{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:AXVJMZHI667BPGU5UA5HRA6T3B","short_pith_number":"pith:AXVJMZHI","canonical_record":{"source":{"id":"1010.0396","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2010-10-03T12:22:13Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"fc702f5f279ae0fd642d0e3f9f0fd95d7891b6699e3c6110ab37bfad58460212","abstract_canon_sha256":"79817bcbd1ea331f797710df330c76d7c2f438522addd1ba533ea498fe2cee13"},"schema_version":"1.0"},"canonical_sha256":"05ea9664e8f7be179a9da03a7883d3d841b15f5b118ec5aaeb9e68b66485984e","source":{"kind":"arxiv","id":"1010.0396","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1010.0396","created_at":"2026-05-18T04:19:33Z"},{"alias_kind":"arxiv_version","alias_value":"1010.0396v3","created_at":"2026-05-18T04:19:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.0396","created_at":"2026-05-18T04:19:33Z"},{"alias_kind":"pith_short_12","alias_value":"AXVJMZHI667B","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_16","alias_value":"AXVJMZHI667BPGU5","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_8","alias_value":"AXVJMZHI","created_at":"2026-05-18T12:26:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:AXVJMZHI667BPGU5UA5HRA6T3B","target":"record","payload":{"canonical_record":{"source":{"id":"1010.0396","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2010-10-03T12:22:13Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"fc702f5f279ae0fd642d0e3f9f0fd95d7891b6699e3c6110ab37bfad58460212","abstract_canon_sha256":"79817bcbd1ea331f797710df330c76d7c2f438522addd1ba533ea498fe2cee13"},"schema_version":"1.0"},"canonical_sha256":"05ea9664e8f7be179a9da03a7883d3d841b15f5b118ec5aaeb9e68b66485984e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:19:33.427167Z","signature_b64":"G/s2LejGZ3C9cupDj0AzTFPzZY75Bo6WVsNjSuxnkBq3qUQEXEpA65mAKCXz+o4mGogH9d8NQcs9++38tGTeAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"05ea9664e8f7be179a9da03a7883d3d841b15f5b118ec5aaeb9e68b66485984e","last_reissued_at":"2026-05-18T04:19:33.426813Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:19:33.426813Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1010.0396","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":"2026-05-18T04:19:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OpiNE6+qXLcWH7U+gXcjFS0fAPd0RXUCo6HfMoQvafiAEMj/OZmL0OzvkZ8zspQcbRZ8lBuuN3XIFq+uzTTWCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T04:20:58.217643Z"},"content_sha256":"e638220163bb6b0c283fa5656f8250c433ebc896c3e9f798ff56e00f1a893c7d","schema_version":"1.0","event_id":"sha256:e638220163bb6b0c283fa5656f8250c433ebc896c3e9f798ff56e00f1a893c7d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:AXVJMZHI667BPGU5UA5HRA6T3B","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Contact Anosov flows and the FBI transform","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.DS","authors_text":"Masato Tsujii","submitted_at":"2010-10-03T12:22:13Z","abstract_excerpt":"This paper is about spectral properties of transfer operators for contact Anosov flows. The main result gives the essential spectral radius of the transfer operators acting on the so-called anisotropic Sobolev space exactly in terms of dynamical exponents. Also we provide a simplified proof by using the FBI transform."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.0396","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":"2026-05-18T04:19:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"42WI+mDBg6Z4jXMBtvtMEWgI7uTeChdADexky387fcYnYOLlUjZan6cjqQPzbkC47s8GCFtrZHyZlgpjy9VyDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T04:20:58.217989Z"},"content_sha256":"1888a688bf7c0c3b39e73bd522e3d272ffc9e8b89ca94d4b7a0843659eb94f94","schema_version":"1.0","event_id":"sha256:1888a688bf7c0c3b39e73bd522e3d272ffc9e8b89ca94d4b7a0843659eb94f94"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AXVJMZHI667BPGU5UA5HRA6T3B/bundle.json","state_url":"https://