{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:XCYGHYUI3AABIZXTJ2GKPPETLB","short_pith_number":"pith:XCYGHYUI","canonical_record":{"source":{"id":"1902.06895","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2019-02-19T05:04:11Z","cross_cats_sorted":["math.CO","math.GT"],"title_canon_sha256":"49f7caabf30a46e7a35f81e83529f2f24212238c6a3453090e3e891742d21b0c","abstract_canon_sha256":"a607bf72bffff7f298697c006b7d180e3edf1d6a4b147b88a1f57273140f9cce"},"schema_version":"1.0"},"canonical_sha256":"b8b063e288d8001466f34e8ca7bc9358721fbda6bde0e10ce089ad416bcd2376","source":{"kind":"arxiv","id":"1902.06895","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1902.06895","created_at":"2026-05-17T23:53:40Z"},{"alias_kind":"arxiv_version","alias_value":"1902.06895v1","created_at":"2026-05-17T23:53:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.06895","created_at":"2026-05-17T23:53:40Z"},{"alias_kind":"pith_short_12","alias_value":"XCYGHYUI3AAB","created_at":"2026-05-18T12:33:33Z"},{"alias_kind":"pith_short_16","alias_value":"XCYGHYUI3AABIZXT","created_at":"2026-05-18T12:33:33Z"},{"alias_kind":"pith_short_8","alias_value":"XCYGHYUI","created_at":"2026-05-18T12:33:33Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:XCYGHYUI3AABIZXTJ2GKPPETLB","target":"record","payload":{"canonical_record":{"source":{"id":"1902.06895","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2019-02-19T05:04:11Z","cross_cats_sorted":["math.CO","math.GT"],"title_canon_sha256":"49f7caabf30a46e7a35f81e83529f2f24212238c6a3453090e3e891742d21b0c","abstract_canon_sha256":"a607bf72bffff7f298697c006b7d180e3edf1d6a4b147b88a1f57273140f9cce"},"schema_version":"1.0"},"canonical_sha256":"b8b063e288d8001466f34e8ca7bc9358721fbda6bde0e10ce089ad416bcd2376","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:53:40.497599Z","signature_b64":"hyugiCdm8oKiWbCWWrXJlIBszxO1Ta00WqDhMnMnh064MlxYwFciHOObRHSRjrXK43unLxpaZEj7qzQUPRvACQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b8b063e288d8001466f34e8ca7bc9358721fbda6bde0e10ce089ad416bcd2376","last_reissued_at":"2026-05-17T23:53:40.497143Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:53:40.497143Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1902.06895","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:53:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"o79h6LsSD3X+KGDAFxjc8ZjiiclmdK1yww47zV7UVLj0/auAidXS+qmw/cEiNmxeLzZGPFaxct5831qCjz0pAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-20T05:04:56.820345Z"},"content_sha256":"c3d6a259db04962301918e6c7831bbe1a14caf5ccabe767c5772c6af69d34976","schema_version":"1.0","event_id":"sha256:c3d6a259db04962301918e6c7831bbe1a14caf5ccabe767c5772c6af69d34976"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:XCYGHYUI3AABIZXTJ2GKPPETLB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Lickorish type construction of manifolds over simple polytopes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.GT"],"primary_cat":"math.AT","authors_text":"Li Yu, Wei Wang, Zhi L\\\"u","submitted_at":"2019-02-19T05:04:11Z","abstract_excerpt":"This paper is a survey on the Lickorish type construction of some kind of closed manifolds over simple convex polytopes. Inspired by Lickorish's theorem, we propose a method to describe certain families of manifolds over simple convex polytopes with torus action. Under this construction, many classical classification results of these families of manifolds could be interpreted by this construction and some further problems will be discussed."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.06895","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:53:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pwYXn7SOCtOQejNWqD3OCmYbLqosQhcZ7CGmgAWl01iD1a+A22pJc5N0BsX1/DzDn3Q4BxJKw8QApCzI2LukCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-20T05:04:56.821074Z"},"content_sha256":"8f2272dbf929983fc772ff46e68de26fdf521cbdf1be93aa4be9645e82d6924a","schema_version":"1.0","event_id":"sha256:8f2272dbf929983fc772ff46e68de26fdf521cbdf1be93aa4be9645e82d6924a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XCYGHYUI3AABIZXTJ2GKPPETLB/bundle.json","state_url":"https://pith.science/pith/XCYGHYUI3AABIZXTJ2GKPPETLB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XCYGHYUI3AABIZXTJ2GKPPETLB/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-20T05:04:56Z","links":{"resolver":"https://pith.science/pith/XCYGHYUI3AABIZXTJ2GKPPETLB","bundle":"https://pith.science/pith/XCYGHYUI3AABIZXTJ2GKPPETLB/bundle.json","state":"https://pith.science/pith/XCYGHYUI3AABIZXTJ2GKPPETLB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XCYGHYUI3AABIZXTJ2GKPPETLB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:XCYGHYUI3AABIZXTJ2GKPPETLB","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"a607bf72bffff7f298697c006b7d180e3edf1d6a4b147b88a1f57273140f9cce","cross_cats_sorted":["math.CO","math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2019-02-19T05:04:11Z","title_canon_sha256":"49f7caabf30a46e7a35f81e83529f2f24212238c6a3453090e3e891742d21b0c"},"schema_version":"1.0","source":{"id":"1902.06895","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1902.06895","created_at":"2026-05-17T23:53:40Z"},{"alias_kind":"arxiv_version","alias_value":"1902.06895v1","created_at":"2026-05-17T23:53:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.06895","created_at":"2026-05-17T23:53:40Z"},{"alias_kind":"pith_short_12","alias_value":"XCYGHYUI3AAB","created_at":"2026-05-18T12:33:33Z"},{"alias_kind":"pith_short_16","alias_value":"XCYGHYUI3AABIZXT","created_at":"2026-05-18T12:33:33Z"},{"alias_kind":"pith_short_8","alias_value":"XCYGHYUI","created_at":"2026-05-18T12:33:33Z"}],"graph_snapshots":[{"event_id":"sha256:8f2272dbf929983fc772ff46e68de26fdf521cbdf1be93aa4be9645e82d6924a","target":"graph","created_at":"2026-05-17T23:53:40Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"This paper is a survey on the Lickorish type construction of some kind of closed manifolds over simple convex polytopes. Inspired by Lickorish's theorem, we propose a method to describe certain families of manifolds over simple convex polytopes with torus action. Under this construction, many classical classification results of these families of manifolds could be interpreted by this construction and some further problems will be discussed.","authors_text":"Li Yu, Wei Wang, Zhi L\\\"u","cross_cats":["math.CO","math.GT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2019-02-19T05:04:11Z","title":"Lickorish type construction of manifolds over simple polytopes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.06895","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:c3d6a259db04962301918e6c7831bbe1a14caf5ccabe767c5772c6af69d34976","target":"record","created_at":"2026-05-17T23:53:40Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"a607bf72bffff7f298697c006b7d180e3edf1d6a4b147b88a1f57273140f9cce","cross_cats_sorted":["math.CO","math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2019-02-19T05:04:11Z","title_canon_sha256":"49f7caabf30a46e7a35f81e83529f2f24212238c6a3453090e3e891742d21b0c"},"schema_version":"1.0","source":{"id":"1902.06895","kind":"arxiv","version":1}},"canonical_sha256":"b8b063e288d8001466f34e8ca7bc9358721fbda6bde0e10ce089ad416bcd2376","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b8b063e288d8001466f34e8ca7bc9358721fbda6bde0e10ce089ad416bcd2376","first_computed_at":"2026-05-17T23:53:40.497143Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:53:40.497143Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hyugiCdm8oKiWbCWWrXJlIBszxO1Ta00WqDhMnMnh064MlxYwFciHOObRHSRjrXK43unLxpaZEj7qzQUPRvACQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:53:40.497599Z","signed_message":"canonical_sha256_bytes"},"source_id":"1902.06895","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c3d6a259db04962301918e6c7831bbe1a14caf5ccabe767c5772c6af69d34976","sha256:8f2272dbf929983fc772ff46e68de26fdf521cbdf1be93aa4be9645e82d6924a"],"state_sha256":"80820066a203db719b4b29707144380c41856bf20d20b0417b9c6ae5dd32b14b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LWkG6fSsdTgl8XA+vbjXruBS1SeZ932BLlgplsfx/nmGD9meb3UUfDznYPlhwqa0syi4DZhYLENiNGoaTSLcCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-20T05:04:56.824949Z","bundle_sha256":"1fe90fe20124490168c20bacc6ee63fb87a42521898ff1fe5bae63653359c26b"}}