{"as_of":"2026-08-07T15:25:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:59c81348ee286713bd6f91820146e43ec5272a2de86d67c681b28950c78f6132","coverage":[{"denominator":0,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":0,"source":"paper_references, paper_reference_links","source_observed_at":null,"state":"measured"},{"denominator":8,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":8,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-07T06:34:17.273281+00:00","state":"measured"},{"denominator":8,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":8,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-05T23:50:29.825225Z","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":"2026-05-23T18:33:19.727524Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2402.16831","last_updated":"2024-02-26T18:56:46Z","snapshot_observed_at":"2026-07-06T17:35:41.168780Z","submitted_at":"2024-02-26T18:56:46Z","title":"The Physics of (good) LDPC Codes II. Product constructions","version":1},"cited_work":{"arxiv_id":"2402.16831","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2402.16831","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"product constructions","venue":null,"work_id":"f908d071-3cf0-47ac-adfe-7daecfad6f3d","year":2024},"citing_paper":{"arxiv_id":"2410.16250","last_updated":"2025-12-27T21:52:26Z","snapshot_observed_at":"2026-08-02T07:46:23.650899Z","submitted_at":"2024-10-21T17:53:17Z","title":"Cups and Gates I: Cohomology invariants and logical quantum operations","version":2},"reference_index":54,"source":"pdf_text","source_observed_at":"2026-05-23T18:30:24.895557Z"},"links":{"cited_paper":"/paper/2402.16831","citing_paper":"/paper/2410.16250"},"observation_digest":"sha256:c2b2a5949bc0a1173ad5a419dbfe76b078198c482a594bb093a85453bc6fae2a","observation_id":"e8635dbb-9332-4445-a7a1-a46f670e5215","resolution":{"observed_at":"2026-05-23T18:33:19.730470Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2402.16831","last_updated":"2024-02-26T18:56:46Z","snapshot_observed_at":"2026-07-06T17:35:41.168780Z","submitted_at":"2024-02-26T18:56:46Z","title":"The Physics of (good) LDPC Codes II. Product constructions","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2402.16831","snapshot_observed_at":"2026-08-05T23:50:18.422566Z","title":"The physics of (good) ldpc codes ii","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2508.04794","last_updated":"2025-08-06T18:10:37Z","snapshot_observed_at":"2026-08-06T07:25:20.927061Z","submitted_at":"2025-08-06T18:10:37Z","title":"Automorphism gadgets in homological product codes","version":1},"reference_index":79,"source":"arxiv_source","source_observed_at":"2026-08-05T23:50:18.422566Z"},"links":{"cited_paper":"/paper/2402.16831","citing_paper":"/paper/2508.04794"},"observation_digest":"sha256:a1f8b3312d09edb96896fe147c37ec74a48a367f8ea143db0ff5a97b9a1b4a48","observation_id":"55f1cb8b-7b89-49ed-a67b-b4fbcb4c7932","resolution":{"observed_at":"2026-08-05T23:50:18.422566Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2402.16831","last_updated":"2024-02-26T18:56:46Z","snapshot_observed_at":"2026-07-06T17:35:41.168780Z","submitted_at":"2024-02-26T18:56:46Z","title":"The Physics of (good) LDPC Codes II. Product constructions","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2402.16831","snapshot_observed_at":"2026-08-05T23:50:29.825225Z","title":"The physics of (good) ldpc codes ii","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2508.04796","last_updated":"2026-07-02T23:06:55Z","snapshot_observed_at":"2026-08-06T12:35:36.047653Z","submitted_at":"2025-08-06T18:14:43Z","title":"Parity-Aware Byte-Pair Encoding: Improving Cross-lingual Fairness in Tokenization","version":3},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-05T23:50:29.825225Z"},"links":{"cited_paper":"/paper/2402.16831","citing_paper":"/paper/2508.04796"},"observation_digest":"sha256:87f6d26d7b57d45b2f1f636299b038d98e6bcd42ee55ad8f3495f47b73077631","observation_id":"202779f0-e632-418d-ba39-5fd4a057acb0","resolution":{"observed_at":"2026-08-05T23:50:29.825225Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2402.16831","last_updated":"2024-02-26T18:56:46Z","snapshot_observed_at":"2026-07-06T17:35:41.168780Z","submitted_at":"2024-02-26T18:56:46Z","title":"The Physics of (good) LDPC Codes II. Product constructions","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2402.16831","snapshot_observed_at":"2026-08-05T21:18:47.049742Z","title":"The Physics of (good) LDPC Codes II","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2508.09082","last_updated":"2025-08-12T17:03:59Z","snapshot_observed_at":"2026-08-05T21:18:35.909389Z","submitted_at":"2025-08-12T17:03:59Z","title":"Generalized Bicycle Codes with Low Connectivity: Minimum Distance Bounds and Hook Errors","version":1},"reference_index":13,"source":"arxiv_source","source_observed_at":"2026-08-05T21:18:47.049742Z"},"links":{"cited_paper":"/paper/2402.16831","citing_paper":"/paper/2508.09082"},"observation_digest":"sha256:98162c1a7e4e01d92e43d492fe2f5d56ab20c3e5760e4d4cdfa0d4f986d8d5b8","observation_id":"d5372506-c4e9-4304-af9a-390124e16cff","resolution":{"observed_at":"2026-08-05T21:18:47.049742Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2402.16831","last_updated":"2024-02-26T18:56:46Z","snapshot_observed_at":"2026-07-06T17:35:41.168780Z","submitted_at":"2024-02-26T18:56:46Z","title":"The