{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:GD6642HIJCZLNCK5V2OWZAIKNK","short_pith_number":"pith:GD6642HI","canonical_record":{"source":{"id":"1003.0513","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-03-02T07:31:21Z","cross_cats_sorted":["math.DS","math.MP","math.SP"],"title_canon_sha256":"8a234444cfca020b2341abc791df4923a8a0154e988ff715d7d015b84f5b9deb","abstract_canon_sha256":"d0478f9d4ff5fff9bec71b487e85027d9c0b13b1477bb681a22c392a44038e59"},"schema_version":"1.0"},"canonical_sha256":"30fdee68e848b2b6895dae9d6c810a6ab8a101721583dc26ca05923f6361c658","source":{"kind":"arxiv","id":"1003.0513","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1003.0513","created_at":"2026-05-18T02:08:47Z"},{"alias_kind":"arxiv_version","alias_value":"1003.0513v1","created_at":"2026-05-18T02:08:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1003.0513","created_at":"2026-05-18T02:08:47Z"},{"alias_kind":"pith_short_12","alias_value":"GD6642HIJCZL","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_16","alias_value":"GD6642HIJCZLNCK5","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_8","alias_value":"GD6642HI","created_at":"2026-05-18T12:26:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:GD6642HIJCZLNCK5V2OWZAIKNK","target":"record","payload":{"canonical_record":{"source":{"id":"1003.0513","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-03-02T07:31:21Z","cross_cats_sorted":["math.DS","math.MP","math.SP"],"title_canon_sha256":"8a234444cfca020b2341abc791df4923a8a0154e988ff715d7d015b84f5b9deb","abstract_canon_sha256":"d0478f9d4ff5fff9bec71b487e85027d9c0b13b1477bb681a22c392a44038e59"},"schema_version":"1.0"},"canonical_sha256":"30fdee68e848b2b6895dae9d6c810a6ab8a101721583dc26ca05923f6361c658","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:08:47.740253Z","signature_b64":"54ozZzjLFjU8JmnB97u/KY8CqMwM94lgnh+Jk8UGFSN8/shoy8F3pr/mrfSE9fF+/iXrh/cjhtflu7IYiMiUBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"30fdee68e848b2b6895dae9d6c810a6ab8a101721583dc26ca05923f6361c658","last_reissued_at":"2026-05-18T02:08:47.739735Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:08:47.739735Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1003.0513","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":"2026-05-18T02:08:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YCLhLRoGx+5Rp56obPN200yzvgVBJVVyT9jeTRZVrt38ZduckxH6cXoLx9UId14l6zA5/jvluAHDOdWslUs4BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T04:41:31.052110Z"},"content_sha256":"4b37c5e86b6739e7fccbc48e4ee6a9ce41439703af58e48038756c67bd72f660","schema_version":"1.0","event_id":"sha256:4b37c5e86b6739e7fccbc48e4ee6a9ce41439703af58e48038756c67bd72f660"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:GD6642HIJCZLNCK5V2OWZAIKNK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Upper bound on the density of Ruelle resonances for Anosov flows","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","math.MP","math.SP"],"primary_cat":"math-ph","authors_text":"Fr\\'ed\\'eric Faure (IF), Johannes Sjoestrand (IMB)","submitted_at":"2010-03-02T07:31:21Z","abstract_excerpt":"Using a semiclassical approach we show that the spectrum of a smooth Anosov vector field V on a compact manifold is discrete (in suitable anisotropic Sobolev spaces) and then we provide an upper bound for the density of eigenvalues of the operator (-i)V, called Ruelle resonances, close to the real axis and for large real parts."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1003.0513","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":"2026-05-18T02:08:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Nh/ZHCwhwEwl0nN5z6apqPk4QTnIH+rF/p3P6YpERZMJcbILS6GSK39jk280dyd1aLDe2rH/BpzkmzOgcbBhCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T04:41:31.052770Z"},"content_sha256":"2e7bde7a7de682e29b8b14498cd02e6cf6ae66eb2a9d2194dd82a18bfff4ee40","schema_version":"1.0","event_id":"sha256:2e7bde7a7de682e29b8b14498cd02e6cf6ae66eb2a9d2194dd82a18bfff4ee40"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GD6642HIJCZLNCK5V2OWZAIKNK/bundle.json","state_url":"https://pith.science/