{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:JYTS5YWT75C7VRGN76TWVTX4UL","short_pith_number":"pith:JYTS5YWT","canonical_record":{"source":{"id":"0903.3109","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2009-03-18T09:02:38Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"9c76e4b914ac6a78f2d179c17f37ef6e7b69953e970183b79db3626c70a006d8","abstract_canon_sha256":"8a8ddab699d07c9c7bd3d443d6aad9dd1b3ba9393501c3633a33fc0a56396c94"},"schema_version":"1.0"},"canonical_sha256":"4e272ee2d3ff45fac4cdffa76acefca2d6301b4c35333717d6fb55834e789093","source":{"kind":"arxiv","id":"0903.3109","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0903.3109","created_at":"2026-05-18T02:51:48Z"},{"alias_kind":"arxiv_version","alias_value":"0903.3109v2","created_at":"2026-05-18T02:51:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0903.3109","created_at":"2026-05-18T02:51:48Z"},{"alias_kind":"pith_short_12","alias_value":"JYTS5YWT75C7","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_16","alias_value":"JYTS5YWT75C7VRGN","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_8","alias_value":"JYTS5YWT","created_at":"2026-05-18T12:26:00Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:JYTS5YWT75C7VRGN76TWVTX4UL","target":"record","payload":{"canonical_record":{"source":{"id":"0903.3109","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2009-03-18T09:02:38Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"9c76e4b914ac6a78f2d179c17f37ef6e7b69953e970183b79db3626c70a006d8","abstract_canon_sha256":"8a8ddab699d07c9c7bd3d443d6aad9dd1b3ba9393501c3633a33fc0a56396c94"},"schema_version":"1.0"},"canonical_sha256":"4e272ee2d3ff45fac4cdffa76acefca2d6301b4c35333717d6fb55834e789093","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:51:48.862769Z","signature_b64":"eTm6FZ7Oocd7EC41OXGhEsNc2QvSzf++m47enSQuGt9Z1mxeUR4A2CpI0MIFsoz82VNiI2Y+C66yR3hvuptLAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4e272ee2d3ff45fac4cdffa76acefca2d6301b4c35333717d6fb55834e789093","last_reissued_at":"2026-05-18T02:51:48.862286Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:51:48.862286Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0903.3109","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":"2026-05-18T02:51:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5wMQF2BIB2m1ISxaCbcseNZR2K1+4PmBAsdmbDpHwu4WxzqjTPbDX3i/tG5HxPU8XP519IDJF5jP5YzwUDNDBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T18:41:31.998377Z"},"content_sha256":"3c6e1d5f48563d6050b544c8056493364a5cdfb3b8a7bae8c7c1205aa9e0814c","schema_version":"1.0","event_id":"sha256:3c6e1d5f48563d6050b544c8056493364a5cdfb3b8a7bae8c7c1205aa9e0814c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:JYTS5YWT75C7VRGN76TWVTX4UL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A note on quasi-similarity of Koopman operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.DS","authors_text":"Krzysztof Fraczek, Mariusz Lemanczyk","submitted_at":"2009-03-18T09:02:38Z","abstract_excerpt":"Answering a question of A. Vershik we construct two non-weakly isomorphic ergodic automorphisms for which the associated unitary (Koopman) representations are Markov quasi-similar. We also discuss metric invariants of Markov quasi-similarity in the class of ergodic automorphisms."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0903.3109","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":"2026-05-18T02:51:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7z2/rArFbTK/paYyKlxqRowGjIqrcJ8qw5DtR6nTJHnabY1BNeNhH6utw14ATGUl7IPAEd7/z8f5+xLwv8DpBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T18:41:31.999053Z"},"content_sha256":"fbec68d01656c44cd6c90e021baf9e52fa7bc3e3e209e5ef4caff9546649343a","schema_version":"1.0","event_id":"sha256:fbec68d01656c44cd6c90e021baf9e52fa7bc3e3e209e5ef4caff9546649343a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JYTS5YWT75C7VRGN76TWVTX4UL/bundle.json","state_url":"https://pith.science