{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2020:3EMKWUGNLDEIRBPI6UGDR7R4MB","short_pith_number":"pith:3EMKWUGN","schema_version":"1.0","canonical_sha256":"d918ab50cd58c88885e8f50c38fe3c60426a2ba6e335fe0677d58380f119a1c2","source":{"kind":"arxiv","id":"2003.14361","version":1},"attestation_state":"computed","paper":{"title":"Graph structure via local occupancy","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Ewan Davies, Fran\\c{c}ois Pirot, Jean-S\\'ebastien Sereni, Ross J. Kang","submitted_at":"2020-03-31T16:42:57Z","abstract_excerpt":"The first author together with Jenssen, Perkins and Roberts (2017) recently showed how local properties of the hard-core model on triangle-free graphs guarantee the existence of large independent sets, of size matching the best-known asymptotics due to Shearer (1983). The present work strengthens this in two ways: first, by guaranteeing stronger graph structure in terms of colourings through applications of the Lov\\'asz local lemma; and second, by extending beyond triangle-free graphs in terms of local sparsity, treating for example graphs of bounded local edge density, of bounded local Hall r"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2003.14361","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2020-03-31T16:42:57Z","cross_cats_sorted":[],"title_canon_sha256":"0c61103e10efa514df92979879dd3a79ecc62741eb47db5577f6eeb7d2a9f2f8","abstract_canon_sha256":"f8e1a3bb2047db91200bd74b2452d37ca9336712524b9ebd0461544972cfdc26"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:51:49.757583Z","signature_b64":"QKGETOusqk2fYkXEN15ncUtLEHr/y89dGEb1xinW9c79IePo8/Ht8KRvCHBrfuDkCxG/DY3FzdamvwSzyJXIBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d918ab50cd58c88885e8f50c38fe3c60426a2ba6e335fe0677d58380f119a1c2","last_reissued_at":"2026-07-05T00:51:49.757090Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:51:49.757090Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Graph structure via local occupancy","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Ewan Davies, Fran\\c{c}ois Pirot, Jean-S\\'ebastien Sereni, Ross J. Kang","submitted_at":"2020-03-31T16:42:57Z","abstract_excerpt":"The first author together with Jenssen, Perkins and Roberts (2017) recently showed how local properties of the hard-core model on triangle-free graphs guarantee the existence of large independent sets, of size matching the best-known asymptotics due to Shearer (1983). The present work strengthens this in two ways: first, by guaranteeing stronger graph structure in terms of colourings through applications of the Lov\\'asz local lemma; and second, by extending beyond triangle-free graphs in terms of local sparsity, treating for example graphs of bounded local edge density, of bounded local Hall r"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2003.14361","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2003.14361/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"2003.14361","created_at":"2026-07-05T00:51:49.757152+00:00"},{"alias_kind":"arxiv_version","alias_value":"2003.14361v1","created_at":"2026-07-05T00:51:49.757152+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2003.14361","created_at":"2026-07-05T00:51:49.757152+00:00"},{"alias_kind":"pith_short_12","alias_value":"3EMKWUGNLDEI","created_at":"2026-07-05T00:51:49.757152+00:00"},{"alias_kind":"pith_short_16","alias_value":"3EMKWUGNLDEIRBPI","created_at":"2026-07-05T00:51:49.757152+00:00"},{"alias_kind":"pith_short_8","alias_value":"3EMKWUGN","created_at":"2026-07-05T00:51:49.757152+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":8,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2606.18048","citing_title":"The independence number of uncrowded hypergraphs: bounds matching the shattering threshold","ref_index":20,"is_internal_anchor":false},{"citing_arxiv_id":"2210.05915","citing_title":"Coloring, List Coloring, and Painting Squares of Graphs (and other related problems)","ref_index":67,"is_internal_anchor":false},{"citing_arxiv_id":"2603.17730","citing_title":"Fractional coloring via entropy","ref_index":14,"is_internal_anchor":false},{"citing_arxiv_id":"2604.28046","citing_title":"Hypergraph independence bounds: from maximum degree to average degree","ref_index":5,"is_internal_anchor":false},{"citing_arxiv_id":"2604.28046","citing_title":"Hypergraph independence bounds: from maximum degree to average degree","ref_index":5,"is_internal_anchor":false},{"citing_arxiv_id":"2605.05618","citing_title":"Algorithmic Phase Transition for Large Independent Sets in Dense Hypergraphs","ref_index":25,"is_internal_anchor":false},{"citing_arxiv_id":"2604.14006","citing_title":"Coloring powers of random graphs","ref_index":13,"is_internal_anchor":false},{"citing_arxiv_id":"2605.05149","citing_title":"Degree-sequence bounds for independent sets via multivariate local occupancy","ref_index":15,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/3EMKWUGNLDEIRBPI6UGDR7R4MB","json":"https://pith.science/pith/3EMKWUGNLDEIRBPI6UGDR7R4MB.json","graph_json":"https://pith.science/api/pith-number/3EMKWUGNLDEIRBPI6UGDR7R4MB/graph.json","events_json":"https://pith.science/api/pith-number/3EMKWUGNLDEIRBPI6UGDR7R4MB/events.json","paper":"https://pith.science/paper/3EMKWUGN"},"agent_actions":{"view_html":"https://pith.science/pith/3EMKWUGNLDEIRBPI6UGDR7R4MB","download_json":"https://pith.science/pith/3EMKWUGNLDEIRBPI6UGDR7R4MB.json","view_paper":"https://pith.science/paper/3EMKWUGN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2003.14361&json=true","fetch_graph":"https://pith.science/api/pith-number/3EMKWUGNLDEIRBPI6UGDR7R4MB/graph.json","fetch_events":"https://pith.science/api/pith-number/3EMKWUGNLDEIRBPI6UGDR7R4MB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3EMKWUGNLDEIRBPI6UGDR7R4MB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3EMKWUGNLDEIRBPI6UGDR7R4MB/action/storage_attestation","attest_author":"https://pith.science/pith/3EMKWUGNLDEIRBPI6UGDR7R4MB/action/author_attestation","sign_citation":"https://pith.science/pith/3EMKWUGNLDEIRBPI6UGDR7R4MB/action/citation_signature","submit_replication":"https://pith.science/pith/3EMKWUGNLDEIRBPI6UGDR7R4MB/action/replication_record"}},"created_at":"2026-07-05T00:51:49.757152+00:00","updated_at":"2026-07-05T00:51:49.757152+00:00"}