{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:TVDC2RS5SJKRA3YWOXD2RNVZJB","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":"69f7987af0f88075919941ffd40a4cdcbad0e5aa4275f553f549b65ede59293d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2017-05-10T16:52:02Z","title_canon_sha256":"f5717ec294322ee978c81c12417c6fc4164e5b752c233bf6380b5c307ee48404"},"schema_version":"1.0","source":{"id":"1705.03884","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.03884","created_at":"2026-05-18T00:44:41Z"},{"alias_kind":"arxiv_version","alias_value":"1705.03884v1","created_at":"2026-05-18T00:44:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.03884","created_at":"2026-05-18T00:44:41Z"},{"alias_kind":"pith_short_12","alias_value":"TVDC2RS5SJKR","created_at":"2026-05-18T12:31:46Z"},{"alias_kind":"pith_short_16","alias_value":"TVDC2RS5SJKRA3YW","created_at":"2026-05-18T12:31:46Z"},{"alias_kind":"pith_short_8","alias_value":"TVDC2RS5","created_at":"2026-05-18T12:31:46Z"}],"graph_snapshots":[{"event_id":"sha256:769028561a5adf38d3029824189f2f73c456bca3039c9e153e2066a018951cfd","target":"graph","created_at":"2026-05-18T00:44:41Z","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 that for any pair of non-trivial finite groups, their coproduct in the category of finite groups is not representable.","authors_text":"Chris Hall","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2017-05-10T16:52:02Z","title":"Coproducts of Finite Groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.03884","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":"sha256:3e35efae967c6761ef3b4e82ae0c14609029532f1d052f944e99ee0e57d19c8c","target":"record","created_at":"2026-05-18T00:44:41Z","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":"69f7987af0f88075919941ffd40a4cdcbad0e5aa4275f553f549b65ede59293d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2017-05-10T16:52:02Z","title_canon_sha256":"f5717ec294322ee978c81c12417c6fc4164e5b752c233bf6380b5c307ee48404"},"schema_version":"1.0","source":{"id":"1705.03884","kind":"arxiv","version":1}},"canonical_sha256":"9d462d465d9255106f1675c7a8b6b9486678f50d5dfd13dfc42954deefc5408d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9d462d465d9255106f1675c7a8b6b9486678f50d5dfd13dfc42954deefc5408d","first_computed_at":"2026-05-18T00:44:41.878910Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:44:41.878910Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Abn3J9qN30wWFRR8k7oMxxNfQaPVwekrOMyep+Zo36k3LhpbrTx+YQCtf9fehATauA5UFKTV2eGNBRLZPFzsCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:44:41.879326Z","signed_message":"canonical_sha256_bytes"},"source_id":"1705.03884","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3e35efae967c6761ef3b4e82ae0c14609029532f1d052f944e99ee0e57d19c8c","sha256:769028561a5adf38d3029824189f2f73c456bca3039c9e153e2066a018951cfd"],"state_sha256":"4a6f193cd5e64c4da64be802a04c17c2c8b843288d61a38619cef0c4f6d30424"}