{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:AHJE6YY2IPV6VELLM4P4OWX2XW","short_pith_number":"pith:AHJE6YY2","canonical_record":{"source":{"id":"1508.00159","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2015-08-01T19:13:52Z","cross_cats_sorted":[],"title_canon_sha256":"f9a281fe1aa2971268ef2d8511130054b14d8ed684010891f3f0940b2a0079b6","abstract_canon_sha256":"fadc0818e3420e70022c25b9e3c4eef924a9bebd3a24d17ad620b393e85e7d02"},"schema_version":"1.0"},"canonical_sha256":"01d24f631a43ebea916b671fc75afabda09d34691180cf2d89585d42b5ff79fc","source":{"kind":"arxiv","id":"1508.00159","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.00159","created_at":"2026-05-18T01:13:38Z"},{"alias_kind":"arxiv_version","alias_value":"1508.00159v3","created_at":"2026-05-18T01:13:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.00159","created_at":"2026-05-18T01:13:38Z"},{"alias_kind":"pith_short_12","alias_value":"AHJE6YY2IPV6","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_16","alias_value":"AHJE6YY2IPV6VELL","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_8","alias_value":"AHJE6YY2","created_at":"2026-05-18T12:29:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:AHJE6YY2IPV6VELLM4P4OWX2XW","target":"record","payload":{"canonical_record":{"source":{"id":"1508.00159","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2015-08-01T19:13:52Z","cross_cats_sorted":[],"title_canon_sha256":"f9a281fe1aa2971268ef2d8511130054b14d8ed684010891f3f0940b2a0079b6","abstract_canon_sha256":"fadc0818e3420e70022c25b9e3c4eef924a9bebd3a24d17ad620b393e85e7d02"},"schema_version":"1.0"},"canonical_sha256":"01d24f631a43ebea916b671fc75afabda09d34691180cf2d89585d42b5ff79fc","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:13:38.119425Z","signature_b64":"TXjz2ceNz2cO/bLI+LLdCo+hNH8WlzR4gwQ6eCB6sn8H3n1QBMdxfbLKluw6S95UYH8OBbTvRkgoqQZsAATtDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"01d24f631a43ebea916b671fc75afabda09d34691180cf2d89585d42b5ff79fc","last_reissued_at":"2026-05-18T01:13:38.118657Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:13:38.118657Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1508.00159","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:13:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1k56PanrgRZKAjOdBOIxl3bh+8ZfRQEjob0AsNPTPAn/qxc6Zz48UkPjSkW1Unebq2tf/0HehU4Vh6N1A5g0DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T07:31:33.646806Z"},"content_sha256":"4c04e42c660e38220dd1a78a1b66c8b2bc6b85c50953ba155a081acf6cfd909c","schema_version":"1.0","event_id":"sha256:4c04e42c660e38220dd1a78a1b66c8b2bc6b85c50953ba155a081acf6cfd909c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:AHJE6YY2IPV6VELLM4P4OWX2XW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the cohomology of moment-angle complexes associated to Gorenstein* complexes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Feifei Fan, Xiangjun Wang","submitted_at":"2015-08-01T19:13:52Z","abstract_excerpt":"The main goal of this article is to study the cohomology rings and their applications of moment-angle complexes associated to Gorenstein* complexes, especially, the applications in combinatorial commutative algebra and combinatorics. First, we give a topological characterization of Gorenstein* complexes in terms of Alexander duality (as an application we give a topological proof of Stanley's Theorem). Next we give some cohomological transformation formulae of $\\mathcal {Z}_{K}$, which are induced by some combinatorial operations on the Gorenstein* complex $K$, such as the connected sum operati"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.00159","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:13:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GSdkVxlR1vGRN5v9diSdERmOj2tB6NDXGF08wjR2QvbLtYyEIMwpTvVe5v59DfnXX4ytuxaz6QwYlOCjUJAGBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T07:31:33.647183Z"},"content_sha256":"37b0910b6f1b37480f860837c3da30885819bd3c7c924151701656d2e3289db8","schema_version":"1.0","event_id":"sha256:37b0910b6f1b37480f860837c3da30885819bd3c7c924151701656d2e3289db8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AHJE6YY2IPV6VELLM4P4OWX2XW/bundle.json","state_url":"https://pith.science/pith/AHJE6YY2IPV6VELLM4P4OWX2XW