{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:FGK3WUD3UNDJJUHXFZF73E4ISO","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":"2ee03926a89f4f56493103daaaefb2f59406f6b2a04934f98cda57ecdc118ef4","cross_cats_sorted":["math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2008-08-12T22:54:36Z","title_canon_sha256":"9314f0c22ac74b58688d879240479d7a967f5c42893da8bbb5b2d8ee6de88e46"},"schema_version":"1.0","source":{"id":"0808.1749","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0808.1749","created_at":"2026-05-18T04:25:28Z"},{"alias_kind":"arxiv_version","alias_value":"0808.1749v1","created_at":"2026-05-18T04:25:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0808.1749","created_at":"2026-05-18T04:25:28Z"},{"alias_kind":"pith_short_12","alias_value":"FGK3WUD3UNDJ","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_16","alias_value":"FGK3WUD3UNDJJUHX","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_8","alias_value":"FGK3WUD3","created_at":"2026-05-18T12:25:57Z"}],"graph_snapshots":[{"event_id":"sha256:5d49d6c08ee6dec2fd492ca52c102d1646888f2e3bbaf65cfcadac03b9398e1f","target":"graph","created_at":"2026-05-18T04:25:28Z","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":"James McClure recently showed that the domain for the intersection pairing of PL chains on a PL manifold $M$ is a subcomplex of $C_*(M)\\otimes C_*(M)$ that is quasi-isomorphic to $C_*(M)\\otimes C_*(M)$ and, more generally, that the intersection pairing endows $C_*(M)$ with the structure of a partially-defined commutative DGA. We generalize this theorem to intersection pairings of PL intersection chains on PL stratified pseudomanifolds and demonstrate the existence of a partial restricted commutative DGA structure. This structure is shown to generalize the iteration of the Goresky-MacPherson in","authors_text":"Greg Friedman","cross_cats":["math.AT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2008-08-12T22:54:36Z","title":"On the chain-level intersection pairing for PL pseudomanifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0808.1749","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:da6a63e754d3286029e11cb9a32d59d9871f009712a22f99554d2c5c9b635202","target":"record","created_at":"2026-05-18T04:25:28Z","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":"2ee03926a89f4f56493103daaaefb2f59406f6b2a04934f98cda57ecdc118ef4","cross_cats_sorted":["math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2008-08-12T22:54:36Z","title_canon_sha256":"9314f0c22ac74b58688d879240479d7a967f5c42893da8bbb5b2d8ee6de88e46"},"schema_version":"1.0","source":{"id":"0808.1749","kind":"arxiv","version":1}},"canonical_sha256":"2995bb507ba34694d0f72e4bfd9388938fa13bce13cb8dc80b22e12dbab1b536","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2995bb507ba34694d0f72e4bfd9388938fa13bce13cb8dc80b22e12dbab1b536","first_computed_at":"2026-05-18T04:25:28.849687Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:25:28.849687Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mq0mYEE0s/wvQDfYJ84KbF/ak+A1d3TJR4EpNiJjfWKj1w0Ak72tLtkfjsMO0taB+F6qmrGS647ES8UyN/fLDg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:25:28.850144Z","signed_message":"canonical_sha256_bytes"},"source_id":"0808.1749","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:da6a63e754d3286029e11cb9a32d59d9871f009712a22f99554d2c5c9b635202","sha256:5d49d6c08ee6dec2fd492ca52c102d1646888f2e3bbaf65cfcadac03b9398e1f"],"state_sha256":"c56b342b7c94a898b3baf1206f3787f548576c99b5027ff67b7bd60aeeb91b70"}