{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:M7NQGGDSRCTVUVOZJYNQ4Q2AAX","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":"d03b5ff2c0371d1501604c558e5a1593223dfa65de43be3a55ff647c0787a58c","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2012-12-19T15:01:29Z","title_canon_sha256":"eced1b7be16f18e2d62bede6852e7471ac4b480a12b32325d99ce5c99db74e75"},"schema_version":"1.0","source":{"id":"1212.4689","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.4689","created_at":"2026-05-18T00:06:16Z"},{"alias_kind":"arxiv_version","alias_value":"1212.4689v1","created_at":"2026-05-18T00:06:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.4689","created_at":"2026-05-18T00:06:16Z"},{"alias_kind":"pith_short_12","alias_value":"M7NQGGDSRCTV","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_16","alias_value":"M7NQGGDSRCTVUVOZ","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_8","alias_value":"M7NQGGDS","created_at":"2026-05-18T12:27:14Z"}],"graph_snapshots":[{"event_id":"sha256:cb945ec1df7648ccaf8f2f461ffb6c9a8fd10488377d2f3c7ba81f7d1e43ce29","target":"graph","created_at":"2026-05-18T00:06:16Z","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 show the existence of Hall polynomials for representation-finite cluster-tilted algebras.","authors_text":"Changjian Fu","cross_cats":["math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2012-12-19T15:01:29Z","title":"Hall polynomials for representation-finite cluster-tilted algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.4689","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":"sha256:6c1018e421708ca860a22fd75cad7d12568ca0ab96cdfe91e0fc20fb74b56225","target":"record","created_at":"2026-05-18T00:06:16Z","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":"d03b5ff2c0371d1501604c558e5a1593223dfa65de43be3a55ff647c0787a58c","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2012-12-19T15:01:29Z","title_canon_sha256":"eced1b7be16f18e2d62bede6852e7471ac4b480a12b32325d99ce5c99db74e75"},"schema_version":"1.0","source":{"id":"1212.4689","kind":"arxiv","version":1}},"canonical_sha256":"67db03187288a75a55d94e1b0e434005e89992bafac6a00d8477680a40c484b1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"67db03187288a75a55d94e1b0e434005e89992bafac6a00d8477680a40c484b1","first_computed_at":"2026-05-18T00:06:16.529401Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:06:16.529401Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7H7RoAdzh756wHe2OBSwIa1m6asKcUyYgcM0t3vnIpm4fVTwGqNf/Td18PiI5GH8MB1R5Er/ykB9O2NRoDr5BA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:06:16.529962Z","signed_message":"canonical_sha256_bytes"},"source_id":"1212.4689","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6c1018e421708ca860a22fd75cad7d12568ca0ab96cdfe91e0fc20fb74b56225","sha256:cb945ec1df7648ccaf8f2f461ffb6c9a8fd10488377d2f3c7ba81f7d1e43ce29"],"state_sha256":"a9eb931519236c0d0f0d5054f7fa1f9ba5b1cdece2902cc4e83e6f03ba632236"}