{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:WKUAV6JDEWODKUEIZAXW2M3E2M","short_pith_number":"pith:WKUAV6JD","schema_version":"1.0","canonical_sha256":"b2a80af923259c355088c82f6d3364d33ff4575eb0bf093241c81e8c2bb205cf","source":{"kind":"arxiv","id":"2606.00533","version":1},"attestation_state":"computed","paper":{"title":"The number of cut-edges and conflict-free connection number in planar graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Dang Dinh Hanh, Pham Hoang Ha, Vu Quang Minh","submitted_at":"2026-05-30T04:53:19Z","abstract_excerpt":"A \\textit{cut-edge} of a connected graph is an edge whose deletion increases the number of components. In this paper, we first state some conditions for a planar graph to have a few cut-edges. After that, we use the main results to study the conditions for a colored planar graph to have a bounded conflict-free connection number."},"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":"2606.00533","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2026-05-30T04:53:19Z","cross_cats_sorted":[],"title_canon_sha256":"2d714bd0bd25a71d70ceeb12ac2500e152d966b21457f7bb120c06b56fbaa975","abstract_canon_sha256":"e862e8024f0dc6ee436c16507ace747d5b7a42d477b2c5249e36b155b887c475"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-02T01:03:57.371573Z","signature_b64":"zr0lnwfA9EMvzdNqWUFTbqQtaKyIACFERAyExrLffmvQAHeDuYoUK9RXo+z0/jen7lDQ5igNJYaMgPjVQGrLAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b2a80af923259c355088c82f6d3364d33ff4575eb0bf093241c81e8c2bb205cf","last_reissued_at":"2026-06-02T01:03:57.371053Z","signature_status":"signed_v1","first_computed_at":"2026-06-02T01:03:57.371053Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The number of cut-edges and conflict-free connection number in planar graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Dang Dinh Hanh, Pham Hoang Ha, Vu Quang Minh","submitted_at":"2026-05-30T04:53:19Z","abstract_excerpt":"A \\textit{cut-edge} of a connected graph is an edge whose deletion increases the number of components. In this paper, we first state some conditions for a planar graph to have a few cut-edges. After that, we use the main results to study the conditions for a colored planar graph to have a bounded conflict-free connection number."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.00533","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/2606.00533/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":"2606.00533","created_at":"2026-06-02T01:03:57.371133+00:00"},{"alias_kind":"arxiv_version","alias_value":"2606.00533v1","created_at":"2026-06-02T01:03:57.371133+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.00533","created_at":"2026-06-02T01:03:57.371133+00:00"},{"alias_kind":"pith_short_12","alias_value":"WKUAV6JDEWOD","created_at":"2026-06-02T01:03:57.371133+00:00"},{"alias_kind":"pith_short_16","alias_value":"WKUAV6JDEWODKUEI","created_at":"2026-06-02T01:03:57.371133+00:00"},{"alias_kind":"pith_short_8","alias_value":"WKUAV6JD","created_at":"2026-06-02T01:03:57.371133+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/WKUAV6JDEWODKUEIZAXW2M3E2M","json":"https://pith.science/pith/WKUAV6JDEWODKUEIZAXW2M3E2M.json","graph_json":"https://pith.science/api/pith-number/WKUAV6JDEWODKUEIZAXW2M3E2M/graph.json","events_json":"https://pith.science/api/pith-number/WKUAV6JDEWODKUEIZAXW2M3E2M/events.json","paper":"https://pith.science/paper/WKUAV6JD"},"agent_actions":{"view_html":"https://pith.science/pith/WKUAV6JDEWODKUEIZAXW2M3E2M","download_json":"https://pith.science/pith/WKUAV6JDEWODKUEIZAXW2M3E2M.json","view_paper":"https://pith.science/paper/WKUAV6JD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2606.00533&json=true","fetch_graph":"https://pith.science/api/pith-number/WKUAV6JDEWODKUEIZAXW2M3E2M/graph.json","fetch_events":"https://pith.science/api/pith-number/WKUAV6JDEWODKUEIZAXW2M3E2M/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WKUAV6JDEWODKUEIZAXW2M3E2M/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WKUAV6JDEWODKUEIZAXW2M3E2M/action/storage_attestation","attest_author":"https://pith.science/pith/WKUAV6JDEWODKUEIZAXW2M3E2M/action/author_attestation","sign_citation":"https://pith.science/pith/WKUAV6JDEWODKUEIZAXW2M3E2M/action/citation_signature","submit_replication":"https://pith.science/pith/WKUAV6JDEWODKUEIZAXW2M3E2M/action/replication_record"}},"created_at":"2026-06-02T01:03:57.371133+00:00","updated_at":"2026-06-02T01:03:57.371133+00:00"}