{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:7HJRGQ5665KP6A4XWEQKTSHVZI","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":"33bddc7d72165b0c5007feaefcc6568e6e6b74d700714d61b8b1efc35f2443b7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2013-03-01T22:01:22Z","title_canon_sha256":"71c9fa580af2f1d3d29b4a350a3497f855a0b4fba948ce2594b3f9c8950785f5"},"schema_version":"1.0","source":{"id":"1303.0312","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1303.0312","created_at":"2026-05-18T03:27:42Z"},{"alias_kind":"arxiv_version","alias_value":"1303.0312v2","created_at":"2026-05-18T03:27:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.0312","created_at":"2026-05-18T03:27:42Z"},{"alias_kind":"pith_short_12","alias_value":"7HJRGQ5665KP","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_16","alias_value":"7HJRGQ5665KP6A4X","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_8","alias_value":"7HJRGQ56","created_at":"2026-05-18T12:27:36Z"}],"graph_snapshots":[{"event_id":"sha256:86e35cd9efa8596a67140dbf0c24d029178e6d768541ba8a68150586f7aa8bda","target":"graph","created_at":"2026-05-18T03:27:42Z","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":"The concept of assignments was introduced in [GGK99] as a method for extracting geometric information about group actions on manifolds from combinatorial data encoded in the infinitesimal orbit-type stratification. In this paper we will answer in the affirmative a question posed in [GGK99] by showing that the equivariant cohomology ring of $M$ is to a large extent determined by this data.","authors_text":"Catalin Zara, Silvia Sabatini, Victor Guillemin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2013-03-01T22:01:22Z","title":"Polynomial Assignments"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.0312","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:be42d90422a0c412ae41c9b9628829134823577eec86d1ab0dbd635b5c66ad50","target":"record","created_at":"2026-05-18T03:27:42Z","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":"33bddc7d72165b0c5007feaefcc6568e6e6b74d700714d61b8b1efc35f2443b7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2013-03-01T22:01:22Z","title_canon_sha256":"71c9fa580af2f1d3d29b4a350a3497f855a0b4fba948ce2594b3f9c8950785f5"},"schema_version":"1.0","source":{"id":"1303.0312","kind":"arxiv","version":2}},"canonical_sha256":"f9d31343bef754ff0397b120a9c8f5ca170b81ce3339cc6f2f8b7e8f1426ff32","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f9d31343bef754ff0397b120a9c8f5ca170b81ce3339cc6f2f8b7e8f1426ff32","first_computed_at":"2026-05-18T03:27:42.507019Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:27:42.507019Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CxpzjbP+eL5Hi3e/EO/Qpzuaw3IN/epz+Hr4uwrb/okUZLD1VC2Mc2ta9b9jBjr2wwuf/jgaqGGhyKTpZjh5AA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:27:42.507748Z","signed_message":"canonical_sha256_bytes"},"source_id":"1303.0312","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:be42d90422a0c412ae41c9b9628829134823577eec86d1ab0dbd635b5c66ad50","sha256:86e35cd9efa8596a67140dbf0c24d029178e6d768541ba8a68150586f7aa8bda"],"state_sha256":"bb3e2ade2c5a10979bc7ca0189d3c9aed36fe0cb67f2811ff50fa686a8aa7ed2"}