{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:XCU2VZ7CWUVDZ2OAM2AROCRL2M","short_pith_number":"pith:XCU2VZ7C","canonical_record":{"source":{"id":"1702.02657","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-02-09T00:11:02Z","cross_cats_sorted":["math.DS","math.OA"],"title_canon_sha256":"e88e230491bdd1e0c422792352c2137a6f0cee80c159502633b72ac76c3b1a96","abstract_canon_sha256":"5e29f912b5f4c736d37bab886559b3443f57ddd92defc22259f19f6722dc85ef"},"schema_version":"1.0"},"canonical_sha256":"b8a9aae7e2b52a3ce9c06681170a2bd30ad5de77ee6fd0f23de40a92dab299c2","source":{"kind":"arxiv","id":"1702.02657","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.02657","created_at":"2026-05-18T00:51:03Z"},{"alias_kind":"arxiv_version","alias_value":"1702.02657v1","created_at":"2026-05-18T00:51:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.02657","created_at":"2026-05-18T00:51:03Z"},{"alias_kind":"pith_short_12","alias_value":"XCU2VZ7CWUVD","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_16","alias_value":"XCU2VZ7CWUVDZ2OA","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_8","alias_value":"XCU2VZ7C","created_at":"2026-05-18T12:31:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:XCU2VZ7CWUVDZ2OAM2AROCRL2M","target":"record","payload":{"canonical_record":{"source":{"id":"1702.02657","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-02-09T00:11:02Z","cross_cats_sorted":["math.DS","math.OA"],"title_canon_sha256":"e88e230491bdd1e0c422792352c2137a6f0cee80c159502633b72ac76c3b1a96","abstract_canon_sha256":"5e29f912b5f4c736d37bab886559b3443f57ddd92defc22259f19f6722dc85ef"},"schema_version":"1.0"},"canonical_sha256":"b8a9aae7e2b52a3ce9c06681170a2bd30ad5de77ee6fd0f23de40a92dab299c2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:51:03.772609Z","signature_b64":"heWdADjckLBRCpD0lZ2uO/q6ZnZFt9pJQ/J60qZqNeKCoxqHfiVgM267HkBWZbMCTNo7XpbxubFaCrcr9e/TCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b8a9aae7e2b52a3ce9c06681170a2bd30ad5de77ee6fd0f23de40a92dab299c2","last_reissued_at":"2026-05-18T00:51:03.772133Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:51:03.772133Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1702.02657","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:51:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xdnqqYxCpsYHJKcVCor1VkE7pGRlyw/vNMp2mMFSioXyjYsr08PmfjxLerIfjDaL6GXdmqrc2Mky8mnPs9a2CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T08:33:35.941666Z"},"content_sha256":"403f49b7a23eb36c76eef34f4b9af6b7cec41c998f6a337e0236fe88980fb006","schema_version":"1.0","event_id":"sha256:403f49b7a23eb36c76eef34f4b9af6b7cec41c998f6a337e0236fe88980fb006"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:XCU2VZ7CWUVDZ2OAM2AROCRL2M","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Infinite-dimensional transfer operators, endomorphisms, and measurable partitions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","math.OA"],"primary_cat":"math.FA","authors_text":"Palle E.T. Jorgensen, Sergey Bezuglyi","submitted_at":"2017-02-09T00:11:02Z","abstract_excerpt":"We develop a new duality between endomorphisms of measure spaces, on the one hand, and a certain family of positive operators, called transfer operators, acting in spaces of measurable functions on, on the other. A framework of standard Borel spaces is adopted; and this generality is wide enough to cover a host of applications. While the mathematical structures of positive operators, endomorphisms, transfer operators, measurable partitions, and Markov processes arise in a host of settings, both pure and applied, we propose here a unified study. This is the general setting of dynamics in Borel "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.02657","kind":"arxiv","version":1},"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":"2026-05-18T00:51:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"01DQzsfjjtLmJlwXFmOZLndL1yqLbt0ft7YGJlx4zvTCcC8Oeq337c+UsJQhgQrcDcnhw0ua3p6GkCPsK+vcCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T08:33:35.942016Z"},"content_sha256":"d3cbf3198272f368ce9c45a47fe3fd32bd4ec02b41852b818059d4cae45a0fd2","schema_version":"1.0","event_id":"sha256:d3cbf3198272f368ce9c45a47fe3fd32bd4ec02b41852b818059d4cae45a0fd2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XCU2VZ7CWUVDZ2OAM2AROCRL2M/bundle.json","state_url":"https://pith.science/pith/XCU2VZ7CWUVDZ2OAM2AROCRL2M/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XCU2VZ7CWUVDZ2OAM2AROCRL2M/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":"2026-05-28T08:33:35Z","links":{"resolver":"https://pith.science/pith/XCU2VZ7CWUVDZ2OAM2AROCRL2M","bundle":"https://pith.science/pith/XCU2VZ7CWUVDZ2OAM2AROCRL2M/bundle.json","state":"https://pith.science/pith/XCU2VZ7CWUVDZ2OAM2AROCRL2M/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XCU2VZ7CWUVDZ2OAM2AROCRL2M/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:XCU2VZ7CWUVDZ2OAM2AROCRL2M","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":"5e29f912b5f4c736d37bab886559b3443f57ddd92defc22259f19f6722dc85ef","cross_cats_sorted":["math.DS","math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-02-09T00:11:02Z","title_canon_sha256":"e88e230491bdd1e0c422792352c2137a6f0cee80c159502633b72ac76c3b1a96"},"schema_version":"1.0","source":{"id":"1702.02657","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.02657","created_at":"2026-05-18T00:51:03Z"},{"alias_kind":"arxiv_version","alias_value":"1702.02657v1","created_at":"2026-05-18T00:51:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.02657","created_at":"2026-05-18T00:51:03Z"},{"alias_kind":"pith_short_12","alias_value":"XCU2VZ7CWUVD","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_16","alias_value":"XCU2VZ7CWUVDZ2OA","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_8","alias_value":"XCU2VZ7C","created_at":"2026-05-18T12:31:53Z"}],"graph_snapshots":[{"event_id":"sha256:d3cbf3198272f368ce9c45a47fe3fd32bd4ec02b41852b818059d4cae45a0fd2","target":"graph","created_at":"2026-05-18T00:51:03Z","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":"We develop a new duality between endomorphisms of measure spaces, on the one hand, and a certain family of positive operators, called transfer operators, acting in spaces of measurable functions on, on the other. A framework of standard Borel spaces is adopted; and this generality is wide enough to cover a host of applications. While the mathematical structures of positive operators, endomorphisms, transfer operators, measurable partitions, and Markov processes arise in a host of settings, both pure and applied, we propose here a unified study. This is the general setting of dynamics in Borel ","authors_text":"Palle E.T. Jorgensen, Sergey Bezuglyi","cross_cats":["math.DS","math.OA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-02-09T00:11:02Z","title":"Infinite-dimensional transfer operators, endomorphisms, and measurable partitions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.02657","kind":"arxiv","version":1},"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":"sha256:403f49b7a23eb36c76eef34f4b9af6b7cec41c998f6a337e0236fe88980fb006","target":"record","created_at":"2026-05-18T00:51:03Z","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":"5e29f912b5f4c736d37bab886559b3443f57ddd92defc22259f19f6722dc85ef","cross_cats_sorted":["math.DS","math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-02-09T00:11:02Z","title_canon_sha256":"e88e230491bdd1e0c422792352c2137a6f0cee80c159502633b72ac76c3b1a96"},"schema_version":"1.0","source":{"id":"1702.02657","kind":"arxiv","version":1}},"canonical_sha256":"b8a9aae7e2b52a3ce9c06681170a2bd30ad5de77ee6fd0f23de40a92dab299c2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b8a9aae7e2b52a3ce9c06681170a2bd30ad5de77ee6fd0f23de40a92dab299c2","first_computed_at":"2026-05-18T00:51:03.772133Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:51:03.772133Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"heWdADjckLBRCpD0lZ2uO/q6ZnZFt9pJQ/J60qZqNeKCoxqHfiVgM267HkBWZbMCTNo7XpbxubFaCrcr9e/TCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:51:03.772609Z","signed_message":"canonical_sha256_bytes"},"source_id":"1702.02657","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:403f49b7a23eb36c76eef34f4b9af6b7cec41c998f6a337e0236fe88980fb006","sha256:d3cbf3198272f368ce9c45a47fe3fd32bd4ec02b41852b818059d4cae45a0fd2"],"state_sha256":"db94f9bff0f4eccbbbbda442424fab87815019c307671058bda07bcb28ec9603"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Rsi5siLxi2Ung3nq49QWoa55mJq02d1D9uW6dl8bl8f21j7aqLCG9qVZJsxN96f1/iImukgnwZTR4YSBLFNUDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T08:33:35.944041Z","bundle_sha256":"395a993f4b752f8b5e9569770026d56af6181f616c88a95bf1591a75ed08f27f"}}