{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:LQYBCJNMODUHMKP2VPZ5DVJEOU","short_pith_number":"pith:LQYBCJNM","canonical_record":{"source":{"id":"1903.06976","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2019-03-16T19:31:42Z","cross_cats_sorted":["math.AP","math.CA","math.FA"],"title_canon_sha256":"7303078e2bf212f52f8580218d8e0af6ec605839479a9dde3dc4fb895af370f3","abstract_canon_sha256":"ec7e78ef03233e77a4234c00ff1d25566c2d40483795a6e26247f65698f0710c"},"schema_version":"1.0"},"canonical_sha256":"5c301125ac70e87629faabf3d1d524750203e4a9d843b233a6d53dc873e5170e","source":{"kind":"arxiv","id":"1903.06976","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1903.06976","created_at":"2026-07-05T02:41:26Z"},{"alias_kind":"arxiv_version","alias_value":"1903.06976v2","created_at":"2026-07-05T02:41:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.06976","created_at":"2026-07-05T02:41:26Z"},{"alias_kind":"pith_short_12","alias_value":"LQYBCJNMODUH","created_at":"2026-07-05T02:41:26Z"},{"alias_kind":"pith_short_16","alias_value":"LQYBCJNMODUHMKP2","created_at":"2026-07-05T02:41:26Z"},{"alias_kind":"pith_short_8","alias_value":"LQYBCJNM","created_at":"2026-07-05T02:41:26Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:LQYBCJNMODUHMKP2VPZ5DVJEOU","target":"record","payload":{"canonical_record":{"source":{"id":"1903.06976","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2019-03-16T19:31:42Z","cross_cats_sorted":["math.AP","math.CA","math.FA"],"title_canon_sha256":"7303078e2bf212f52f8580218d8e0af6ec605839479a9dde3dc4fb895af370f3","abstract_canon_sha256":"ec7e78ef03233e77a4234c00ff1d25566c2d40483795a6e26247f65698f0710c"},"schema_version":"1.0"},"canonical_sha256":"5c301125ac70e87629faabf3d1d524750203e4a9d843b233a6d53dc873e5170e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:41:26.369237Z","signature_b64":"abw2keTAOBV8DijhqJ4zulsde4kFwsWy18avrL92Z8S+e7F5Kxtx3FVyktNtYnoYEbsdAIM7bIooXGlUYv7iDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5c301125ac70e87629faabf3d1d524750203e4a9d843b233a6d53dc873e5170e","last_reissued_at":"2026-07-05T02:41:26.368836Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:41:26.368836Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1903.06976","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":"2026-07-05T02:41:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bjvNqYbKFN2yLLTtu1F1cl6lzYtQHNBlBZUAztKPclmvtjBJvS0ARPL0kco19FZNG3il4WWDnw8iFQPhbPm2Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T19:47:25.146403Z"},"content_sha256":"3773a618668fa4cb30f37be05ca4fbd99a911f707586a0562966d061b5fe2868","schema_version":"1.0","event_id":"sha256:3773a618668fa4cb30f37be05ca4fbd99a911f707586a0562966d061b5fe2868"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:LQYBCJNMODUHMKP2VPZ5DVJEOU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Transfer operators, atomic decomposition and the Bestiary","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.CA","math.FA"],"primary_cat":"math.DS","authors_text":"Daniel Smania","submitted_at":"2019-03-16T19:31:42Z","abstract_excerpt":"Arbieto and S. recently used atomic decomposition to study transfer operators. We give a long list of old and new expanding dynamical systems for which those results can be applied, obtaining the quasi-compactness of transfer operator acting on Besov spaces of measure spaces with a good grid."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.06976","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1903.06976/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T02:41:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"b144rylTtcOCJvxXZ1NqiPBW32o4cLJnsSV3QG5OyPj9i5dYLq5RSWD5Rn7dZ6ZIiSXafrj6YireTWcwv5kLDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T19:47:25.147398Z"},"content_sha256":"ae4c652a3fad931b8006e7bf0503a840ccda0edb6933668747789dc2c176d984","schema_version":"1.0","event_id":"sha256:ae4c652a3fad931b8006e7bf0503a840ccda0edb6933668747789dc2c176d984"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LQYBCJNMODUHMKP2VPZ5DVJEOU/bundle.json","state_url":"https://pith.science/pith/LQYBCJNMODUHMKP2VPZ5DVJEOU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LQYBCJNMODUHMKP2VPZ5DVJEOU/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":"2026-08-09T19:47:25Z","links":{"resolver":"https://pith.science/pith/LQYBCJNMODUHMKP2VPZ5DVJEOU","bundle":"https://pith.science/pith/LQYBCJNMODUHMKP2VPZ5DVJEOU/bundle.json","state":"https://pith.science/pith/LQYBCJNMODUHMKP2VPZ5DVJEOU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LQYBCJNMODUHMKP2VPZ5DVJEOU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:LQYBCJNMODUHMKP2VPZ5DVJEOU","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":"ec7e78ef03233e77a4234c00ff1d25566c2d40483795a6e26247f65698f0710c","cross_cats_sorted":["math.AP","math.CA","math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2019-03-16T19:31:42Z","title_canon_sha256":"7303078e2bf212f52f8580218d8e0af6ec605839479a9dde3dc4fb895af370f3"},"schema_version":"1.0","source":{"id":"1903.06976","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1903.06976","created_at":"2026-07-05T02:41:26Z"},{"alias_kind":"arxiv_version","alias_value":"1903.06976v2","created_at":"2026-07-05T02:41:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.06976","created_at":"2026-07-05T02:41:26Z"},{"alias_kind":"pith_short_12","alias_value":"LQYBCJNMODUH","created_at":"2026-07-05T02:41:26Z"},{"alias_kind":"pith_short_16","alias_value":"LQYBCJNMODUHMKP2","created_at":"2026-07-05T02:41:26Z"},{"alias_kind":"pith_short_8","alias_value":"LQYBCJNM","created_at":"2026-07-05T02:41:26Z"}],"graph_snapshots":[{"event_id":"sha256:ae4c652a3fad931b8006e7bf0503a840ccda0edb6933668747789dc2c176d984","target":"graph","created_at":"2026-07-05T02:41:26Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1903.06976/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Arbieto and S. recently used atomic decomposition to study transfer operators. We give a long list of old and new expanding dynamical systems for which those results can be applied, obtaining the quasi-compactness of transfer operator acting on Besov spaces of measure spaces with a good grid.","authors_text":"Daniel Smania","cross_cats":["math.AP","math.CA","math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2019-03-16T19:31:42Z","title":"Transfer operators, atomic decomposition and the Bestiary"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.06976","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":"sha256:3773a618668fa4cb30f37be05ca4fbd99a911f707586a0562966d061b5fe2868","target":"record","created_at":"2026-07-05T02:41:26Z","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":"ec7e78ef03233e77a4234c00ff1d25566c2d40483795a6e26247f65698f0710c","cross_cats_sorted":["math.AP","math.CA","math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2019-03-16T19:31:42Z","title_canon_sha256":"7303078e2bf212f52f8580218d8e0af6ec605839479a9dde3dc4fb895af370f3"},"schema_version":"1.0","source":{"id":"1903.06976","kind":"arxiv","version":2}},"canonical_sha256":"5c301125ac70e87629faabf3d1d524750203e4a9d843b233a6d53dc873e5170e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5c301125ac70e87629faabf3d1d524750203e4a9d843b233a6d53dc873e5170e","first_computed_at":"2026-07-05T02:41:26.368836Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:41:26.368836Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"abw2keTAOBV8DijhqJ4zulsde4kFwsWy18avrL92Z8S+e7F5Kxtx3FVyktNtYnoYEbsdAIM7bIooXGlUYv7iDw==","signature_status":"signed_v1","signed_at":"2026-07-05T02:41:26.369237Z","signed_message":"canonical_sha256_bytes"},"source_id":"1903.06976","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3773a618668fa4cb30f37be05ca4fbd99a911f707586a0562966d061b5fe2868","sha256:ae4c652a3fad931b8006e7bf0503a840ccda0edb6933668747789dc2c176d984"],"state_sha256":"fe54c951c80410af34ccd22b024b278323c7cd43b232f73b650d42d2026d75f7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ivXDLLHWI51w7aLQgC4ocp2Y136dxqqdSso9Apt7mPl+tBOInph3XyHRGTSaGPk1Q3Xec79JVPC4wsd016ziDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-09T19:47:25.153327Z","bundle_sha256":"bef5a2408cf69e9ab6a1b33a33e8c626afcba3d0beeafda35c603848ed0107ff"}}