Physics of (good) LDPC Codes II. Product constructions","version":1},"cited_work":{"arxiv_id":"2402.16831","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2402.16831","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"product constructions","venue":null,"work_id":"f908d071-3cf0-47ac-adfe-7daecfad6f3d","year":2024},"citing_paper":{"arxiv_id":"2511.04430","last_updated":"2026-05-06T23:02:15Z","snapshot_observed_at":"2026-07-06T22:35:02.737645Z","submitted_at":"2025-11-06T15:05:17Z","title":"Symmetry-enriched topological order and quasifractonic behavior in $\\mathbb{Z}_N$ stabilizer codes","version":2},"reference_index":52,"source":"pdf_text","source_observed_at":"2026-05-18T01:01:08.043585Z"},"links":{"cited_paper":"/paper/2402.16831","citing_paper":"/paper/2511.04430"},"observation_digest":"sha256:18d8a17edc1d527e72c904cac48dd4f56e6ebb0fb7ac215a716762b7083ad1ef","observation_id":"b59aa199-f0dd-44bf-8c30-95391cddb6eb","resolution":{"observed_at":"2026-05-18T01:02:15.403965Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2402.16831","last_updated":"2024-02-26T18:56:46Z","snapshot_observed_at":"2026-07-06T17:35:41.168780Z","submitted_at":"2024-02-26T18:56:46Z","title":"The Physics of (good) LDPC Codes II. Product constructions","version":1},"cited_work":{"arxiv_id":"2402.16831","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2402.16831","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"product constructions","venue":null,"work_id":"f908d071-3cf0-47ac-adfe-7daecfad6f3d","year":2024},"citing_paper":{"arxiv_id":"2603.08711","last_updated":"2026-05-04T00:04:29Z","snapshot_observed_at":"2026-07-06T22:48:26.306802Z","submitted_at":"2026-03-09T17:59:59Z","title":"Coupled-Layer Construction of Quantum Product Codes","version":2},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-05-15T14:26:04.369018Z"},"links":{"cited_paper":"/paper/2402.16831","citing_paper":"/paper/2603.08711"},"observation_digest":"sha256:8ad119a0638770ab1dd7172245e058f42b05e6111fc52463a437d7555bbc3940","observation_id":"b419d760-4a70-470a-a9c1-738bb3036ccd","resolution":{"observed_at":"2026-05-15T14:30:03.732024Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2402.16831","last_updated":"2024-02-26T18:56:46Z","snapshot_observed_at":"2026-07-06T17:35:41.168780Z","submitted_at":"2024-02-26T18:56:46Z","title":"The Physics of (good) LDPC Codes II. Product constructions","version":1},"cited_work":{"arxiv_id":"2402.16831","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2402.16831","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"product constructions","venue":null,"work_id":"f908d071-3cf0-47ac-adfe-7daecfad6f3d","year":2024},"citing_paper":{"arxiv_id":"2605.19298","last_updated":"2026-05-19T03:18:11Z","snapshot_observed_at":"2026-07-29T14:49:16.049487Z","submitted_at":"2026-05-19T03:18:11Z","title":"Translation-invariant quantum low-density parity-check codes from compactified fracton models","version":1},"reference_index":77,"source":"pdf_text","source_observed_at":"2026-05-20T06:28:11.017427Z"},"links":{"cited_paper":"/paper/2402.16831","citing_paper":"/paper/2605.19298"},"observation_digest":"sha256:9f20154324f941194205b16656556cf060c561d2e9e51a3900905d39843b80b8","observation_id":"5746324d-8e6d-4c87-976d-f74577dcb9bd","resolution":{"observed_at":"2026-05-20T06:33:05.933803Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2402.16831","last_updated":"2024-02-26T18:56:46Z","snapshot_observed_at":"2026-07-06T17:35:41.168780Z","submitted_at":"2024-02-26T18:56:46Z","title":"The Physics of (good) LDPC Codes II. Product constructions","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2402.16831","snapshot_observed_at":"2026-08-01T09:57:10.423950Z","title":"Rakovszky and V","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2607.20421","last_updated":"2026-07-22T17:58:00Z","snapshot_observed_at":"2026-08-07T04:38:30.358412Z","submitted_at":"2026-07-22T17:58:00Z","title":"Stable valleys in the glassy landscape of a low-density parity-check (LDPC) code","version":1},"reference_index":76,"source":"pdf_text","source_observed_at":"2026-08-01T09:57:10.423950Z"},"links":{"cited_paper":"/paper/2402.16831","citing_paper":"/paper/2607.20421"},"observation_digest":"sha256:b1e5b797e9d9e2b85bace9bee6fa0cfaa4b31baeee651df630dae4677c1e7607","observation_id":"9976db3c-7ff4-4c2a-8923-d90157c1f32c","resolution":{"observed_at":"2026-08-01T09:57:10.423950Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"links":{"evidence":"/evidence","html":"/paper/2402.16831/citation-record","integrity":"/paper/2402.16831/integrity","json":"/paper/2402.16831/citation-record.json","paper":"/paper/2402.16831"},"outbound":[],"paper":{"arxiv_id":"2402.16831","last_updated":"2024-02-26T18:56:46Z","latest_version":1,"primary_category":"quant-ph","snapshot_observed_at":"2026-07-06T17:35:41.168780Z","submitted_at":"2024-02-26T18:56:46Z","title":"The Physics of (good) LDPC Codes II. Product constructions"},"reference_resolution":{"displayed":0,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":0,"verified_exact":0,"verified_fuzzy":0},"total_outbound_references":0},"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":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"thesis":"As of 7 August 2026, this Paper Citation Record lists 0 of 0 outbound references and 8 inbound Pith citation observations for arXiv:2402.16831."}