pith/GD6642HIJCZLNCK5V2OWZAIKNK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GD6642HIJCZLNCK5V2OWZAIKNK/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":"2026-06-07T04:41:31Z","links":{"resolver":"https://pith.science/pith/GD6642HIJCZLNCK5V2OWZAIKNK","bundle":"https://pith.science/pith/GD6642HIJCZLNCK5V2OWZAIKNK/bundle.json","state":"https://pith.science/pith/GD6642HIJCZLNCK5V2OWZAIKNK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GD6642HIJCZLNCK5V2OWZAIKNK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:GD6642HIJCZLNCK5V2OWZAIKNK","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":"d0478f9d4ff5fff9bec71b487e85027d9c0b13b1477bb681a22c392a44038e59","cross_cats_sorted":["math.DS","math.MP","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-03-02T07:31:21Z","title_canon_sha256":"8a234444cfca020b2341abc791df4923a8a0154e988ff715d7d015b84f5b9deb"},"schema_version":"1.0","source":{"id":"1003.0513","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1003.0513","created_at":"2026-05-18T02:08:47Z"},{"alias_kind":"arxiv_version","alias_value":"1003.0513v1","created_at":"2026-05-18T02:08:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1003.0513","created_at":"2026-05-18T02:08:47Z"},{"alias_kind":"pith_short_12","alias_value":"GD6642HIJCZL","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_16","alias_value":"GD6642HIJCZLNCK5","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_8","alias_value":"GD6642HI","created_at":"2026-05-18T12:26:07Z"}],"graph_snapshots":[{"event_id":"sha256:2e7bde7a7de682e29b8b14498cd02e6cf6ae66eb2a9d2194dd82a18bfff4ee40","target":"graph","created_at":"2026-05-18T02:08:47Z","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":"Using a semiclassical approach we show that the spectrum of a smooth Anosov vector field V on a compact manifold is discrete (in suitable anisotropic Sobolev spaces) and then we provide an upper bound for the density of eigenvalues of the operator (-i)V, called Ruelle resonances, close to the real axis and for large real parts.","authors_text":"Fr\\'ed\\'eric Faure (IF), Johannes Sjoestrand (IMB)","cross_cats":["math.DS","math.MP","math.SP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-03-02T07:31:21Z","title":"Upper bound on the density of Ruelle resonances for Anosov flows"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1003.0513","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":"sha256:4b37c5e86b6739e7fccbc48e4ee6a9ce41439703af58e48038756c67bd72f660","target":"record","created_at":"2026-05-18T02:08:47Z","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":"d0478f9d4ff5fff9bec71b487e85027d9c0b13b1477bb681a22c392a44038e59","cross_cats_sorted":["math.DS","math.MP","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-03-02T07:31:21Z","title_canon_sha256":"8a234444cfca020b2341abc791df4923a8a0154e988ff715d7d015b84f5b9deb"},"schema_version":"1.0","source":{"id":"1003.0513","kind":"arxiv","version":1}},"canonical_sha256":"30fdee68e848b2b6895dae9d6c810a6ab8a101721583dc26ca05923f6361c658","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"30fdee68e848b2b6895dae9d6c810a6ab8a101721583dc26ca05923f6361c658","first_computed_at":"2026-05-18T02:08:47.739735Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:08:47.739735Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"54ozZzjLFjU8JmnB97u/KY8CqMwM94lgnh+Jk8UGFSN8/shoy8F3pr/mrfSE9fF+/iXrh/cjhtflu7IYiMiUBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:08:47.740253Z","signed_message":"canonical_sha256_bytes"},"source_id":"1003.0513","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4b37c5e86b6739e7fccbc48e4ee6a9ce41439703af58e48038756c67bd72f660","sha256:2e7bde7a7de682e29b8b14498cd02e6cf6ae66eb2a9d2194dd82a18bfff4ee40"],"state_sha256":"8fb4a5f713b5ef2086de74b3bc8d88dc5ca8521a386c3c641943534afe5cedc8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vJSOcWT2z589vkHm4LFvKA5dcJQQ7HC6w3yplP01aDPKp22SbGnZTrFutDWvKJchvw60/BfT2TzVfH3acVgcCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T04:41:31.055940Z","bundle_sha256":"86e34a4484777c69cdc119496004ac82253fd5bea6bc34b50a1c65837fc7fc73"}}