{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:ZJFDHMAHXOX777UIMTY3Y52SVF","short_pith_number":"pith:ZJFDHMAH","schema_version":"1.0","canonical_sha256":"ca4a33b007bbaffffe8864f1bc7752a974c8f198934cedbb7f5aae151f11a7dd","source":{"kind":"arxiv","id":"2401.11525","version":1},"attestation_state":"computed","paper":{"title":"Weak rainbow saturation numbers of graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Jie Ma, Tianying Xie, Xihe Li","submitted_at":"2024-01-21T15:37:47Z","abstract_excerpt":"For a fixed graph $H$, we say that an edge-colored graph $G$ is \\emph{weakly $H$-rainbow saturated} if there exists an ordering $e_1, e_2, \\ldots, e_m$ of $E\\left(\\overline{G}\\right)$ such that, for any list $c_1, c_2, \\ldots, c_m$ of pairwise distinct colors from $\\mathbb{N}$, the non-edges $e_i$ in color $c_i$ can be added to $G$, one at a time, so that every added edge creates a new rainbow copy of $H$. The \\emph{weak rainbow saturation number} of $H$, denoted by $rwsat(n,H)$, is the minimum number of edges in a weakly $H$-rainbow saturated graph on $n$ vertices. In this paper, we show that"},"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":"2401.11525","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2024-01-21T15:37:47Z","cross_cats_sorted":[],"title_canon_sha256":"cd7dd6fbfd478fab0e446199e1ea1e6b4b370c95fb073c7a49bc336f066b7119","abstract_canon_sha256":"dab1538bf865668da8c6fa5af7bf6d5d9230ec579709ed6ab97bad632a8e0ddf"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:57:19.087081Z","signature_b64":"hLaSCgjWbncccUPOH1pq2AX7TY8hVHrmecYxrcf+I5Bt0yv4uZd6MUzpgOuD7l7sP45sbl12QzjHYavr8ojXAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ca4a33b007bbaffffe8864f1bc7752a974c8f198934cedbb7f5aae151f11a7dd","last_reissued_at":"2026-07-05T09:57:19.086564Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:57:19.086564Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Weak rainbow saturation numbers of graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Jie Ma, Tianying Xie, Xihe Li","submitted_at":"2024-01-21T15:37:47Z","abstract_excerpt":"For a fixed graph $H$, we say that an edge-colored graph $G$ is \\emph{weakly $H$-rainbow saturated} if there exists an ordering $e_1, e_2, \\ldots, e_m$ of $E\\left(\\overline{G}\\right)$ such that, for any list $c_1, c_2, \\ldots, c_m$ of pairwise distinct colors from $\\mathbb{N}$, the non-edges $e_i$ in color $c_i$ can be added to $G$, one at a time, so that every added edge creates a new rainbow copy of $H$. The \\emph{weak rainbow saturation number} of $H$, denoted by $rwsat(n,H)$, is the minimum number of edges in a weakly $H$-rainbow saturated graph on $n$ vertices. In this paper, we show that"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2401.11525","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/2401.11525/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":"2401.11525","created_at":"2026-07-05T09:57:19.086631+00:00"},{"alias_kind":"arxiv_version","alias_value":"2401.11525v1","created_at":"2026-07-05T09:57:19.086631+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2401.11525","created_at":"2026-07-05T09:57:19.086631+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZJFDHMAHXOX7","created_at":"2026-07-05T09:57:19.086631+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZJFDHMAHXOX777UI","created_at":"2026-07-05T09:57:19.086631+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZJFDHMAH","created_at":"2026-07-05T09:57:19.086631+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/ZJFDHMAHXOX777UIMTY3Y52SVF","json":"https://pith.science/pith/ZJFDHMAHXOX777UIMTY3Y52SVF.json","graph_json":"https://pith.science/api/pith-number/ZJFDHMAHXOX777UIMTY3Y52SVF/graph.json","events_json":"https://pith.science/api/pith-number/ZJFDHMAHXOX777UIMTY3Y52SVF/events.json","paper":"https://pith.science/paper/ZJFDHMAH"},"agent_actions":{"view_html":"https://pith.science/pith/ZJFDHMAHXOX777UIMTY3Y52SVF","download_json":"https://pith.science/pith/ZJFDHMAHXOX777UIMTY3Y52SVF.json","view_paper":"https://pith.science/paper/ZJFDHMAH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2401.11525&json=true","fetch_graph":"https://pith.science/api/pith-number/ZJFDHMAHXOX777UIMTY3Y52SVF/graph.json","fetch_events":"https://pith.science/api/pith-number/ZJFDHMAHXOX777UIMTY3Y52SVF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZJFDHMAHXOX777UIMTY3Y52SVF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZJFDHMAHXOX777UIMTY3Y52SVF/action/storage_attestation","attest_author":"https://pith.science/pith/ZJFDHMAHXOX777UIMTY3Y52SVF/action/author_attestation","sign_citation":"https://pith.science/pith/ZJFDHMAHXOX777UIMTY3Y52SVF/action/citation_signature","submit_replication":"https://pith.science/pith/ZJFDHMAHXOX777UIMTY3Y52SVF/action/replication_record"}},"created_at":"2026-07-05T09:57:19.086631+00:00","updated_at":"2026-07-05T09:57:19.086631+00:00"}