{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:D2HFE4WPJTOCPYT4PQYOBKMTZV","short_pith_number":"pith:D2HFE4WP","schema_version":"1.0","canonical_sha256":"1e8e5272cf4cdc27e27c7c30e0a993cd6caae146d3df3a3e77e53c8b1707e6ad","source":{"kind":"arxiv","id":"1003.4122","version":1},"attestation_state":"computed","paper":{"title":"Covariogram of non-convex sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"Carlo Benassi, Gabriele Bianchi, Giuliana D'Ercole","submitted_at":"2010-03-22T10:49:43Z","abstract_excerpt":"The covariogram of a compact set A contained in R^n is the function that to each x in R^n associates the volume of A intersected with (A+x). Recently it has been proved that the covariogram determines any planar convex body, in the class of all convex bodies. We extend the class of sets in which a planar convex body is determined by its covariogram. Moreover, we prove that there is no pair of  non-congruent planar polyominoes consisting of less than 9 points that have equal discrete covariogram."},"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":"1003.4122","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2010-03-22T10:49:43Z","cross_cats_sorted":[],"title_canon_sha256":"a172b91e93fcb3cc9d1b97c986c1142a1885638e94ecb868a3f22af6680174da","abstract_canon_sha256":"f054412094df0c1d22ff1790b6121f138ec76dacb461e0cbb7cb46b78c7d031d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:41:26.126147Z","signature_b64":"0pWQrqJbpEqeis7X37KRq7dF+JR6Uvncl4cMxN3z+2HnrhZbMtuifpYzuHRVehLfoLgIqcbKD5PHxfhaCmtGAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1e8e5272cf4cdc27e27c7c30e0a993cd6caae146d3df3a3e77e53c8b1707e6ad","last_reissued_at":"2026-05-18T04:41:26.125568Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:41:26.125568Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Covariogram of non-convex sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"Carlo Benassi, Gabriele Bianchi, Giuliana D'Ercole","submitted_at":"2010-03-22T10:49:43Z","abstract_excerpt":"The covariogram of a compact set A contained in R^n is the function that to each x in R^n associates the volume of A intersected with (A+x). Recently it has been proved that the covariogram determines any planar convex body, in the class of all convex bodies. We extend the class of sets in which a planar convex body is determined by its covariogram. Moreover, we prove that there is no pair of  non-congruent planar polyominoes consisting of less than 9 points that have equal discrete covariogram."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1003.4122","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":"1003.4122","created_at":"2026-05-18T04:41:26.125655+00:00"},{"alias_kind":"arxiv_version","alias_value":"1003.4122v1","created_at":"2026-05-18T04:41:26.125655+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1003.4122","created_at":"2026-05-18T04:41:26.125655+00:00"},{"alias_kind":"pith_short_12","alias_value":"D2HFE4WPJTOC","created_at":"2026-05-18T12:26:06.534383+00:00"},{"alias_kind":"pith_short_16","alias_value":"D2HFE4WPJTOCPYT4","created_at":"2026-05-18T12:26:06.534383+00:00"},{"alias_kind":"pith_short_8","alias_value":"D2HFE4WP","created_at":"2026-05-18T12:26:06.534383+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/D2HFE4WPJTOCPYT4PQYOBKMTZV","json":"https://pith.science/pith/D2HFE4WPJTOCPYT4PQYOBKMTZV.json","graph_json":"https://pith.science/api/pith-number/D2HFE4WPJTOCPYT4PQYOBKMTZV/graph.json","events_json":"https://pith.science/api/pith-number/D2HFE4WPJTOCPYT4PQYOBKMTZV/events.json","paper":"https://pith.science/paper/D2HFE4WP"},"agent_actions":{"view_html":"https://pith.science/pith/D2HFE4WPJTOCPYT4PQYOBKMTZV","download_json":"https://pith.science/pith/D2HFE4WPJTOCPYT4PQYOBKMTZV.json","view_paper":"https://pith.science/paper/D2HFE4WP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1003.4122&json=true","fetch_graph":"https://pith.science/api/pith-number/D2HFE4WPJTOCPYT4PQYOBKMTZV/graph.json","fetch_events":"https://pith.science/api/pith-number/D2HFE4WPJTOCPYT4PQYOBKMTZV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/D2HFE4WPJTOCPYT4PQYOBKMTZV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/D2HFE4WPJTOCPYT4PQYOBKMTZV/action/storage_attestation","attest_author":"https://pith.science/pith/D2HFE4WPJTOCPYT4PQYOBKMTZV/action/author_attestation","sign_citation":"https://pith.science/pith/D2HFE4WPJTOCPYT4PQYOBKMTZV/action/citation_signature","submit_replication":"https://pith.science/pith/D2HFE4WPJTOCPYT4PQYOBKMTZV/action/replication_record"}},"created_at":"2026-05-18T04:41:26.125655+00:00","updated_at":"2026-05-18T04:41:26.125655+00:00"}