{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:ANEEEPXHG4WJ62YMS5M4PKTSUF","short_pith_number":"pith:ANEEEPXH","schema_version":"1.0","canonical_sha256":"0348423ee7372c9f6b0c9759c7aa72a161ab9f5021e37663b1cc91ff45af3dde","source":{"kind":"arxiv","id":"2407.02102","version":1},"attestation_state":"computed","paper":{"title":"Separating the edges of a graph by cycles and by subdivisions of $K_4$","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"F\\'abio Botler, T\\'assio Naia","submitted_at":"2024-07-02T09:40:20Z","abstract_excerpt":"A separating system of a graph $G$ is a family $\\mathcal{S}$ of subgraphs of $G$ for which the following holds: for all distinct edges $e$ and $f$ of $G$, there exists an element in $\\mathcal{S}$ that contains $e$ but not $f$. Recently, it has been shown that every graph of order $n$ admits a separating system consisting of $19n$ paths [Bonamy, Botler, Dross, Naia, Skokan, Separating the Edges of a Graph by a Linear Number of Paths, Adv. Comb., October 2023], improving the previous almost linear bound of $\\mathrm{O}(n\\log^\\star n)$ [S. Letzter, Separating paths systems of almost linear size, T"},"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":"2407.02102","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2024-07-02T09:40:20Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"4752db4b6d452da0b370b0a8615adf0175c3bbd27b0230ecaf27da9773955524","abstract_canon_sha256":"125988d3830e1a8f6763657c517a5d2c65be07fdfe220bb57385a0ca2120e8d7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:39:10.113457Z","signature_b64":"YR3u4p2+LJTGuXWT1/07PzkrQxPpqsLXf79rn5a7h/scLyYpiPyrHFIIb7RgwzIViOFUvNtQ870VTxG060yiDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0348423ee7372c9f6b0c9759c7aa72a161ab9f5021e37663b1cc91ff45af3dde","last_reissued_at":"2026-07-05T08:39:10.112959Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:39:10.112959Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Separating the edges of a graph by cycles and by subdivisions of $K_4$","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"F\\'abio Botler, T\\'assio Naia","submitted_at":"2024-07-02T09:40:20Z","abstract_excerpt":"A separating system of a graph $G$ is a family $\\mathcal{S}$ of subgraphs of $G$ for which the following holds: for all distinct edges $e$ and $f$ of $G$, there exists an element in $\\mathcal{S}$ that contains $e$ but not $f$. Recently, it has been shown that every graph of order $n$ admits a separating system consisting of $19n$ paths [Bonamy, Botler, Dross, Naia, Skokan, Separating the Edges of a Graph by a Linear Number of Paths, Adv. Comb., October 2023], improving the previous almost linear bound of $\\mathrm{O}(n\\log^\\star n)$ [S. Letzter, Separating paths systems of almost linear size, T"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2407.02102","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/2407.02102/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":"2407.02102","created_at":"2026-07-05T08:39:10.113015+00:00"},{"alias_kind":"arxiv_version","alias_value":"2407.02102v1","created_at":"2026-07-05T08:39:10.113015+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2407.02102","created_at":"2026-07-05T08:39:10.113015+00:00"},{"alias_kind":"pith_short_12","alias_value":"ANEEEPXHG4WJ","created_at":"2026-07-05T08:39:10.113015+00:00"},{"alias_kind":"pith_short_16","alias_value":"ANEEEPXHG4WJ62YM","created_at":"2026-07-05T08:39:10.113015+00:00"},{"alias_kind":"pith_short_8","alias_value":"ANEEEPXH","created_at":"2026-07-05T08:39:10.113015+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/ANEEEPXHG4WJ62YMS5M4PKTSUF","json":"https://pith.science/pith/ANEEEPXHG4WJ62YMS5M4PKTSUF.json","graph_json":"https://pith.science/api/pith-number/ANEEEPXHG4WJ62YMS5M4PKTSUF/graph.json","events_json":"https://pith.science/api/pith-number/ANEEEPXHG4WJ62YMS5M4PKTSUF/events.json","paper":"https://pith.science/paper/ANEEEPXH"},"agent_actions":{"view_html":"https://pith.science/pith/ANEEEPXHG4WJ62YMS5M4PKTSUF","download_json":"https://pith.science/pith/ANEEEPXHG4WJ62YMS5M4PKTSUF.json","view_paper":"https://pith.science/paper/ANEEEPXH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2407.02102&json=true","fetch_graph":"https://pith.science/api/pith-number/ANEEEPXHG4WJ62YMS5M4PKTSUF/graph.json","fetch_events":"https://pith.science/api/pith-number/ANEEEPXHG4WJ62YMS5M4PKTSUF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ANEEEPXHG4WJ62YMS5M4PKTSUF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ANEEEPXHG4WJ62YMS5M4PKTSUF/action/storage_attestation","attest_author":"https://pith.science/pith/ANEEEPXHG4WJ62YMS5M4PKTSUF/action/author_attestation","sign_citation":"https://pith.science/pith/ANEEEPXHG4WJ62YMS5M4PKTSUF/action/citation_signature","submit_replication":"https://pith.science/pith/ANEEEPXHG4WJ62YMS5M4PKTSUF/action/replication_record"}},"created_at":"2026-07-05T08:39:10.113015+00:00","updated_at":"2026-07-05T08:39:10.113015+00:00"}