{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:MTFGI77ONGYMA3CNIKIOS5X4S5","short_pith_number":"pith:MTFGI77O","schema_version":"1.0","canonical_sha256":"64ca647fee69b0c06c4d4290e976fc974d4ab01b380d461b7cef8db21a4c44cd","source":{"kind":"arxiv","id":"1510.00354","version":3},"attestation_state":"computed","paper":{"title":"On the Sensitivity of k-Uniform Hypergraph Properties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Ang Li, Kevin Cuddy, Min Jae Song, Stella Biderman","submitted_at":"2015-10-01T18:19:55Z","abstract_excerpt":"In this paper we present a graph property with sensitivity $\\Theta(\\sqrt{n})$, where $n={v\\choose2}$ is the number of variables, and generalize it to a $k$-uniform hypergraph property with sensitivity $\\Theta(\\sqrt{n})$, where $n={v\\choose k}$ is again the number of variables. This yields the smallest sensitivity yet achieved for a $k$-uniform hypergraph property. We then show that, for even $k$, there is a $k$-uniform hypergraph property that demonstrates a quadratic gap between sensitivity and block sensitivity. This matches the largest known gap found by Ambainis and Sun (2011) for Boolean "},"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":"1510.00354","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2015-10-01T18:19:55Z","cross_cats_sorted":[],"title_canon_sha256":"335adad21c7cdb98b717f286b088ab5069f0451f63c92123b51b1c22ba58ab38","abstract_canon_sha256":"c46a611f1d850b2bf2406cd079f03ae988d21375fca419dd68cf3fb29fed394a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:34:31.893205Z","signature_b64":"NoXL4KwNzItsEXEpxqlAXU/sgT5x7yPV8Y0B43fkgyFytKJnbrFYl4qk4jt5OYeKOVhTQWIBOIUjScOiD64rDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"64ca647fee69b0c06c4d4290e976fc974d4ab01b380d461b7cef8db21a4c44cd","last_reissued_at":"2026-05-18T00:34:31.892861Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:34:31.892861Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the Sensitivity of k-Uniform Hypergraph Properties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Ang Li, Kevin Cuddy, Min Jae Song, Stella Biderman","submitted_at":"2015-10-01T18:19:55Z","abstract_excerpt":"In this paper we present a graph property with sensitivity $\\Theta(\\sqrt{n})$, where $n={v\\choose2}$ is the number of variables, and generalize it to a $k$-uniform hypergraph property with sensitivity $\\Theta(\\sqrt{n})$, where $n={v\\choose k}$ is again the number of variables. This yields the smallest sensitivity yet achieved for a $k$-uniform hypergraph property. We then show that, for even $k$, there is a $k$-uniform hypergraph property that demonstrates a quadratic gap between sensitivity and block sensitivity. This matches the largest known gap found by Ambainis and Sun (2011) for Boolean "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.00354","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":"1510.00354","created_at":"2026-05-18T00:34:31.892914+00:00"},{"alias_kind":"arxiv_version","alias_value":"1510.00354v3","created_at":"2026-05-18T00:34:31.892914+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.00354","created_at":"2026-05-18T00:34:31.892914+00:00"},{"alias_kind":"pith_short_12","alias_value":"MTFGI77ONGYM","created_at":"2026-05-18T12:29:32.376354+00:00"},{"alias_kind":"pith_short_16","alias_value":"MTFGI77ONGYMA3CN","created_at":"2026-05-18T12:29:32.376354+00:00"},{"alias_kind":"pith_short_8","alias_value":"MTFGI77O","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/MTFGI77ONGYMA3CNIKIOS5X4S5","json":"https://pith.science/pith/MTFGI77ONGYMA3CNIKIOS5X4S5.json","graph_json":"https://pith.science/api/pith-number/MTFGI77ONGYMA3CNIKIOS5X4S5/graph.json","events_json":"https://pith.science/api/pith-number/MTFGI77ONGYMA3CNIKIOS5X4S5/events.json","paper":"https://pith.science/paper/MTFGI77O"},"agent_actions":{"view_html":"https://pith.science/pith/MTFGI77ONGYMA3CNIKIOS5X4S5","download_json":"https://pith.science/pith/MTFGI77ONGYMA3CNIKIOS5X4S5.json","view_paper":"https://pith.science/paper/MTFGI77O","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1510.00354&json=true","fetch_graph":"https://pith.science/api/pith-number/MTFGI77ONGYMA3CNIKIOS5X4S5/graph.json","fetch_events":"https://pith.science/api/pith-number/MTFGI77ONGYMA3CNIKIOS5X4S5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MTFGI77ONGYMA3CNIKIOS5X4S5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MTFGI77ONGYMA3CNIKIOS5X4S5/action/storage_attestation","attest_author":"https://pith.science/pith/MTFGI77ONGYMA3CNIKIOS5X4S5/action/author_attestation","sign_citation":"https://pith.science/pith/MTFGI77ONGYMA3CNIKIOS5X4S5/action/citation_signature","submit_replication":"https://pith.science/pith/MTFGI77ONGYMA3CNIKIOS5X4S5/action/replication_record"}},"created_at":"2026-05-18T00:34:31.892914+00:00","updated_at":"2026-05-18T00:34:31.892914+00:00"}