{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:INYU3TYCZWLXZMEEP5BADTGFUI","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":"ed9b2bec3d800b28a1c2cb421376fc911e8c14699c536f922b0602f4e69f902b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2018-12-23T10:39:13Z","title_canon_sha256":"c6f6402c88dd542b7dd68c93e3e657d53ee27790437d50a56b94c98b18e9abad"},"schema_version":"1.0","source":{"id":"1812.09686","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.09686","created_at":"2026-05-17T23:57:27Z"},{"alias_kind":"arxiv_version","alias_value":"1812.09686v1","created_at":"2026-05-17T23:57:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.09686","created_at":"2026-05-17T23:57:27Z"},{"alias_kind":"pith_short_12","alias_value":"INYU3TYCZWLX","created_at":"2026-05-18T12:32:31Z"},{"alias_kind":"pith_short_16","alias_value":"INYU3TYCZWLXZMEE","created_at":"2026-05-18T12:32:31Z"},{"alias_kind":"pith_short_8","alias_value":"INYU3TYC","created_at":"2026-05-18T12:32:31Z"}],"graph_snapshots":[{"event_id":"sha256:24f6710e56db7f7cc7831bce2944440545b518535aabd76c896291b8a1ee9f02","target":"graph","created_at":"2026-05-17T23:57:27Z","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 with an augmented differential graded algebra $R= R^{\\geq 0}$ is a homotopy invariant ${\\mathcal T}(R)$. This is a graded vector space, and if $H^0(R)$ is the ground field and $H^{>N}(R)= 0$ then dim$\\, {\\mathcal T}(R)= 1$ if and only if $H(R)$ is a Poincar\\'e duality algebra. In the case of Sullivan extensions $\\land W\\to \\land W\\otimes \\land Z\\to \\land Z$ in which dim$\\, H(\\land Z)<\\infty$ we show that $${\\mathcal T}(\\land W\\otimes \\land Z)= {\\mathcal T}(\\land W)\\otimes {\\mathcal T}(\\land Z).$$ This is applied to finite dimensional CW complexes $X$ where the fundamental group $G$ ","authors_text":"Steve Halperin, Yves Felix","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2018-12-23T10:39:13Z","title":"A note on Gorenstein spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.09686","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":"sha256:00dea1bef0b3d772ebaab050678ad500d464433f67aa0962b63c372b05079712","target":"record","created_at":"2026-05-17T23:57:27Z","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":"ed9b2bec3d800b28a1c2cb421376fc911e8c14699c536f922b0602f4e69f902b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2018-12-23T10:39:13Z","title_canon_sha256":"c6f6402c88dd542b7dd68c93e3e657d53ee27790437d50a56b94c98b18e9abad"},"schema_version":"1.0","source":{"id":"1812.09686","kind":"arxiv","version":1}},"canonical_sha256":"43714dcf02cd977cb0847f4201ccc5a21519f7b81d5e9a33c97c42f035492b9e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"43714dcf02cd977cb0847f4201ccc5a21519f7b81d5e9a33c97c42f035492b9e","first_computed_at":"2026-05-17T23:57:27.108013Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:57:27.108013Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xee+X88iTlDoVxxYBMF2J0gZpxgTFRgCaKYjKaThOkdbSI0mcBExKN6/VyMj4c/WHnGcbDO9FXd1WZWqO+MHBg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:57:27.108642Z","signed_message":"canonical_sha256_bytes"},"source_id":"1812.09686","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:00dea1bef0b3d772ebaab050678ad500d464433f67aa0962b63c372b05079712","sha256:24f6710e56db7f7cc7831bce2944440545b518535aabd76c896291b8a1ee9f02"],"state_sha256":"4b030410aa615e1f9259b3ae1d4952b462cb4a7bddb6d0154303c7005d1b6e6d"}