{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2005:5GZZL2RMXBDW464Y53I4MKQJX3","short_pith_number":"pith:5GZZL2RM","canonical_record":{"source":{"id":"math/0512497","kind":"arxiv","version":4},"metadata":{"license":"","primary_cat":"math.AT","submitted_at":"2005-12-21T16:26:42Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"41036ec909fe5b57a832ad4270e4a65e843b3ca38ecb90e0b160967179fbdb7e","abstract_canon_sha256":"a5ee4e4b537f55fbb62fc20283149f04afee4548d1dc0a12e00ebae541feb454"},"schema_version":"1.0"},"canonical_sha256":"e9b395ea2cb8476e7b98eed1c62a09befa62201ef05a3773a7cdad500a6eb772","source":{"kind":"arxiv","id":"math/0512497","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0512497","created_at":"2026-05-18T03:04:34Z"},{"alias_kind":"arxiv_version","alias_value":"math/0512497v4","created_at":"2026-05-18T03:04:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0512497","created_at":"2026-05-18T03:04:34Z"},{"alias_kind":"pith_short_12","alias_value":"5GZZL2RMXBDW","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"5GZZL2RMXBDW464Y","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"5GZZL2RM","created_at":"2026-05-18T12:25:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2005:5GZZL2RMXBDW464Y53I4MKQJX3","target":"record","payload":{"canonical_record":{"source":{"id":"math/0512497","kind":"arxiv","version":4},"metadata":{"license":"","primary_cat":"math.AT","submitted_at":"2005-12-21T16:26:42Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"41036ec909fe5b57a832ad4270e4a65e843b3ca38ecb90e0b160967179fbdb7e","abstract_canon_sha256":"a5ee4e4b537f55fbb62fc20283149f04afee4548d1dc0a12e00ebae541feb454"},"schema_version":"1.0"},"canonical_sha256":"e9b395ea2cb8476e7b98eed1c62a09befa62201ef05a3773a7cdad500a6eb772","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:04:34.349110Z","signature_b64":"Kh6kHQhagB3WCbUi44pn4wsIANVZ8SoaU5HyNCpuqXpcD+8ea2oUpMb+bsMfZS1NKaYeRUfHzPM6FpObkFNuDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e9b395ea2cb8476e7b98eed1c62a09befa62201ef05a3773a7cdad500a6eb772","last_reissued_at":"2026-05-18T03:04:34.348337Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:04:34.348337Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0512497","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:04:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Fufp8s5e6xIWaFCDPolgalg66yA6+rgGxq/HXrLB8Iw2aN766qOCI3MXl0Tcc2P5oUbmqc89KjaXzHUfHd6sBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T06:50:47.725055Z"},"content_sha256":"a2895642b693ce802e75846ade2f0b37c986585648e3fca513f766e1c8ac3de3","schema_version":"1.0","event_id":"sha256:a2895642b693ce802e75846ade2f0b37c986585648e3fca513f766e1c8ac3de3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2005:5GZZL2RMXBDW464Y53I4MKQJX3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Moment-angle complexes, monomial ideals, and Massey products","license":"","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AT","authors_text":"Alexander I. Suciu, Graham Denham","submitted_at":"2005-12-21T16:26:42Z","abstract_excerpt":"Associated to every finite simplicial complex K there is a \"moment-angle\" finite CW-complex, Z_K; if K is a triangulation of a sphere, Z_K is a smooth, compact manifold. Building on work of Buchstaber, Panov, and Baskakov, we study the cohomology ring, the homotopy groups, and the triple Massey products of a moment-angle complex, relating these topological invariants to the algebraic combinatorics of the underlying simplicial complex. Applications to the study of non-formal manifolds and subspace arrangements are given."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0512497","kind":"arxiv","version":4},"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":"2026-05-18T03:04:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"g75YfUsdqR8C+KMiyTd0gHtfJTcKkYPsBC07WY74s8WRxuY47c5PPdPnFsCoCKBGktlXbwx/RqXXV0Nlho4NBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T06:50:47.725406Z"},"content_sha256":"142beb1eed054b9d39962e9738b538c99740ddba6ead0f8299e038aeaea956ee","schema_version":"1.0","event_id":"sha256:142beb1eed054b9d39962e9738b538c99740ddba6ead0f8299e038aeaea956ee"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5GZZL2RMXBDW464Y53I4MKQJX3/bundle.json","state_url":"https://