{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:EBLMAGZQ52KKVAIDN5XFTNG526","short_pith_number":"pith:EBLMAGZQ","schema_version":"1.0","canonical_sha256":"2056c01b30ee94aa81036f6e59b4ddd785ae50ec17747b9a7a0fd1d3965a9f8a","source":{"kind":"arxiv","id":"1610.04400","version":2},"attestation_state":"computed","paper":{"title":"Pairwise intersecting homothets of a convex body","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.MG","authors_text":"Alexandr Polyanskii","submitted_at":"2016-10-14T10:36:19Z","abstract_excerpt":"We show that the maximum number of pairwise intersecting positive homothets of a $d$-dimensional centrally symmetric convex body, none of which contains the center of another in its interior, is at most $3^{d+1}$. Also, we improve upper bounds for cardinalities of $k$-distance sets in Minkowski spaces."},"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":"1610.04400","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2016-10-14T10:36:19Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"f4df300d922781f7a47926b166c88ba2679e8d808a4cbf4e1f9cb343ced8d734","abstract_canon_sha256":"37cddd96c6792f1c33eada0c14cd835005cd354b5e68c937731951c1e4767892"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:48:47.903885Z","signature_b64":"QAg+MCL1CNRQH6IwCBWCLbG9NkqvfrMVkf5V+xWu70UFgqlS3lR/7p3kTWt5Ydy+ctzDQkqK061v5rjPEATkBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2056c01b30ee94aa81036f6e59b4ddd785ae50ec17747b9a7a0fd1d3965a9f8a","last_reissued_at":"2026-05-17T23:48:47.903328Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:48:47.903328Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Pairwise intersecting homothets of a convex body","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.MG","authors_text":"Alexandr Polyanskii","submitted_at":"2016-10-14T10:36:19Z","abstract_excerpt":"We show that the maximum number of pairwise intersecting positive homothets of a $d$-dimensional centrally symmetric convex body, none of which contains the center of another in its interior, is at most $3^{d+1}$. Also, we improve upper bounds for cardinalities of $k$-distance sets in Minkowski spaces."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.04400","kind":"arxiv","version":2},"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":"1610.04400","created_at":"2026-05-17T23:48:47.903413+00:00"},{"alias_kind":"arxiv_version","alias_value":"1610.04400v2","created_at":"2026-05-17T23:48:47.903413+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.04400","created_at":"2026-05-17T23:48:47.903413+00:00"},{"alias_kind":"pith_short_12","alias_value":"EBLMAGZQ52KK","created_at":"2026-05-18T12:30:12.583610+00:00"},{"alias_kind":"pith_short_16","alias_value":"EBLMAGZQ52KKVAID","created_at":"2026-05-18T12:30:12.583610+00:00"},{"alias_kind":"pith_short_8","alias_value":"EBLMAGZQ","created_at":"2026-05-18T12:30:12.583610+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/EBLMAGZQ52KKVAIDN5XFTNG526","json":"https://pith.science/pith/EBLMAGZQ52KKVAIDN5XFTNG526.json","graph_json":"https://pith.science/api/pith-number/EBLMAGZQ52KKVAIDN5XFTNG526/graph.json","events_json":"https://pith.science/api/pith-number/EBLMAGZQ52KKVAIDN5XFTNG526/events.json","paper":"https://pith.science/paper/EBLMAGZQ"},"agent_actions":{"view_html":"https://pith.science/pith/EBLMAGZQ52KKVAIDN5XFTNG526","download_json":"https://pith.science/pith/EBLMAGZQ52KKVAIDN5XFTNG526.json","view_paper":"https://pith.science/paper/EBLMAGZQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1610.04400&json=true","fetch_graph":"https://pith.science/api/pith-number/EBLMAGZQ52KKVAIDN5XFTNG526/graph.json","fetch_events":"https://pith.science/api/pith-number/EBLMAGZQ52KKVAIDN5XFTNG526/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/EBLMAGZQ52KKVAIDN5XFTNG526/action/timestamp_anchor","attest_storage":"https://pith.science/pith/EBLMAGZQ52KKVAIDN5XFTNG526/action/storage_attestation","attest_author":"https://pith.science/pith/EBLMAGZQ52KKVAIDN5XFTNG526/action/author_attestation","sign_citation":"https://pith.science/pith/EBLMAGZQ52KKVAIDN5XFTNG526/action/citation_signature","submit_replication":"https://pith.science/pith/EBLMAGZQ52KKVAIDN5XFTNG526/action/replication_record"}},"created_at":"2026-05-17T23:48:47.903413+00:00","updated_at":"2026-05-17T23:48:47.903413+00:00"}