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AHJE6YY2IPV6VELLM4P4OWX2XW/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":"2026-06-07T07:31:33Z","links":{"resolver":"https://pith.science/pith/AHJE6YY2IPV6VELLM4P4OWX2XW","bundle":"https://pith.science/pith/AHJE6YY2IPV6VELLM4P4OWX2XW/bundle.json","state":"https://pith.science/pith/AHJE6YY2IPV6VELLM4P4OWX2XW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AHJE6YY2IPV6VELLM4P4OWX2XW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:AHJE6YY2IPV6VELLM4P4OWX2XW","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":"fadc0818e3420e70022c25b9e3c4eef924a9bebd3a24d17ad620b393e85e7d02","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2015-08-01T19:13:52Z","title_canon_sha256":"f9a281fe1aa2971268ef2d8511130054b14d8ed684010891f3f0940b2a0079b6"},"schema_version":"1.0","source":{"id":"1508.00159","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.00159","created_at":"2026-05-18T01:13:38Z"},{"alias_kind":"arxiv_version","alias_value":"1508.00159v3","created_at":"2026-05-18T01:13:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.00159","created_at":"2026-05-18T01:13:38Z"},{"alias_kind":"pith_short_12","alias_value":"AHJE6YY2IPV6","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_16","alias_value":"AHJE6YY2IPV6VELL","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_8","alias_value":"AHJE6YY2","created_at":"2026-05-18T12:29:10Z"}],"graph_snapshots":[{"event_id":"sha256:37b0910b6f1b37480f860837c3da30885819bd3c7c924151701656d2e3289db8","target":"graph","created_at":"2026-05-18T01:13:38Z","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":"The main goal of this article is to study the cohomology rings and their applications of moment-angle complexes associated to Gorenstein* complexes, especially, the applications in combinatorial commutative algebra and combinatorics. First, we give a topological characterization of Gorenstein* complexes in terms of Alexander duality (as an application we give a topological proof of Stanley's Theorem). Next we give some cohomological transformation formulae of $\\mathcal {Z}_{K}$, which are induced by some combinatorial operations on the Gorenstein* complex $K$, such as the connected sum operati","authors_text":"Feifei Fan, Xiangjun Wang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2015-08-01T19:13:52Z","title":"On the cohomology of moment-angle complexes associated to Gorenstein* complexes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.00159","kind":"arxiv","version":3},"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":"sha256:4c04e42c660e38220dd1a78a1b66c8b2bc6b85c50953ba155a081acf6cfd909c","target":"record","created_at":"2026-05-18T01:13:38Z","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":"fadc0818e3420e70022c25b9e3c4eef924a9bebd3a24d17ad620b393e85e7d02","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2015-08-01T19:13:52Z","title_canon_sha256":"f9a281fe1aa2971268ef2d8511130054b14d8ed684010891f3f0940b2a0079b6"},"schema_version":"1.0","source":{"id":"1508.00159","kind":"arxiv","version":3}},"canonical_sha256":"01d24f631a43ebea916b671fc75afabda09d34691180cf2d89585d42b5ff79fc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"01d24f631a43ebea916b671fc75afabda09d34691180cf2d89585d42b5ff79fc","first_computed_at":"2026-05-18T01:13:38.118657Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:13:38.118657Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TXjz2ceNz2cO/bLI+LLdCo+hNH8WlzR4gwQ6eCB6sn8H3n1QBMdxfbLKluw6S95UYH8OBbTvRkgoqQZsAATtDw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:13:38.119425Z","signed_message":"canonical_sha256_bytes"},"source_id":"1508.00159","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4c04e42c660e38220dd1a78a1b66c8b2bc6b85c50953ba155a081acf6cfd909c","sha256:37b0910b6f1b37480f860837c3da30885819bd3c7c924151701656d2e3289db8"],"state_sha256":"53f6c60811b2d7949574135a24c93df1b319c9000b6b0e172f65f3b356af59f7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VCPSpXsyOrm5zYoucXzSiKXEbCsiYaegH3MRvk86TGbN5I00eXPXi4peOTIUBZ1pD1AM8ho89TeQhhARommiDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T07:31:33.650543Z","bundle_sha256":"376073c07968f6526315ecc63bf05382ab738b3692fb7f81f68a5fe8ac2f1736"}}