/pith/JYTS5YWT75C7VRGN76TWVTX4UL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JYTS5YWT75C7VRGN76TWVTX4UL/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":"2026-06-02T18:41:32Z","links":{"resolver":"https://pith.science/pith/JYTS5YWT75C7VRGN76TWVTX4UL","bundle":"https://pith.science/pith/JYTS5YWT75C7VRGN76TWVTX4UL/bundle.json","state":"https://pith.science/pith/JYTS5YWT75C7VRGN76TWVTX4UL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JYTS5YWT75C7VRGN76TWVTX4UL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:JYTS5YWT75C7VRGN76TWVTX4UL","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":"8a8ddab699d07c9c7bd3d443d6aad9dd1b3ba9393501c3633a33fc0a56396c94","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2009-03-18T09:02:38Z","title_canon_sha256":"9c76e4b914ac6a78f2d179c17f37ef6e7b69953e970183b79db3626c70a006d8"},"schema_version":"1.0","source":{"id":"0903.3109","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0903.3109","created_at":"2026-05-18T02:51:48Z"},{"alias_kind":"arxiv_version","alias_value":"0903.3109v2","created_at":"2026-05-18T02:51:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0903.3109","created_at":"2026-05-18T02:51:48Z"},{"alias_kind":"pith_short_12","alias_value":"JYTS5YWT75C7","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_16","alias_value":"JYTS5YWT75C7VRGN","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_8","alias_value":"JYTS5YWT","created_at":"2026-05-18T12:26:00Z"}],"graph_snapshots":[{"event_id":"sha256:fbec68d01656c44cd6c90e021baf9e52fa7bc3e3e209e5ef4caff9546649343a","target":"graph","created_at":"2026-05-18T02:51:48Z","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":"Answering a question of A. Vershik we construct two non-weakly isomorphic ergodic automorphisms for which the associated unitary (Koopman) representations are Markov quasi-similar. We also discuss metric invariants of Markov quasi-similarity in the class of ergodic automorphisms.","authors_text":"Krzysztof Fraczek, Mariusz Lemanczyk","cross_cats":["math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2009-03-18T09:02:38Z","title":"A note on quasi-similarity of Koopman operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0903.3109","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":"sha256:3c6e1d5f48563d6050b544c8056493364a5cdfb3b8a7bae8c7c1205aa9e0814c","target":"record","created_at":"2026-05-18T02:51:48Z","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":"8a8ddab699d07c9c7bd3d443d6aad9dd1b3ba9393501c3633a33fc0a56396c94","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2009-03-18T09:02:38Z","title_canon_sha256":"9c76e4b914ac6a78f2d179c17f37ef6e7b69953e970183b79db3626c70a006d8"},"schema_version":"1.0","source":{"id":"0903.3109","kind":"arxiv","version":2}},"canonical_sha256":"4e272ee2d3ff45fac4cdffa76acefca2d6301b4c35333717d6fb55834e789093","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4e272ee2d3ff45fac4cdffa76acefca2d6301b4c35333717d6fb55834e789093","first_computed_at":"2026-05-18T02:51:48.862286Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:51:48.862286Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"eTm6FZ7Oocd7EC41OXGhEsNc2QvSzf++m47enSQuGt9Z1mxeUR4A2CpI0MIFsoz82VNiI2Y+C66yR3hvuptLAw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:51:48.862769Z","signed_message":"canonical_sha256_bytes"},"source_id":"0903.3109","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3c6e1d5f48563d6050b544c8056493364a5cdfb3b8a7bae8c7c1205aa9e0814c","sha256:fbec68d01656c44cd6c90e021baf9e52fa7bc3e3e209e5ef4caff9546649343a"],"state_sha256":"3176309aa559111ef25354448242a3acd25d89708b568acec39891d545c0c26a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zAZuBxRmb4fFR77FY+MnbajxAmSzdr24zqmZN0r+2/VXTeEZRgttFnN6ccVR0tpMPYknYNuOCUrJYFd+iLfOBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T18:41:32.002278Z","bundle_sha256":"d9ca0adb33e07118c7ce3959b6734438b59b3d4e6f23207acbb0bd0695bf4d0b"}}