{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:WRYJMPLXBTLUIBAGLVDG5FJL7Q","short_pith_number":"pith:WRYJMPLX","schema_version":"1.0","canonical_sha256":"b470963d770cd74404065d466e952bfc397bfefd9b54e40af44f7874b4494401","source":{"kind":"arxiv","id":"2307.08266","version":1},"attestation_state":"computed","paper":{"title":"Phase Transitions of Structured Codes of Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.IT"],"primary_cat":"math.CO","authors_text":"Bo Bai, Jie Ma, Yu Gao, Yuze Wu","submitted_at":"2023-07-17T06:15:36Z","abstract_excerpt":"We consider the symmetric difference of two graphs on the same vertex set $[n]$, which is the graph on $[n]$ whose edge set consists of all edges that belong to exactly one of the two graphs. Let $\\mathcal{F}$ be a class of graphs, and let $M_{\\mathcal{F}}(n)$ denote the maximum possible cardinality of a family $\\mathcal{G}$ of graphs on $[n]$ such that the symmetric difference of any two members in $\\mathcal{G}$ belongs to $\\mathcal{F}$. These concepts are recently investigated by Alon, Gujgiczer, K\\\"{o}rner, Milojevi\\'{c}, and Simonyi, with the aim of providing a new graphic approach to codi"},"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":"2307.08266","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2023-07-17T06:15:36Z","cross_cats_sorted":["cs.IT","math.IT"],"title_canon_sha256":"b824f37684aed09f88dd236dee7081119569f75add76791c70b233eff0f53961","abstract_canon_sha256":"5f31c664a0fa71091b2b64de77aeea509ef9eadef4a336d2929cc1c9af8a4986"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:31:22.451563Z","signature_b64":"ROxg/P+FbV6AG6/LdnhO4/FZHMG+VFPQOFXxKWcLaezmqsa6jwtCpZG85T8g/36xAWyrCahtelMSo6bxvJ8wDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b470963d770cd74404065d466e952bfc397bfefd9b54e40af44f7874b4494401","last_reissued_at":"2026-07-05T06:31:22.451084Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:31:22.451084Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Phase Transitions of Structured Codes of Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.IT"],"primary_cat":"math.CO","authors_text":"Bo Bai, Jie Ma, Yu Gao, Yuze Wu","submitted_at":"2023-07-17T06:15:36Z","abstract_excerpt":"We consider the symmetric difference of two graphs on the same vertex set $[n]$, which is the graph on $[n]$ whose edge set consists of all edges that belong to exactly one of the two graphs. Let $\\mathcal{F}$ be a class of graphs, and let $M_{\\mathcal{F}}(n)$ denote the maximum possible cardinality of a family $\\mathcal{G}$ of graphs on $[n]$ such that the symmetric difference of any two members in $\\mathcal{G}$ belongs to $\\mathcal{F}$. These concepts are recently investigated by Alon, Gujgiczer, K\\\"{o}rner, Milojevi\\'{c}, and Simonyi, with the aim of providing a new graphic approach to codi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2307.08266","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/2307.08266/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":"2307.08266","created_at":"2026-07-05T06:31:22.451141+00:00"},{"alias_kind":"arxiv_version","alias_value":"2307.08266v1","created_at":"2026-07-05T06:31:22.451141+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2307.08266","created_at":"2026-07-05T06:31:22.451141+00:00"},{"alias_kind":"pith_short_12","alias_value":"WRYJMPLXBTLU","created_at":"2026-07-05T06:31:22.451141+00:00"},{"alias_kind":"pith_short_16","alias_value":"WRYJMPLXBTLUIBAG","created_at":"2026-07-05T06:31:22.451141+00:00"},{"alias_kind":"pith_short_8","alias_value":"WRYJMPLX","created_at":"2026-07-05T06:31:22.451141+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/WRYJMPLXBTLUIBAGLVDG5FJL7Q","json":"https://pith.science/pith/WRYJMPLXBTLUIBAGLVDG5FJL7Q.json","graph_json":"https://pith.science/api/pith-number/WRYJMPLXBTLUIBAGLVDG5FJL7Q/graph.json","events_json":"https://pith.science/api/pith-number/WRYJMPLXBTLUIBAGLVDG5FJL7Q/events.json","paper":"https://pith.science/paper/WRYJMPLX"},"agent_actions":{"view_html":"https://pith.science/pith/WRYJMPLXBTLUIBAGLVDG5FJL7Q","download_json":"https://pith.science/pith/WRYJMPLXBTLUIBAGLVDG5FJL7Q.json","view_paper":"https://pith.science/paper/WRYJMPLX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2307.08266&json=true","fetch_graph":"https://pith.science/api/pith-number/WRYJMPLXBTLUIBAGLVDG5FJL7Q/graph.json","fetch_events":"https://pith.science/api/pith-number/WRYJMPLXBTLUIBAGLVDG5FJL7Q/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WRYJMPLXBTLUIBAGLVDG5FJL7Q/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WRYJMPLXBTLUIBAGLVDG5FJL7Q/action/storage_attestation","attest_author":"https://pith.science/pith/WRYJMPLXBTLUIBAGLVDG5FJL7Q/action/author_attestation","sign_citation":"https://pith.science/pith/WRYJMPLXBTLUIBAGLVDG5FJL7Q/action/citation_signature","submit_replication":"https://pith.science/pith/WRYJMPLXBTLUIBAGLVDG5FJL7Q/action/replication_record"}},"created_at":"2026-07-05T06:31:22.451141+00:00","updated_at":"2026-07-05T06:31:22.451141+00:00"}