{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:AMYJARSS6XS5NJJTMYNQEH7WYQ","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":"1cf8e16fdda375445a76e4fbafd7b544265ebcc047f88bdef01a6e7b2c08447b","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2012-04-04T06:48:45Z","title_canon_sha256":"d59b0fb239ae08711358771aab4409613cce5a35744706443989d7431785eae0"},"schema_version":"1.0","source":{"id":"1204.0876","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.0876","created_at":"2026-05-18T03:21:31Z"},{"alias_kind":"arxiv_version","alias_value":"1204.0876v2","created_at":"2026-05-18T03:21:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.0876","created_at":"2026-05-18T03:21:31Z"},{"alias_kind":"pith_short_12","alias_value":"AMYJARSS6XS5","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_16","alias_value":"AMYJARSS6XS5NJJT","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_8","alias_value":"AMYJARSS","created_at":"2026-05-18T12:26:58Z"}],"graph_snapshots":[{"event_id":"sha256:29e235681adb8756a1b5023fcb33650f04ebe51937afd8706f949c4e77c12684","target":"graph","created_at":"2026-05-18T03:21:31Z","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":"This is a biased survey for the Johnson homomorphisms of the automorphism groups of free groups. We just exposit some well known facts and recent developments for the Johnson homomorphisms and its related topics.","authors_text":"Takao Satoh","cross_cats":["math.GR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2012-04-04T06:48:45Z","title":"A survey of the Johnson homomorphisms of the automorphism groups of free groups and related topics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.0876","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":"sha256:9c2ba52c6edd96819bf5f6e8fa1f021458ec7c7b06afc04206a7d6de4add252b","target":"record","created_at":"2026-05-18T03:21:31Z","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":"1cf8e16fdda375445a76e4fbafd7b544265ebcc047f88bdef01a6e7b2c08447b","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2012-04-04T06:48:45Z","title_canon_sha256":"d59b0fb239ae08711358771aab4409613cce5a35744706443989d7431785eae0"},"schema_version":"1.0","source":{"id":"1204.0876","kind":"arxiv","version":2}},"canonical_sha256":"0330904652f5e5d6a533661b021ff6c43ca8742aaeba5d911cec4f95871fa306","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0330904652f5e5d6a533661b021ff6c43ca8742aaeba5d911cec4f95871fa306","first_computed_at":"2026-05-18T03:21:31.878841Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:21:31.878841Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FYixlQSKyWY5F5z7TLIZuQ/gKH6TlOpoKImx+O0f5xB9ZYYYIsvrYCVV7bF0RMYRr/zY/mbZ/9ZZl4TPGhp7AQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:21:31.879642Z","signed_message":"canonical_sha256_bytes"},"source_id":"1204.0876","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9c2ba52c6edd96819bf5f6e8fa1f021458ec7c7b06afc04206a7d6de4add252b","sha256:29e235681adb8756a1b5023fcb33650f04ebe51937afd8706f949c4e77c12684"],"state_sha256":"8174e718eb842b7e784a00a0225e894e0f72897f6d96c091e500873c8fb45c62"}