21.872061Z","title":"The spectral gap for some spin chains with discrete symmetry breaking","venue":null,"work_id":"6b6d244b-f642-43b7-8eab-90596061ba5e","year":1996},"citing_paper":{"arxiv_id":"1909.01516","last_updated":"2019-09-04T01:44:31Z","snapshot_observed_at":"2026-08-15T02:51:51.724306Z","submitted_at":"2019-09-04T01:44:31Z","title":"Improved local spectral gap thresholds for lattices of finite dimension","version":1},"reference_index":26,"source":"arxiv_source","source_observed_at":"2026-08-14T05:29:21.503913Z"},"links":{"citing_paper":"/paper/1909.01516"},"observation_digest":"sha256:1d077850ef1496faff4faf449677fec35f01b96581b15a9e820cb7fa03bc3905","observation_id":"6fc94ce2-a128-4c19-b522-4ebda42a4431","resolution":{"observed_at":"2026-08-14T05:29:21.883299Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T05:29:21.840466Z","title":"Lieb-robinson bounds and the exponential clustering theorem","venue":null,"work_id":"dd3ec80b-0c1f-42af-9458-9e10f846c02b","year":2006},"citing_paper":{"arxiv_id":"1909.01516","last_updated":"2019-09-04T01:44:31Z","snapshot_observed_at":"2026-08-15T02:51:51.724306Z","submitted_at":"2019-09-04T01:44:31Z","title":"Improved local spectral gap thresholds for lattices of finite dimension","version":1},"reference_index":27,"source":"arxiv_source","source_observed_at":"2026-08-14T05:29:21.509485Z"},"links":{"citing_paper":"/paper/1909.01516"},"observation_digest":"sha256:db1b26acba5a9e68aa974d12e17aeba79e5d03c3e334831db2f72ca4e11d4fbe","observation_id":"4296e1d3-444f-4950-8776-302cc78ecafb","resolution":{"observed_at":"2026-08-14T05:29:21.850881Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"1909.01516","last_updated":"2019-09-04T01:44:31Z","latest_version":1,"primary_category":"quant-ph","snapshot_observed_at":"2026-08-15T02:51:51.724306Z","submitted_at":"2019-09-04T01:44:31Z","title":"Improved local spectral gap thresholds for lattices of finite dimension"},"reference_resolution":{"displayed":27,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":9,"verified_exact":2,"verified_fuzzy":16},"total_outbound_references":27},"refusal":"A citation records a reference. It does not transfer a finding from one paper to another.","schema":"pith.paper-citation-record.v1","standing_sources":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"thesis":"As of 16 August 2026, this Paper Citation Record lists 27 of 27 outbound references and 1 inbound Pith citation observation for arXiv:1909.01516."}