{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:JP2FSECPDHFGE43QOA47PCNWHA","short_pith_number":"pith:JP2FSECP","canonical_record":{"source":{"id":"1508.03366","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-08-13T21:40:19Z","cross_cats_sorted":[],"title_canon_sha256":"6e9943b488a59c5a4cd66ec53534a3af98e66238b28568796e05c0730447b029","abstract_canon_sha256":"5f72ad5ea033e3279f86ba7c92632af5a9195c9431c4e72822abbfff185eeec5"},"schema_version":"1.0"},"canonical_sha256":"4bf459104f19ca6273707039f789b6383fd47e38bc4828b5f16dc57729a5f48e","source":{"kind":"arxiv","id":"1508.03366","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.03366","created_at":"2026-05-18T00:51:07Z"},{"alias_kind":"arxiv_version","alias_value":"1508.03366v2","created_at":"2026-05-18T00:51:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.03366","created_at":"2026-05-18T00:51:07Z"},{"alias_kind":"pith_short_12","alias_value":"JP2FSECPDHFG","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_16","alias_value":"JP2FSECPDHFGE43Q","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_8","alias_value":"JP2FSECP","created_at":"2026-05-18T12:29:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:JP2FSECPDHFGE43QOA47PCNWHA","target":"record","payload":{"canonical_record":{"source":{"id":"1508.03366","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-08-13T21:40:19Z","cross_cats_sorted":[],"title_canon_sha256":"6e9943b488a59c5a4cd66ec53534a3af98e66238b28568796e05c0730447b029","abstract_canon_sha256":"5f72ad5ea033e3279f86ba7c92632af5a9195c9431c4e72822abbfff185eeec5"},"schema_version":"1.0"},"canonical_sha256":"4bf459104f19ca6273707039f789b6383fd47e38bc4828b5f16dc57729a5f48e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:51:07.546637Z","signature_b64":"5YkeEFTHUo+NV5BatsV085K4M4xrnKCk1AXIdROW1LGIQt/KaqWvwuFUxY0FisWNYIiBHqtW2oIBmYql0VLjBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4bf459104f19ca6273707039f789b6383fd47e38bc4828b5f16dc57729a5f48e","last_reissued_at":"2026-05-18T00:51:07.546138Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:51:07.546138Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1508.03366","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":"2026-05-18T00:51:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NgqcYji3TAmjsDNKV9Mt3dux8rR3EW3I+wlFAiqVkIRSDzZdRmYb7P/MTuskR7B4iJmYVMhd9RTI6McgyDnXDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T00:30:26.573789Z"},"content_sha256":"04d2e16c6040b2be9012d6d605735c02d3293f9f8ec8cac8c1b3e4aab305af75","schema_version":"1.0","event_id":"sha256:04d2e16c6040b2be9012d6d605735c02d3293f9f8ec8cac8c1b3e4aab305af75"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:JP2FSECPDHFGE43QOA47PCNWHA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Uniformly rigid models for rigid actions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Sebastian Donoso, Song Shao","submitted_at":"2015-08-13T21:40:19Z","abstract_excerpt":"In this article we show that any ergodic rigid system can be topologically realized by a uniformly rigid and (topologically) weak mixing topological dynamical system."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.03366","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":"2026-05-18T00:51:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"G3lZzTDBJzP8Sc3f68mqI28jJdAiqClAWxJzG2nWB0lzNvMIimwr0+WxSdN/U7lM/sA85VqRlQd3T8MlR8ekCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T00:30:26.574129Z"},"content_sha256":"9a7268bcf6f45b2192f5bab0e1063e6bfb2ad8fa5bb5fab2bb5b5d959399b117","schema_version":"1.0","event_id":"sha256:9a7268bcf6f45b2192f5bab0e1063e6bfb2ad8fa5bb5fab2bb5b5d959399b117"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JP2FSECPDHFGE43QOA47PCNWHA/bundle.json","state_url":"https://pith.science