{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:CBMGABW3WTR27CD7XKHBHVOFJ5","short_pith_number":"pith:CBMGABW3","canonical_record":{"source":{"id":"1406.5425","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-06-20T15:24:40Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"ff0e663c41bfd6617d29dfdff0d719b6b9c819049e9c741a515f12c7f7ac8e44","abstract_canon_sha256":"cacf57af27b35b8ac55a9ce98a5f4c66aa2877b2e6ec3463e463679caabd0707"},"schema_version":"1.0"},"canonical_sha256":"10586006dbb4e3af887fba8e13d5c54f71547dbfbe932a0e3ef28c9e1ec6d213","source":{"kind":"arxiv","id":"1406.5425","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.5425","created_at":"2026-05-18T01:29:05Z"},{"alias_kind":"arxiv_version","alias_value":"1406.5425v1","created_at":"2026-05-18T01:29:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.5425","created_at":"2026-05-18T01:29:05Z"},{"alias_kind":"pith_short_12","alias_value":"CBMGABW3WTR2","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_16","alias_value":"CBMGABW3WTR27CD7","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_8","alias_value":"CBMGABW3","created_at":"2026-05-18T12:28:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:CBMGABW3WTR27CD7XKHBHVOFJ5","target":"record","payload":{"canonical_record":{"source":{"id":"1406.5425","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-06-20T15:24:40Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"ff0e663c41bfd6617d29dfdff0d719b6b9c819049e9c741a515f12c7f7ac8e44","abstract_canon_sha256":"cacf57af27b35b8ac55a9ce98a5f4c66aa2877b2e6ec3463e463679caabd0707"},"schema_version":"1.0"},"canonical_sha256":"10586006dbb4e3af887fba8e13d5c54f71547dbfbe932a0e3ef28c9e1ec6d213","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:29:05.673923Z","signature_b64":"TPu6vB+Nxx2DdkXNX9rIKH5Tz02FTbHVfzIpLrYeFhMrQOpoeXR/9acQ4j4FMA5wSS4BRwrCu/wFFTCerQz7AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"10586006dbb4e3af887fba8e13d5c54f71547dbfbe932a0e3ef28c9e1ec6d213","last_reissued_at":"2026-05-18T01:29:05.673282Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:29:05.673282Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1406.5425","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":"2026-05-18T01:29:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zZfDTBP2/4y4Pk/AdAAxtaFLev7ogg1UJJPEXbac/k9NC8laJMsNVt9MNPxJAHTbJrTICjICnQdpqbg7azlTDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T18:50:52.764379Z"},"content_sha256":"4aa844a23dd986dbea66ee8176809e37ba655b46fc1f1b67c83c941f0d190fb0","schema_version":"1.0","event_id":"sha256:4aa844a23dd986dbea66ee8176809e37ba655b46fc1f1b67c83c941f0d190fb0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:CBMGABW3WTR27CD7XKHBHVOFJ5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Regularity of invariant densities for 1D-systems with random switching","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.DS","authors_text":"Jonathan C. Mattingly, Tobias Hurth, Yuri Bakhtin","submitted_at":"2014-06-20T15:24:40Z","abstract_excerpt":"This is a detailed analysis of invariant measures for one-dimensional dynamical systems with random switching. In particular, we prove smoothness of the invariant densities away from critical points and describe the asymptotics of the invariant densities at critical points."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.5425","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":"2026-05-18T01:29:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HV+V8/KxxGSHAwwcShmJol1ms4J6zgzq7Pg0oRKk7pefZNZA5zquTAj45lwiseU3vC5ZiQWQI69VhaquFf2tAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T18:50:52.764801Z"},"content_sha256":"f914dbf380b586f3431b06754576ff13df5d7318b4970cecfbec1f2291385ff5","schema_version":"1.0","event_id":"sha256:f914dbf380b586f3431b06754576ff13df5d7318b4970cecfbec1f2291385ff5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CBMGABW3WTR27CD7XKHBHVOFJ5/bundle.json","state_url":"https://pith.