{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:MZUB7YRG5L2EUS572FVV4LHFOE","short_pith_number":"pith:MZUB7YRG","schema_version":"1.0","canonical_sha256":"66681fe226eaf44a4bbfd16b5e2ce5710038e4c2dcf1bd18bade7ec8366f97cf","source":{"kind":"arxiv","id":"1511.08647","version":3},"attestation_state":"computed","paper":{"title":"Tight Bounds for Gomory-Hu-like Cut Counting","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.DS","authors_text":"Lior Kamma, Rajesh Chitnis, Robert Krauthgamer","submitted_at":"2015-11-27T12:40:24Z","abstract_excerpt":"By a classical result of Gomory and Hu (1961), in every edge-weighted graph $G=(V,E,w)$, the minimum $st$-cut values, when ranging over all $s,t\\in V$, take at most $|V|-1$ distinct values. That is, these $\\binom{|V|}{2}$ instances exhibit redundancy factor $\\Omega(|V|)$. They further showed how to construct from $G$ a tree $(V,E',w')$ that stores all minimum $st$-cut values. Motivated by this result, we obtain tight bounds for the redundancy factor of several generalizations of the minimum $st$-cut problem.\n  1. Group-Cut: Consider the minimum $(A,B)$-cut, ranging over all subsets $A,B\\subset"},"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":"1511.08647","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-11-27T12:40:24Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"0f239e733d6314030891509850c8723f933c25ca942a9876c931b3b3384f25a6","abstract_canon_sha256":"133b1b85250ca751a5aabb209b1f5c0f563f0ba7c005bd1fa055b352c39df00e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:28:57.178456Z","signature_b64":"yx5bJqKw2/EZr9S8TPmbiBXEdo9JhB9Z43/l59XlfgNPsyG5x+TfbHXh6Ha6iRiB6Wri+I+5HdmrGxVrXxt3Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"66681fe226eaf44a4bbfd16b5e2ce5710038e4c2dcf1bd18bade7ec8366f97cf","last_reissued_at":"2026-05-18T00:28:57.177996Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:28:57.177996Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Tight Bounds for Gomory-Hu-like Cut Counting","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.DS","authors_text":"Lior Kamma, Rajesh Chitnis, Robert Krauthgamer","submitted_at":"2015-11-27T12:40:24Z","abstract_excerpt":"By a classical result of Gomory and Hu (1961), in every edge-weighted graph $G=(V,E,w)$, the minimum $st$-cut values, when ranging over all $s,t\\in V$, take at most $|V|-1$ distinct values. That is, these $\\binom{|V|}{2}$ instances exhibit redundancy factor $\\Omega(|V|)$. They further showed how to construct from $G$ a tree $(V,E',w')$ that stores all minimum $st$-cut values. Motivated by this result, we obtain tight bounds for the redundancy factor of several generalizations of the minimum $st$-cut problem.\n  1. Group-Cut: Consider the minimum $(A,B)$-cut, ranging over all subsets $A,B\\subset"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.08647","kind":"arxiv","version":3},"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":"1511.08647","created_at":"2026-05-18T00:28:57.178066+00:00"},{"alias_kind":"arxiv_version","alias_value":"1511.08647v3","created_at":"2026-05-18T00:28:57.178066+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.08647","created_at":"2026-05-18T00:28:57.178066+00:00"},{"alias_kind":"pith_short_12","alias_value":"MZUB7YRG5L2E","created_at":"2026-05-18T12:29:32.376354+00:00"},{"alias_kind":"pith_short_16","alias_value":"MZUB7YRG5L2EUS57","created_at":"2026-05-18T12:29:32.376354+00:00"},{"alias_kind":"pith_short_8","alias_value":"MZUB7YRG","created_at":"2026-05-18T12:29:32.376354+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/MZUB7YRG5L2EUS572FVV4LHFOE","json":"https://pith.science/pith/MZUB7YRG5L2EUS572FVV4LHFOE.json","graph_json":"https://pith.science/api/pith-number/MZUB7YRG5L2EUS572FVV4LHFOE/graph.json","events_json":"https://pith.science/api/pith-number/MZUB7YRG5L2EUS572FVV4LHFOE/events.json","paper":"https://pith.science/paper/MZUB7YRG"},"agent_actions":{"view_html":"https://pith.science/pith/MZUB7YRG5L2EUS572FVV4LHFOE","download_json":"https://pith.science/pith/MZUB7YRG5L2EUS572FVV4LHFOE.json","view_paper":"https://pith.science/paper/MZUB7YRG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1511.08647&json=true","fetch_graph":"https://pith.science/api/pith-number/MZUB7YRG5L2EUS572FVV4LHFOE/graph.json","fetch_events":"https://pith.science/api/pith-number/MZUB7YRG5L2EUS572FVV4LHFOE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MZUB7YRG5L2EUS572FVV4LHFOE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MZUB7YRG5L2EUS572FVV4LHFOE/action/storage_attestation","attest_author":"https://pith.science/pith/MZUB7YRG5L2EUS572FVV4LHFOE/action/author_attestation","sign_citation":"https://pith.science/pith/MZUB7YRG5L2EUS572FVV4LHFOE/action/citation_signature","submit_replication":"https://pith.science/pith/MZUB7YRG5L2EUS572FVV4LHFOE/action/replication_record"}},"created_at":"2026-05-18T00:28:57.178066+00:00","updated_at":"2026-05-18T00:28:57.178066+00:00"}