/pith/JP2FSECPDHFGE43QOA47PCNWHA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JP2FSECPDHFGE43QOA47PCNWHA/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":"2026-06-23T00:30:26Z","links":{"resolver":"https://pith.science/pith/JP2FSECPDHFGE43QOA47PCNWHA","bundle":"https://pith.science/pith/JP2FSECPDHFGE43QOA47PCNWHA/bundle.json","state":"https://pith.science/pith/JP2FSECPDHFGE43QOA47PCNWHA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JP2FSECPDHFGE43QOA47PCNWHA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:JP2FSECPDHFGE43QOA47PCNWHA","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":"5f72ad5ea033e3279f86ba7c92632af5a9195c9431c4e72822abbfff185eeec5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-08-13T21:40:19Z","title_canon_sha256":"6e9943b488a59c5a4cd66ec53534a3af98e66238b28568796e05c0730447b029"},"schema_version":"1.0","source":{"id":"1508.03366","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.03366","created_at":"2026-05-18T00:51:07Z"},{"alias_kind":"arxiv_version","alias_value":"1508.03366v2","created_at":"2026-05-18T00:51:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.03366","created_at":"2026-05-18T00:51:07Z"},{"alias_kind":"pith_short_12","alias_value":"JP2FSECPDHFG","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_16","alias_value":"JP2FSECPDHFGE43Q","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_8","alias_value":"JP2FSECP","created_at":"2026-05-18T12:29:27Z"}],"graph_snapshots":[{"event_id":"sha256:9a7268bcf6f45b2192f5bab0e1063e6bfb2ad8fa5bb5fab2bb5b5d959399b117","target":"graph","created_at":"2026-05-18T00:51:07Z","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":"In this article we show that any ergodic rigid system can be topologically realized by a uniformly rigid and (topologically) weak mixing topological dynamical system.","authors_text":"Sebastian Donoso, Song Shao","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-08-13T21:40:19Z","title":"Uniformly rigid models for rigid actions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.03366","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":"sha256:04d2e16c6040b2be9012d6d605735c02d3293f9f8ec8cac8c1b3e4aab305af75","target":"record","created_at":"2026-05-18T00:51:07Z","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":"5f72ad5ea033e3279f86ba7c92632af5a9195c9431c4e72822abbfff185eeec5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-08-13T21:40:19Z","title_canon_sha256":"6e9943b488a59c5a4cd66ec53534a3af98e66238b28568796e05c0730447b029"},"schema_version":"1.0","source":{"id":"1508.03366","kind":"arxiv","version":2}},"canonical_sha256":"4bf459104f19ca6273707039f789b6383fd47e38bc4828b5f16dc57729a5f48e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4bf459104f19ca6273707039f789b6383fd47e38bc4828b5f16dc57729a5f48e","first_computed_at":"2026-05-18T00:51:07.546138Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:51:07.546138Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5YkeEFTHUo+NV5BatsV085K4M4xrnKCk1AXIdROW1LGIQt/KaqWvwuFUxY0FisWNYIiBHqtW2oIBmYql0VLjBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:51:07.546637Z","signed_message":"canonical_sha256_bytes"},"source_id":"1508.03366","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:04d2e16c6040b2be9012d6d605735c02d3293f9f8ec8cac8c1b3e4aab305af75","sha256:9a7268bcf6f45b2192f5bab0e1063e6bfb2ad8fa5bb5fab2bb5b5d959399b117"],"state_sha256":"a8bf2d9c8b6bd20f7f66313d7bc9b111c5cdaf58bd4521c32abde20c7841ac20"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"grfw0+VksGg7HD46DiQvhrgtYF/8sM3NdQtOjZ8jJJRjklU1JhPtt/fR/c/A5JfIXbKmD/TGeKp0p649bd+GBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T00:30:26.576202Z","bundle_sha256":"2f149338c44bb626b4f46a769ff0356fc06f073ed10f8eb5499843355e1f94f8"}}