{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2008:23Y4QRHVXUZ3QY4FFNY25UV5QC","short_pith_number":"pith:23Y4QRHV","canonical_record":{"source":{"id":"0802.2909","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2008-02-20T17:49:18Z","cross_cats_sorted":["math.MP","math.PR"],"title_canon_sha256":"b36ea249d1df66431def6281018b15ca8f49dc6351248489d99abc2d5c76c2b7","abstract_canon_sha256":"3767d97321fe88ede523b65f9209d57a2517cb3cb767f8882dc287bfaca8fffc"},"schema_version":"1.0"},"canonical_sha256":"d6f1c844f5bd33b863852b71aed2bd80a213e2f97d90ea4bb749158016df2a91","source":{"kind":"arxiv","id":"0802.2909","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0802.2909","created_at":"2026-05-18T04:35:15Z"},{"alias_kind":"arxiv_version","alias_value":"0802.2909v3","created_at":"2026-05-18T04:35:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0802.2909","created_at":"2026-05-18T04:35:15Z"},{"alias_kind":"pith_short_12","alias_value":"23Y4QRHVXUZ3","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"23Y4QRHVXUZ3QY4F","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"23Y4QRHV","created_at":"2026-05-18T12:25:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2008:23Y4QRHVXUZ3QY4FFNY25UV5QC","target":"record","payload":{"canonical_record":{"source":{"id":"0802.2909","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2008-02-20T17:49:18Z","cross_cats_sorted":["math.MP","math.PR"],"title_canon_sha256":"b36ea249d1df66431def6281018b15ca8f49dc6351248489d99abc2d5c76c2b7","abstract_canon_sha256":"3767d97321fe88ede523b65f9209d57a2517cb3cb767f8882dc287bfaca8fffc"},"schema_version":"1.0"},"canonical_sha256":"d6f1c844f5bd33b863852b71aed2bd80a213e2f97d90ea4bb749158016df2a91","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:35:15.127728Z","signature_b64":"nnOASCr53CUx9JbvQ8+DmVA4dmOL2QY3l6Y5uGLVuS3RmCLQiuH5dJ/QD4WZw9r5sLUy1mHCeBdGIp/sDcK9Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d6f1c844f5bd33b863852b71aed2bd80a213e2f97d90ea4bb749158016df2a91","last_reissued_at":"2026-05-18T04:35:15.127332Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:35:15.127332Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0802.2909","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:35:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ntea0DL9Q6zXkkCgeiMWUh5s+Dj5gPjHnkVXGVJyRI317jtrQcx4lqwCBKOE9RY04I/3efSPVa4tTNTjp0x8Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T23:37:10.993181Z"},"content_sha256":"674e7a0eefd783f64b9564a9366501a18d56fab2fee30b40f35a521e53dbe64e","schema_version":"1.0","event_id":"sha256:674e7a0eefd783f64b9564a9366501a18d56fab2fee30b40f35a521e53dbe64e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2008:23Y4QRHVXUZ3QY4FFNY25UV5QC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Random Lie group actions on compact manifolds: A perturbative analysis","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","math.PR"],"primary_cat":"math-ph","authors_text":"Christian Sadel, Hermann Schulz-Baldes","submitted_at":"2008-02-20T17:49:18Z","abstract_excerpt":"A random Lie group action on a compact manifold generates a discrete time Markov process. The main object of this paper is the evaluation of associated Birkhoff sums in a regime of weak, but sufficiently effective coupling of the randomness. This effectiveness is expressed in terms of random Lie algebra elements and replaces the transience or Furstenberg's irreducibility hypothesis in related problems. The Birkhoff sum of any given smooth function then turns out to be equal to its integral w.r.t. a unique smooth measure on the manifold up to errors of the order of the coupling constant. Applic"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0802.2909","kind":"arxiv","version":3},"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":"2026-05-18T04:35:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vtiWAf5IoFGAkmdQKDbEw5M5IG2Fg689AaqMWISLh9TBsmzXoA5lo0ta/QPFpnCWn5HMerzRxEEpG2mvTMcBBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T23:37:10.994329Z"},"content_sha256":"3088019f4b27f1c8af244476c64d1e681a98c03eaa5d66ed69a004848eb9df8f","schema_version":"1.0","event_id":"sha256:3088019f4b27f1c8af244476c64d1e681a98c03eaa5d66ed69a004848eb9df8f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/23Y4QRHVXUZ3QY4FFNY25UV5QC/bundle.json","state_url":"https://pith.science/pith/23