science/pith/CBMGABW3WTR27CD7XKHBHVOFJ5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CBMGABW3WTR27CD7XKHBHVOFJ5/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":"2026-06-23T18:50:52Z","links":{"resolver":"https://pith.science/pith/CBMGABW3WTR27CD7XKHBHVOFJ5","bundle":"https://pith.science/pith/CBMGABW3WTR27CD7XKHBHVOFJ5/bundle.json","state":"https://pith.science/pith/CBMGABW3WTR27CD7XKHBHVOFJ5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CBMGABW3WTR27CD7XKHBHVOFJ5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:CBMGABW3WTR27CD7XKHBHVOFJ5","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":"cacf57af27b35b8ac55a9ce98a5f4c66aa2877b2e6ec3463e463679caabd0707","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-06-20T15:24:40Z","title_canon_sha256":"ff0e663c41bfd6617d29dfdff0d719b6b9c819049e9c741a515f12c7f7ac8e44"},"schema_version":"1.0","source":{"id":"1406.5425","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.5425","created_at":"2026-05-18T01:29:05Z"},{"alias_kind":"arxiv_version","alias_value":"1406.5425v1","created_at":"2026-05-18T01:29:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.5425","created_at":"2026-05-18T01:29:05Z"},{"alias_kind":"pith_short_12","alias_value":"CBMGABW3WTR2","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_16","alias_value":"CBMGABW3WTR27CD7","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_8","alias_value":"CBMGABW3","created_at":"2026-05-18T12:28:22Z"}],"graph_snapshots":[{"event_id":"sha256:f914dbf380b586f3431b06754576ff13df5d7318b4970cecfbec1f2291385ff5","target":"graph","created_at":"2026-05-18T01:29:05Z","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":"This is a detailed analysis of invariant measures for one-dimensional dynamical systems with random switching. In particular, we prove smoothness of the invariant densities away from critical points and describe the asymptotics of the invariant densities at critical points.","authors_text":"Jonathan C. Mattingly, Tobias Hurth, Yuri Bakhtin","cross_cats":["math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-06-20T15:24:40Z","title":"Regularity of invariant densities for 1D-systems with random switching"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.5425","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":"sha256:4aa844a23dd986dbea66ee8176809e37ba655b46fc1f1b67c83c941f0d190fb0","target":"record","created_at":"2026-05-18T01:29:05Z","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":"cacf57af27b35b8ac55a9ce98a5f4c66aa2877b2e6ec3463e463679caabd0707","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-06-20T15:24:40Z","title_canon_sha256":"ff0e663c41bfd6617d29dfdff0d719b6b9c819049e9c741a515f12c7f7ac8e44"},"schema_version":"1.0","source":{"id":"1406.5425","kind":"arxiv","version":1}},"canonical_sha256":"10586006dbb4e3af887fba8e13d5c54f71547dbfbe932a0e3ef28c9e1ec6d213","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"10586006dbb4e3af887fba8e13d5c54f71547dbfbe932a0e3ef28c9e1ec6d213","first_computed_at":"2026-05-18T01:29:05.673282Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:29:05.673282Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TPu6vB+Nxx2DdkXNX9rIKH5Tz02FTbHVfzIpLrYeFhMrQOpoeXR/9acQ4j4FMA5wSS4BRwrCu/wFFTCerQz7AA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:29:05.673923Z","signed_message":"canonical_sha256_bytes"},"source_id":"1406.5425","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4aa844a23dd986dbea66ee8176809e37ba655b46fc1f1b67c83c941f0d190fb0","sha256:f914dbf380b586f3431b06754576ff13df5d7318b4970cecfbec1f2291385ff5"],"state_sha256":"37d0ff638878da352af15b001649d5059b77f4a191da630da29d1abc27bc84b8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Qo0C4+ax9WvVt+uEz4aIXTrd949IjBdxiKTvtgLTQ8XRfR8nKitwvr7K50AsK7zgk0nk/oYvWCdFmbda9ihcCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T18:50:52.767156Z","bundle_sha256":"b3ba810f9e52ccccc76b4c7ce938719de8a31ee1c6816b8984de90c17ce66446"}}