{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:6PPU5SN3SKUWBDDNO5MNZYDOX3","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":"cdc1f7e00bea92c9fd92a88e2ca4bb19cc9e1cbe759cfd0dc69ba65ec3137b30","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2010-01-19T17:42:45Z","title_canon_sha256":"a3460ab2799b813352b6627ec8b37cc0d0b61314a7695dc9cb545f850b3eacf7"},"schema_version":"1.0","source":{"id":"1001.3372","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1001.3372","created_at":"2026-05-18T04:41:43Z"},{"alias_kind":"arxiv_version","alias_value":"1001.3372v2","created_at":"2026-05-18T04:41:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1001.3372","created_at":"2026-05-18T04:41:43Z"},{"alias_kind":"pith_short_12","alias_value":"6PPU5SN3SKUW","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_16","alias_value":"6PPU5SN3SKUWBDDN","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_8","alias_value":"6PPU5SN3","created_at":"2026-05-18T12:26:04Z"}],"graph_snapshots":[{"event_id":"sha256:1e0231b82926a40c97acfcb456b1789f3fbdecc3ef6ef1c32f1300f17689475f","target":"graph","created_at":"2026-05-18T04:41:43Z","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":"Given a family of based CW-pairs $(\\underline{X},\\underline{A})=\\{(X;A)\\}^m_{i=1}$ together with an abstract simplicial complex $K$ with $m$ vertices, there is an associated based CW-complex $Z(K;(\\underline{X},\\underline{A}))$ known as a generalized moment-angle complex.\n  The decomposition theorem of \\cite{bbcg}, \\cite{bbcg2} splits the suspension of $Z(K; (\\underline{X}, \\underline{A}))$ into a bouquet of spaces determined by the full sub-complexes of $K$. Thatdecomposition theorem is used here to describe the ring structure for the cohomology of Z(K; (\\underline{X}, \\underline{A})). Explic","authors_text":"A. Bahri, F. R. Cohen, M. Bendersky, S. Gitler","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2010-01-19T17:42:45Z","title":"Cup-products in generalized moment-angle complexes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1001.3372","kind":"arxiv","version":2},"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":"sha256:2a070e6c325e9bafdda85538cbb42f241705e6ccbb6ac60bcd2e0713c23aaacc","target":"record","created_at":"2026-05-18T04:41:43Z","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":"cdc1f7e00bea92c9fd92a88e2ca4bb19cc9e1cbe759cfd0dc69ba65ec3137b30","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2010-01-19T17:42:45Z","title_canon_sha256":"a3460ab2799b813352b6627ec8b37cc0d0b61314a7695dc9cb545f850b3eacf7"},"schema_version":"1.0","source":{"id":"1001.3372","kind":"arxiv","version":2}},"canonical_sha256":"f3df4ec9bb92a9608c6d7758dce06ebece2a4982dfa2a36b63e2351214a4e9a6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f3df4ec9bb92a9608c6d7758dce06ebece2a4982dfa2a36b63e2351214a4e9a6","first_computed_at":"2026-05-18T04:41:43.994808Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:41:43.994808Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uF/gHlS/yEOQgzP+0IH+mAmk5t0l7r5hXnfRrZURxTJAVts9+wbRojgJy3i2+padiDqTCRAnhtHuLnnvrHCcBg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:41:43.995213Z","signed_message":"canonical_sha256_bytes"},"source_id":"1001.3372","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2a070e6c325e9bafdda85538cbb42f241705e6ccbb6ac60bcd2e0713c23aaacc","sha256:1e0231b82926a40c97acfcb456b1789f3fbdecc3ef6ef1c32f1300f17689475f"],"state_sha256":"360e182d0217ef01830a6f609afd03c999c6cfec34c18e4f201fe843192f5395"}