{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:UJTFOCWJ2ALKGAG74NCULVGM5Y","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":"56cd6cba9f95434d6079e0c6baf0b4461394c6eea4b4ffc805a8377001ce1743","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2017-11-01T17:57:15Z","title_canon_sha256":"4b23553786ce2ff8b48887a3eb473437bb58edc0be38bdc982556596de619046"},"schema_version":"1.0","source":{"id":"1711.00461","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.00461","created_at":"2026-05-18T00:07:11Z"},{"alias_kind":"arxiv_version","alias_value":"1711.00461v2","created_at":"2026-05-18T00:07:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.00461","created_at":"2026-05-18T00:07:11Z"},{"alias_kind":"pith_short_12","alias_value":"UJTFOCWJ2ALK","created_at":"2026-05-18T12:31:46Z"},{"alias_kind":"pith_short_16","alias_value":"UJTFOCWJ2ALKGAG7","created_at":"2026-05-18T12:31:46Z"},{"alias_kind":"pith_short_8","alias_value":"UJTFOCWJ","created_at":"2026-05-18T12:31:46Z"}],"graph_snapshots":[{"event_id":"sha256:ec2d283a18003c2f5ab944ee47c9d510a53e3262c609de12c82675ab1b4ca24f","target":"graph","created_at":"2026-05-18T00:07:11Z","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":"We prove that certain conditions on multigraded Betti numbers of a simplicial complex $K$ imply existence of a higher Massey product in cohomology of a moment-angle-complex $\\mathcal Z_K$, which contains a unique element (a strictly defined product). Using the simplicial multiwedge construction, we find a family $\\mathcal{F}$ of polyhedral products being smooth closed manifolds such that for any $l,r\\geq 2$ there exists an $l$-connected manifold $M\\in\\mathcal F$ with a nontrivial strictly defined $r$-fold Massey product in $H^{*}(M)$. As an application to homological algebra, we determine a wi","authors_text":"Ivan Limonchenko","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2017-11-01T17:57:15Z","title":"Topology of polyhedral products over simplicial multiwedges"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.00461","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:ac7a6949a090429a4b3061fc71f86f559028c81f9b65c7cf777909def74d1cde","target":"record","created_at":"2026-05-18T00:07:11Z","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":"56cd6cba9f95434d6079e0c6baf0b4461394c6eea4b4ffc805a8377001ce1743","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2017-11-01T17:57:15Z","title_canon_sha256":"4b23553786ce2ff8b48887a3eb473437bb58edc0be38bdc982556596de619046"},"schema_version":"1.0","source":{"id":"1711.00461","kind":"arxiv","version":2}},"canonical_sha256":"a266570ac9d016a300dfe34545d4ccee1fd8211f4129bc602bcf217982c5ac8b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a266570ac9d016a300dfe34545d4ccee1fd8211f4129bc602bcf217982c5ac8b","first_computed_at":"2026-05-18T00:07:11.651944Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:07:11.651944Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QuYdLoFXy2grYhe4dycObYZwqUSOaHEmX1ijf8f6hd7Zo4AX82NpSSAxWU/nyjGUpN2UaQvrZqmi9p+iQ8v1Ag==","signature_status":"signed_v1","signed_at":"2026-05-18T00:07:11.652740Z","signed_message":"canonical_sha256_bytes"},"source_id":"1711.00461","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ac7a6949a090429a4b3061fc71f86f559028c81f9b65c7cf777909def74d1cde","sha256:ec2d283a18003c2f5ab944ee47c9d510a53e3262c609de12c82675ab1b4ca24f"],"state_sha256":"34ec3db001dcfd2c479e0922df7f3e425bf32440b7ff676c9fb2febc0eb8c958"}