pith.science/pith/AXVJMZHI667BPGU5UA5HRA6T3B/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AXVJMZHI667BPGU5UA5HRA6T3B/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":"2026-06-23T04:20:58Z","links":{"resolver":"https://pith.science/pith/AXVJMZHI667BPGU5UA5HRA6T3B","bundle":"https://pith.science/pith/AXVJMZHI667BPGU5UA5HRA6T3B/bundle.json","state":"https://pith.science/pith/AXVJMZHI667BPGU5UA5HRA6T3B/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AXVJMZHI667BPGU5UA5HRA6T3B/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:AXVJMZHI667BPGU5UA5HRA6T3B","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":"79817bcbd1ea331f797710df330c76d7c2f438522addd1ba533ea498fe2cee13","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2010-10-03T12:22:13Z","title_canon_sha256":"fc702f5f279ae0fd642d0e3f9f0fd95d7891b6699e3c6110ab37bfad58460212"},"schema_version":"1.0","source":{"id":"1010.0396","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1010.0396","created_at":"2026-05-18T04:19:33Z"},{"alias_kind":"arxiv_version","alias_value":"1010.0396v3","created_at":"2026-05-18T04:19:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.0396","created_at":"2026-05-18T04:19:33Z"},{"alias_kind":"pith_short_12","alias_value":"AXVJMZHI667B","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_16","alias_value":"AXVJMZHI667BPGU5","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_8","alias_value":"AXVJMZHI","created_at":"2026-05-18T12:26:05Z"}],"graph_snapshots":[{"event_id":"sha256:1888a688bf7c0c3b39e73bd522e3d272ffc9e8b89ca94d4b7a0843659eb94f94","target":"graph","created_at":"2026-05-18T04:19:33Z","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 paper is about spectral properties of transfer operators for contact Anosov flows. The main result gives the essential spectral radius of the transfer operators acting on the so-called anisotropic Sobolev space exactly in terms of dynamical exponents. Also we provide a simplified proof by using the FBI transform.","authors_text":"Masato Tsujii","cross_cats":["math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2010-10-03T12:22:13Z","title":"Contact Anosov flows and the FBI transform"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.0396","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:e638220163bb6b0c283fa5656f8250c433ebc896c3e9f798ff56e00f1a893c7d","target":"record","created_at":"2026-05-18T04:19:33Z","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":"79817bcbd1ea331f797710df330c76d7c2f438522addd1ba533ea498fe2cee13","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2010-10-03T12:22:13Z","title_canon_sha256":"fc702f5f279ae0fd642d0e3f9f0fd95d7891b6699e3c6110ab37bfad58460212"},"schema_version":"1.0","source":{"id":"1010.0396","kind":"arxiv","version":3}},"canonical_sha256":"05ea9664e8f7be179a9da03a7883d3d841b15f5b118ec5aaeb9e68b66485984e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"05ea9664e8f7be179a9da03a7883d3d841b15f5b118ec5aaeb9e68b66485984e","first_computed_at":"2026-05-18T04:19:33.426813Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:19:33.426813Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"G/s2LejGZ3C9cupDj0AzTFPzZY75Bo6WVsNjSuxnkBq3qUQEXEpA65mAKCXz+o4mGogH9d8NQcs9++38tGTeAg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:19:33.427167Z","signed_message":"canonical_sha256_bytes"},"source_id":"1010.0396","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e638220163bb6b0c283fa5656f8250c433ebc896c3e9f798ff56e00f1a893c7d","sha256:1888a688bf7c0c3b39e73bd522e3d272ffc9e8b89ca94d4b7a0843659eb94f94"],"state_sha256":"41e0f1dc0b8522c25ce43ed07d42bd81629f813e741d61d479fba0daba3560c6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+9ouesRqZ02FYz5Ts3GIjwd3yb8hkmsZuqFWI4TlrRtxjxvuwSBLQ66kJXEbQS6ChRMATI5usvgynn1cKHakDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T04:20:58.220411Z","bundle_sha256":"7ecd63b8143b3d36095d6bf9edcbead47c06abc64cd0c93372e23cb91d6a39d2"}}