{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:35C3CB56BJIQAC53ZOVLWDK242","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":"a6a5dee3dce2d55830c3ec94a6b3ccb1f2db751620bff5c6f7f77ac691616b20","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2011-01-05T23:46:52Z","title_canon_sha256":"246e50e65f7164c8fc828928fcc0171f3bed8259669955cde9ee2a449fe046c1"},"schema_version":"1.0","source":{"id":"1101.1116","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1101.1116","created_at":"2026-05-18T03:58:49Z"},{"alias_kind":"arxiv_version","alias_value":"1101.1116v2","created_at":"2026-05-18T03:58:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.1116","created_at":"2026-05-18T03:58:49Z"},{"alias_kind":"pith_short_12","alias_value":"35C3CB56BJIQ","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_16","alias_value":"35C3CB56BJIQAC53","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_8","alias_value":"35C3CB56","created_at":"2026-05-18T12:26:18Z"}],"graph_snapshots":[{"event_id":"sha256:4e501396db94e6ac80aebd0145f6d1dbb312a778cdf8dd9f37c9f8d2ce6d6d82","target":"graph","created_at":"2026-05-18T03:58:49Z","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":"Some lower bounds of GK-dimension of Hopf algebras are given.","authors_text":"D.-G. Wang, G. Zhuang, J.J. Zhang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2011-01-05T23:46:52Z","title":"Lower bounds of Growth of Hopf algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.1116","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":"sha256:881d258a88ef73128065a4511f0a2c741ef427a8094ee71e7fdf6f3cd459f0d2","target":"record","created_at":"2026-05-18T03:58:49Z","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":"a6a5dee3dce2d55830c3ec94a6b3ccb1f2db751620bff5c6f7f77ac691616b20","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2011-01-05T23:46:52Z","title_canon_sha256":"246e50e65f7164c8fc828928fcc0171f3bed8259669955cde9ee2a449fe046c1"},"schema_version":"1.0","source":{"id":"1101.1116","kind":"arxiv","version":2}},"canonical_sha256":"df45b107be0a51000bbbcbaabb0d5ae6a05acfea25894647abf4fa0fd6a7253a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"df45b107be0a51000bbbcbaabb0d5ae6a05acfea25894647abf4fa0fd6a7253a","first_computed_at":"2026-05-18T03:58:49.166233Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:58:49.166233Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gALa/MR/H1bjhEPUnnHM9/pAwfXELbiH+zT9Uf1i2lRNFYfwNrqWaZXd5Ce/wc8NQMTvRcXLPnIpV4z9J+7PAw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:58:49.166969Z","signed_message":"canonical_sha256_bytes"},"source_id":"1101.1116","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:881d258a88ef73128065a4511f0a2c741ef427a8094ee71e7fdf6f3cd459f0d2","sha256:4e501396db94e6ac80aebd0145f6d1dbb312a778cdf8dd9f37c9f8d2ce6d6d82"],"state_sha256":"0a1dc7d4e7297b07757b5c5d255799514dc68b01af4894d815108eaf6d86cab0"}