{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:YIFNPMUOFT4HOTPR546RCXFLMN","short_pith_number":"pith:YIFNPMUO","schema_version":"1.0","canonical_sha256":"c20ad7b28e2cf8774df1ef3d115cab63776c1f0555d3059a2375a62c86b7101f","source":{"kind":"arxiv","id":"1703.03320","version":1},"attestation_state":"computed","paper":{"title":"Independence-Domination duality in weighted graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Irina Gorelik, Ron Aharoni","submitted_at":"2017-03-09T16:10:37Z","abstract_excerpt":"Given a partition ${\\mathcal V}=(V_1, \\ldots,V_m)$ of the vertex set of a graph $G$, an {\\em independent transversal} (IT) is an independent set in $G$ that contains one vertex from each $V_i$. A {\\em fractional IT} is a non-negative real valued function on $V(G)$ that represents each part with total weight at least $1$, and belongs as a vector to the convex hull of the incidence vectors of independent sets in the graph. It is known that if the domination number of the graph induced on the union of every $k$ parts $V_i$ is at least $k$, then there is a fractional IT. We prove a weighted versio"},"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":"1703.03320","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-03-09T16:10:37Z","cross_cats_sorted":[],"title_canon_sha256":"c31d757b8e5914ff710c32790879d95843bbd6c586d3955732743c0fecfbe25f","abstract_canon_sha256":"0a3e3bda6f458d3c606a6fd4665882d727a859f54baa58a41a9a507cdf41ccde"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:49:00.688366Z","signature_b64":"lwvq3773916uhaLITtLLa0Q1kLWc4iQK//Yyu4EMqplvoid/2wEE5UeUht9A3ge1UsQjr4hM/mrA/ld9U9/2Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c20ad7b28e2cf8774df1ef3d115cab63776c1f0555d3059a2375a62c86b7101f","last_reissued_at":"2026-05-18T00:49:00.687742Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:49:00.687742Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Independence-Domination duality in weighted graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Irina Gorelik, Ron Aharoni","submitted_at":"2017-03-09T16:10:37Z","abstract_excerpt":"Given a partition ${\\mathcal V}=(V_1, \\ldots,V_m)$ of the vertex set of a graph $G$, an {\\em independent transversal} (IT) is an independent set in $G$ that contains one vertex from each $V_i$. A {\\em fractional IT} is a non-negative real valued function on $V(G)$ that represents each part with total weight at least $1$, and belongs as a vector to the convex hull of the incidence vectors of independent sets in the graph. It is known that if the domination number of the graph induced on the union of every $k$ parts $V_i$ is at least $k$, then there is a fractional IT. We prove a weighted versio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.03320","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":""},"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":"1703.03320","created_at":"2026-05-18T00:49:00.687843+00:00"},{"alias_kind":"arxiv_version","alias_value":"1703.03320v1","created_at":"2026-05-18T00:49:00.687843+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.03320","created_at":"2026-05-18T00:49:00.687843+00:00"},{"alias_kind":"pith_short_12","alias_value":"YIFNPMUOFT4H","created_at":"2026-05-18T12:31:56.362134+00:00"},{"alias_kind":"pith_short_16","alias_value":"YIFNPMUOFT4HOTPR","created_at":"2026-05-18T12:31:56.362134+00:00"},{"alias_kind":"pith_short_8","alias_value":"YIFNPMUO","created_at":"2026-05-18T12:31:56.362134+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/YIFNPMUOFT4HOTPR546RCXFLMN","json":"https://pith.science/pith/YIFNPMUOFT4HOTPR546RCXFLMN.json","graph_json":"https://pith.science/api/pith-number/YIFNPMUOFT4HOTPR546RCXFLMN/graph.json","events_json":"https://pith.science/api/pith-number/YIFNPMUOFT4HOTPR546RCXFLMN/events.json","paper":"https://pith.science/paper/YIFNPMUO"},"agent_actions":{"view_html":"https://pith.science/pith/YIFNPMUOFT4HOTPR546RCXFLMN","download_json":"https://pith.science/pith/YIFNPMUOFT4HOTPR546RCXFLMN.json","view_paper":"https://pith.science/paper/YIFNPMUO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1703.03320&json=true","fetch_graph":"https://pith.science/api/pith-number/YIFNPMUOFT4HOTPR546RCXFLMN/graph.json","fetch_events":"https://pith.science/api/pith-number/YIFNPMUOFT4HOTPR546RCXFLMN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YIFNPMUOFT4HOTPR546RCXFLMN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YIFNPMUOFT4HOTPR546RCXFLMN/action/storage_attestation","attest_author":"https://pith.science/pith/YIFNPMUOFT4HOTPR546RCXFLMN/action/author_attestation","sign_citation":"https://pith.science/pith/YIFNPMUOFT4HOTPR546RCXFLMN/action/citation_signature","submit_replication":"https://pith.science/pith/YIFNPMUOFT4HOTPR546RCXFLMN/action/replication_record"}},"created_at":"2026-05-18T00:49:00.687843+00:00","updated_at":"2026-05-18T00:49:00.687843+00:00"}