pith.science/pith/5GZZL2RMXBDW464Y53I4MKQJX3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5GZZL2RMXBDW464Y53I4MKQJX3/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":"2026-06-20T06:50:47Z","links":{"resolver":"https://pith.science/pith/5GZZL2RMXBDW464Y53I4MKQJX3","bundle":"https://pith.science/pith/5GZZL2RMXBDW464Y53I4MKQJX3/bundle.json","state":"https://pith.science/pith/5GZZL2RMXBDW464Y53I4MKQJX3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5GZZL2RMXBDW464Y53I4MKQJX3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2005:5GZZL2RMXBDW464Y53I4MKQJX3","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":"a5ee4e4b537f55fbb62fc20283149f04afee4548d1dc0a12e00ebae541feb454","cross_cats_sorted":["math.CO"],"license":"","primary_cat":"math.AT","submitted_at":"2005-12-21T16:26:42Z","title_canon_sha256":"41036ec909fe5b57a832ad4270e4a65e843b3ca38ecb90e0b160967179fbdb7e"},"schema_version":"1.0","source":{"id":"math/0512497","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0512497","created_at":"2026-05-18T03:04:34Z"},{"alias_kind":"arxiv_version","alias_value":"math/0512497v4","created_at":"2026-05-18T03:04:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0512497","created_at":"2026-05-18T03:04:34Z"},{"alias_kind":"pith_short_12","alias_value":"5GZZL2RMXBDW","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"5GZZL2RMXBDW464Y","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"5GZZL2RM","created_at":"2026-05-18T12:25:53Z"}],"graph_snapshots":[{"event_id":"sha256:142beb1eed054b9d39962e9738b538c99740ddba6ead0f8299e038aeaea956ee","target":"graph","created_at":"2026-05-18T03:04:34Z","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":"Associated to every finite simplicial complex K there is a \"moment-angle\" finite CW-complex, Z_K; if K is a triangulation of a sphere, Z_K is a smooth, compact manifold. Building on work of Buchstaber, Panov, and Baskakov, we study the cohomology ring, the homotopy groups, and the triple Massey products of a moment-angle complex, relating these topological invariants to the algebraic combinatorics of the underlying simplicial complex. Applications to the study of non-formal manifolds and subspace arrangements are given.","authors_text":"Alexander I. Suciu, Graham Denham","cross_cats":["math.CO"],"headline":"","license":"","primary_cat":"math.AT","submitted_at":"2005-12-21T16:26:42Z","title":"Moment-angle complexes, monomial ideals, and Massey products"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0512497","kind":"arxiv","version":4},"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:a2895642b693ce802e75846ade2f0b37c986585648e3fca513f766e1c8ac3de3","target":"record","created_at":"2026-05-18T03:04:34Z","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":"a5ee4e4b537f55fbb62fc20283149f04afee4548d1dc0a12e00ebae541feb454","cross_cats_sorted":["math.CO"],"license":"","primary_cat":"math.AT","submitted_at":"2005-12-21T16:26:42Z","title_canon_sha256":"41036ec909fe5b57a832ad4270e4a65e843b3ca38ecb90e0b160967179fbdb7e"},"schema_version":"1.0","source":{"id":"math/0512497","kind":"arxiv","version":4}},"canonical_sha256":"e9b395ea2cb8476e7b98eed1c62a09befa62201ef05a3773a7cdad500a6eb772","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e9b395ea2cb8476e7b98eed1c62a09befa62201ef05a3773a7cdad500a6eb772","first_computed_at":"2026-05-18T03:04:34.348337Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:04:34.348337Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Kh6kHQhagB3WCbUi44pn4wsIANVZ8SoaU5HyNCpuqXpcD+8ea2oUpMb+bsMfZS1NKaYeRUfHzPM6FpObkFNuDA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:04:34.349110Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0512497","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a2895642b693ce802e75846ade2f0b37c986585648e3fca513f766e1c8ac3de3","sha256:142beb1eed054b9d39962e9738b538c99740ddba6ead0f8299e038aeaea956ee"],"state_sha256":"ace1723f4c05986f7baa0ac85e4263b4d0372b21b9f4f90d18c249f7b7398e83"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LrtL0bHzJ6c7AcZthAMEwyikmv93WjMHEkoTu161B+/36pBrDTmOmSoFp6MqV5zTT5kIbbQFSaskoeJupHPLBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T06:50:47.727348Z","bundle_sha256":"8c9dedf7d635c36059c3f663ae30e3430c155a2ad37dca11d14a31845cee774f"}}