{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:VEOQ42UOU2TVXCAJOAZKIGW4CV","short_pith_number":"pith:VEOQ42UO","schema_version":"1.0","canonical_sha256":"a91d0e6a8ea6a75b88097032a41adc1579e499c0a7c5c620c5ff54e239d618a5","source":{"kind":"arxiv","id":"1706.03240","version":1},"attestation_state":"computed","paper":{"title":"Example of C-rigid polytopes which are not B-rigid","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AT","authors_text":"Kyoungsuk Park, Suyoung Choi","submitted_at":"2017-06-10T14:19:16Z","abstract_excerpt":"A simple polytope $P$ is said to be \\emph{B-rigid} if its combinatorial structure is characterized by its Tor-algebra, and is said to be \\emph{C-rigid} if its combinatorial structure is characterized by the cohomology ring of a quasitoric manifold over $P$. It is known that a B-rigid simple polytope is C-rigid. In this paper, we, further, show that the B-rigidity is not equivalent to the C-rigidity."},"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":"1706.03240","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2017-06-10T14:19:16Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"4c0c66ff99822c78bbc94ad993203d3e39cfa36639a77e3689b018a6d4dd31dd","abstract_canon_sha256":"ccbaaaa577a42bfa53dbf7fc5851817e8b596e31c0cc7a7901166ed2fdda6f30"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:42:38.084455Z","signature_b64":"nUkgbJ0bKHPOFNY1UU65zMkahOHCPtIZwj3DfW5GHvio/NfeqeLb/t7NuJeKy27yBGf9vZ+wgS3CH1j6x+p8AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a91d0e6a8ea6a75b88097032a41adc1579e499c0a7c5c620c5ff54e239d618a5","last_reissued_at":"2026-05-18T00:42:38.083862Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:42:38.083862Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Example of C-rigid polytopes which are not B-rigid","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AT","authors_text":"Kyoungsuk Park, Suyoung Choi","submitted_at":"2017-06-10T14:19:16Z","abstract_excerpt":"A simple polytope $P$ is said to be \\emph{B-rigid} if its combinatorial structure is characterized by its Tor-algebra, and is said to be \\emph{C-rigid} if its combinatorial structure is characterized by the cohomology ring of a quasitoric manifold over $P$. It is known that a B-rigid simple polytope is C-rigid. In this paper, we, further, show that the B-rigidity is not equivalent to the C-rigidity."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.03240","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":"1706.03240","created_at":"2026-05-18T00:42:38.083957+00:00"},{"alias_kind":"arxiv_version","alias_value":"1706.03240v1","created_at":"2026-05-18T00:42:38.083957+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.03240","created_at":"2026-05-18T00:42:38.083957+00:00"},{"alias_kind":"pith_short_12","alias_value":"VEOQ42UOU2TV","created_at":"2026-05-18T12:31:49.984773+00:00"},{"alias_kind":"pith_short_16","alias_value":"VEOQ42UOU2TVXCAJ","created_at":"2026-05-18T12:31:49.984773+00:00"},{"alias_kind":"pith_short_8","alias_value":"VEOQ42UO","created_at":"2026-05-18T12:31:49.984773+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/VEOQ42UOU2TVXCAJOAZKIGW4CV","json":"https://pith.science/pith/VEOQ42UOU2TVXCAJOAZKIGW4CV.json","graph_json":"https://pith.science/api/pith-number/VEOQ42UOU2TVXCAJOAZKIGW4CV/graph.json","events_json":"https://pith.science/api/pith-number/VEOQ42UOU2TVXCAJOAZKIGW4CV/events.json","paper":"https://pith.science/paper/VEOQ42UO"},"agent_actions":{"view_html":"https://pith.science/pith/VEOQ42UOU2TVXCAJOAZKIGW4CV","download_json":"https://pith.science/pith/VEOQ42UOU2TVXCAJOAZKIGW4CV.json","view_paper":"https://pith.science/paper/VEOQ42UO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1706.03240&json=true","fetch_graph":"https://pith.science/api/pith-number/VEOQ42UOU2TVXCAJOAZKIGW4CV/graph.json","fetch_events":"https://pith.science/api/pith-number/VEOQ42UOU2TVXCAJOAZKIGW4CV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VEOQ42UOU2TVXCAJOAZKIGW4CV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VEOQ42UOU2TVXCAJOAZKIGW4CV/action/storage_attestation","attest_author":"https://pith.science/pith/VEOQ42UOU2TVXCAJOAZKIGW4CV/action/author_attestation","sign_citation":"https://pith.science/pith/VEOQ42UOU2TVXCAJOAZKIGW4CV/action/citation_signature","submit_replication":"https://pith.science/pith/VEOQ42UOU2TVXCAJOAZKIGW4CV/action/replication_record"}},"created_at":"2026-05-18T00:42:38.083957+00:00","updated_at":"2026-05-18T00:42:38.083957+00:00"}