Y4QRHVXUZ3QY4FFNY25UV5QC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/23Y4QRHVXUZ3QY4FFNY25UV5QC/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":"2026-06-07T23:37:10Z","links":{"resolver":"https://pith.science/pith/23Y4QRHVXUZ3QY4FFNY25UV5QC","bundle":"https://pith.science/pith/23Y4QRHVXUZ3QY4FFNY25UV5QC/bundle.json","state":"https://pith.science/pith/23Y4QRHVXUZ3QY4FFNY25UV5QC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/23Y4QRHVXUZ3QY4FFNY25UV5QC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:23Y4QRHVXUZ3QY4FFNY25UV5QC","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":"3767d97321fe88ede523b65f9209d57a2517cb3cb767f8882dc287bfaca8fffc","cross_cats_sorted":["math.MP","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2008-02-20T17:49:18Z","title_canon_sha256":"b36ea249d1df66431def6281018b15ca8f49dc6351248489d99abc2d5c76c2b7"},"schema_version":"1.0","source":{"id":"0802.2909","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0802.2909","created_at":"2026-05-18T04:35:15Z"},{"alias_kind":"arxiv_version","alias_value":"0802.2909v3","created_at":"2026-05-18T04:35:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0802.2909","created_at":"2026-05-18T04:35:15Z"},{"alias_kind":"pith_short_12","alias_value":"23Y4QRHVXUZ3","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"23Y4QRHVXUZ3QY4F","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"23Y4QRHV","created_at":"2026-05-18T12:25:56Z"}],"graph_snapshots":[{"event_id":"sha256:3088019f4b27f1c8af244476c64d1e681a98c03eaa5d66ed69a004848eb9df8f","target":"graph","created_at":"2026-05-18T04:35:15Z","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":"A random Lie group action on a compact manifold generates a discrete time Markov process. The main object of this paper is the evaluation of associated Birkhoff sums in a regime of weak, but sufficiently effective coupling of the randomness. This effectiveness is expressed in terms of random Lie algebra elements and replaces the transience or Furstenberg's irreducibility hypothesis in related problems. The Birkhoff sum of any given smooth function then turns out to be equal to its integral w.r.t. a unique smooth measure on the manifold up to errors of the order of the coupling constant. Applic","authors_text":"Christian Sadel, Hermann Schulz-Baldes","cross_cats":["math.MP","math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2008-02-20T17:49:18Z","title":"Random Lie group actions on compact manifolds: A perturbative analysis"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0802.2909","kind":"arxiv","version":3},"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":"sha256:674e7a0eefd783f64b9564a9366501a18d56fab2fee30b40f35a521e53dbe64e","target":"record","created_at":"2026-05-18T04:35:15Z","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":"3767d97321fe88ede523b65f9209d57a2517cb3cb767f8882dc287bfaca8fffc","cross_cats_sorted":["math.MP","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2008-02-20T17:49:18Z","title_canon_sha256":"b36ea249d1df66431def6281018b15ca8f49dc6351248489d99abc2d5c76c2b7"},"schema_version":"1.0","source":{"id":"0802.2909","kind":"arxiv","version":3}},"canonical_sha256":"d6f1c844f5bd33b863852b71aed2bd80a213e2f97d90ea4bb749158016df2a91","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d6f1c844f5bd33b863852b71aed2bd80a213e2f97d90ea4bb749158016df2a91","first_computed_at":"2026-05-18T04:35:15.127332Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:35:15.127332Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nnOASCr53CUx9JbvQ8+DmVA4dmOL2QY3l6Y5uGLVuS3RmCLQiuH5dJ/QD4WZw9r5sLUy1mHCeBdGIp/sDcK9Bw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:35:15.127728Z","signed_message":"canonical_sha256_bytes"},"source_id":"0802.2909","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:674e7a0eefd783f64b9564a9366501a18d56fab2fee30b40f35a521e53dbe64e","sha256:3088019f4b27f1c8af244476c64d1e681a98c03eaa5d66ed69a004848eb9df8f"],"state_sha256":"96a2694ee1d089327dbc25f75ce159a9e1a0afda58a2755b5ad3e40f0bdebe28"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GEygrMpZVKqvsx4IXzbAcMu4JbIWrHao/uRyv22ygWwSbcsMaoHJFDlHeXFMY3mVQ4PDfZcIVLm+n+/tHe7TBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T23:37:10.998365Z","bundle_sha256":"fe67db92aa42688bd324834a478ee01882adc1220ff36a7d2cc4008faa0d9ce4"}}