{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:7GKQZWVXARZ6LCFJ265GE4GLXQ","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":"0574ef3d2abd36beaa4366a520e8363993a82cf713466f9faa6dbccef7461fe7","cross_cats_sorted":["math.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2012-12-07T12:39:28Z","title_canon_sha256":"e88770c9fad779226ddcbd876db5393065ee08f96e62f50677b9ec3dca5f5272"},"schema_version":"1.0","source":{"id":"1212.1596","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.1596","created_at":"2026-05-18T03:21:12Z"},{"alias_kind":"arxiv_version","alias_value":"1212.1596v2","created_at":"2026-05-18T03:21:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.1596","created_at":"2026-05-18T03:21:12Z"},{"alias_kind":"pith_short_12","alias_value":"7GKQZWVXARZ6","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"7GKQZWVXARZ6LCFJ","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"7GKQZWVX","created_at":"2026-05-18T12:26:56Z"}],"graph_snapshots":[{"event_id":"sha256:fe69ca4ba0b264f6720ef395800d41fb05e183f96e5927b2cc8fd7cf7c40d1a6","target":"graph","created_at":"2026-05-18T03:21:12Z","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":"A homomorphism from a completely metrizable topological group into a free product of groups whose image is not contained in a factor of the free product is shown to be continuous with respect to the discrete topology on the range. In particular, any completely metrizable group topology on a free product is discrete.","authors_text":"Konstantin Slutsky","cross_cats":["math.LO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2012-12-07T12:39:28Z","title":"Automatic continuity for homomorphisms into free products"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.1596","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":"sha256:4b6b3909d2eecd60048949f57b5cb1a170f942172ca9ff85aea73c7c9cf2d307","target":"record","created_at":"2026-05-18T03:21:12Z","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":"0574ef3d2abd36beaa4366a520e8363993a82cf713466f9faa6dbccef7461fe7","cross_cats_sorted":["math.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2012-12-07T12:39:28Z","title_canon_sha256":"e88770c9fad779226ddcbd876db5393065ee08f96e62f50677b9ec3dca5f5272"},"schema_version":"1.0","source":{"id":"1212.1596","kind":"arxiv","version":2}},"canonical_sha256":"f9950cdab70473e588a9d7ba6270cbbc39ac245b4a6120ed6db00c79ed88c1f4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f9950cdab70473e588a9d7ba6270cbbc39ac245b4a6120ed6db00c79ed88c1f4","first_computed_at":"2026-05-18T03:21:12.139644Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:21:12.139644Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Prm/bamvYxRHktLr6NmN119pMT0/ORBi4s5Sfs9P8FS0qJ0wJRxWxUHza2NYhDo200cBF5bd7J031ueKeMUqDw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:21:12.140372Z","signed_message":"canonical_sha256_bytes"},"source_id":"1212.1596","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4b6b3909d2eecd60048949f57b5cb1a170f942172ca9ff85aea73c7c9cf2d307","sha256:fe69ca4ba0b264f6720ef395800d41fb05e183f96e5927b2cc8fd7cf7c40d1a6"],"state_sha256":"a98bfb7a22e5150a569052104dffe5ec9bca9b6e239f1cade34f751ab9d2e271"}