{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:7GKQZWVXARZ6LCFJ265GE4GLXQ","short_pith_number":"pith:7GKQZWVX","canonical_record":{"source":{"id":"1212.1596","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2012-12-07T12:39:28Z","cross_cats_sorted":["math.LO"],"title_canon_sha256":"e88770c9fad779226ddcbd876db5393065ee08f96e62f50677b9ec3dca5f5272","abstract_canon_sha256":"0574ef3d2abd36beaa4366a520e8363993a82cf713466f9faa6dbccef7461fe7"},"schema_version":"1.0"},"canonical_sha256":"f9950cdab70473e588a9d7ba6270cbbc39ac245b4a6120ed6db00c79ed88c1f4","source":{"kind":"arxiv","id":"1212.1596","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:7GKQZWVXARZ6LCFJ265GE4GLXQ","target":"record","payload":{"canonical_record":{"source":{"id":"1212.1596","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2012-12-07T12:39:28Z","cross_cats_sorted":["math.LO"],"title_canon_sha256":"e88770c9fad779226ddcbd876db5393065ee08f96e62f50677b9ec3dca5f5272","abstract_canon_sha256":"0574ef3d2abd36beaa4366a520e8363993a82cf713466f9faa6dbccef7461fe7"},"schema_version":"1.0"},"canonical_sha256":"f9950cdab70473e588a9d7ba6270cbbc39ac245b4a6120ed6db00c79ed88c1f4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:21:12.140372Z","signature_b64":"Prm/bamvYxRHktLr6NmN119pMT0/ORBi4s5Sfs9P8FS0qJ0wJRxWxUHza2NYhDo200cBF5bd7J031ueKeMUqDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f9950cdab70473e588a9d7ba6270cbbc39ac245b4a6120ed6db00c79ed88c1f4","last_reissued_at":"2026-05-18T03:21:12.139644Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:21:12.139644Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1212.1596","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:21:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4PVzNLrPh8VHUeh38yTmn3ypT6TKXwW+Sh3kypRYVj/9w6DjTmqt14WQ6HictEoqw5tRo1vtpe/ncjI+LrLfAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T01:42:37.360834Z"},"content_sha256":"4b6b3909d2eecd60048949f57b5cb1a170f942172ca9ff85aea73c7c9cf2d307","schema_version":"1.0","event_id":"sha256:4b6b3909d2eecd60048949f57b5cb1a170f942172ca9ff85aea73c7c9cf2d307"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:7GKQZWVXARZ6LCFJ265GE4GLXQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Automatic continuity for homomorphisms into free products","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.LO"],"primary_cat":"math.GR","authors_text":"Konstantin Slutsky","submitted_at":"2012-12-07T12:39:28Z","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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.1596","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:21:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TV6vjBTs+DuSw0whKfqDfASLAlNx5zdvI9N4A8kzGy7JUU3jEKrGHLbluG2vUbYAxflkUiy0v4l2U1a69dKjDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T01:42:37.361510Z"},"content_sha256":"fe69ca4ba0b264f6720ef395800d41fb05e183f96e5927b2cc8fd7cf7c40d1a6","schema_version":"1.0","event_id":"sha256:fe69ca4ba0b264f6720ef395800d41fb05e183f96e5927b2cc8fd7cf7c40d1a6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7GKQZWVXARZ6LCFJ265GE4GLXQ/bundle.json","state_url":"https://pith.science/pith/7GKQZWVXARZ6LCFJ265GE4GLXQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7GKQZWVXARZ6LCFJ265GE4GLXQ/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-07T01:42:37Z","links":{"resolver":"https://pith.science/pith/7GKQZWVXARZ6LCFJ265GE4GLXQ","bundle":"https://pith.science/pith/7GKQZWVXARZ6LCFJ265GE4GLXQ/bundle.json","state":"https://pith.science/pith/7GKQZWVXARZ6LCFJ265GE4GLXQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7GKQZWVXARZ6LCFJ265GE4GLXQ/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Sy7RX16u/BrmqWv40434IPbbe99EADHhw73leLEtB5wzv3dhlFIPa13H5pdYqNG4oGVaPGt63MfJiwrmssDABA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T01:42:37.365847Z","bundle_sha256":"fe38b26e8c3b83d4ff8a6f21e8f244f054b6572165fc0ce5e2e02eca3aa921dc"}}