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We show the following new results.\n  1. Given an uncapacitated hypergraph $H$ and an integer $k$ we describe an algorithm that runs in $O(p)$ time to find a subhypergraph $H'$ with sum of degrees $O(kn)$ that preserves all edge-connectivities up to $k$ (a $k$-sparsifie"},"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":"1607.08682","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2016-07-29T03:22:56Z","cross_cats_sorted":[],"title_canon_sha256":"75a1316c43059635b539dcae169b897c3d982a5376ab3ad2b12c312e24e6f92d","abstract_canon_sha256":"4becc9ed72b677bea67364c18e8db28430c179c0cfd3e60ebb72818e0f442c2c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:44:37.074338Z","signature_b64":"5ks4aKQD6GWBj1idISZEC9VO19r/oVGySLlrqxoQqcyUwtiv2AYss8Xj1NlTg8mx9sSmYcdF0gzeby6EwuLSBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"13300828c7f9a1da5cafce2356099813b0c293db9740266371c9f074d8ebaf8c","last_reissued_at":"2026-05-18T00:44:37.073878Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:44:37.073878Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Computing minimum cuts in hypergraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Chandra Chekuri, Chao Xu","submitted_at":"2016-07-29T03:22:56Z","abstract_excerpt":"We study algorithmic and structural aspects of connectivity in hypergraphs. 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Given an uncapacitated hypergraph $H$ and an integer $k$ we describe an algorithm that runs in $O(p)$ time to find a subhypergraph $H'$ with sum of degrees $O(kn)$ that preserves all edge-connectivities up to $k$ (a $k$-sparsifie"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.08682","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":"1607.08682","created_at":"2026-05-18T00:44:37.073941+00:00"},{"alias_kind":"arxiv_version","alias_value":"1607.08682v3","created_at":"2026-05-18T00:44:37.073941+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.08682","created_at":"2026-05-18T00:44:37.073941+00:00"},{"alias_kind":"pith_short_12","alias_value":"CMYAQKGH7GQ5","created_at":"2026-05-18T12:30:09.641336+00:00"},{"alias_kind":"pith_short_16","alias_value":"CMYAQKGH7GQ5UXFP","created_at":"2026-05-18T12:30:09.641336+00:00"},{"alias_kind":"pith_short_8","alias_value":"CMYAQKGH","created_at":"2026-05-18T12:30:09.641336+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/CMYAQKGH7GQ5UXFPZYRVMCMYCO","json":"https://pith.science/pith/CMYAQKGH7GQ5UXFPZYRVMCMYCO.json","graph_json":"https://pith.science/api/pith-number/CMYAQKGH7GQ5UXFPZYRVMCMYCO/graph.json","events_json":"https://pith.science/api/pith-number/CMYAQKGH7GQ5UXFPZYRVMCMYCO/events.json","paper":"https://pith.science/paper/CMYAQKGH"},"agent_actions":{"view_html":"https://pith.science/pith/CMYAQKGH7GQ5UXFPZYRVMCMYCO","download_json":"https://pith.science/pith/CMYAQKGH7GQ5UXFPZYRVMCMYCO.json","view_paper":"https://pith.science/paper/CMYAQKGH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1607.08682&json=true","fetch_graph":"https://pith.science/api/pith-number/CMYAQKGH7GQ5UXFPZYRVMCMYCO/graph.json","fetch_events":"https://pith.science/api/pith-number/CMYAQKGH7GQ5UXFPZYRVMCMYCO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CMYAQKGH7GQ5UXFPZYRVMCMYCO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CMYAQKGH7GQ5UXFPZYRVMCMYCO/action/storage_attestation","attest_author":"https://pith.science/pith/CMYAQKGH7GQ5UXFPZYRVMCMYCO/action/author_attestation","sign_citation":"https://pith.science/pith/CMYAQKGH7GQ5UXFPZYRVMCMYCO/action/citation_signature","submit_replication":"https://pith.science/pith/CMYAQKGH7GQ5UXFPZYRVMCMYCO/action/replication_record"}},"created_at":"2026-05-18T00:44:37.073941+00:00","updated_at":"2026-05-18T00:44:37.073941+00:00"}