{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:CT4Z6XKBB5KCSOMEWDT2UIO4JR","short_pith_number":"pith:CT4Z6XKB","canonical_record":{"source":{"id":"1311.4932","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-11-20T01:03:45Z","cross_cats_sorted":[],"title_canon_sha256":"5cf658cab01fc5f24f553198e4de66982fde1b94538f4d93e29457a1992f92f2","abstract_canon_sha256":"e40c1990673cfcc3d813de9ecba9bd5bc906689abe2219848fbe44d716c6e17b"},"schema_version":"1.0"},"canonical_sha256":"14f99f5d410f54293984b0e7aa21dc4c4b895a1331891dbcb4e67b278a743b35","source":{"kind":"arxiv","id":"1311.4932","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1311.4932","created_at":"2026-05-18T01:02:14Z"},{"alias_kind":"arxiv_version","alias_value":"1311.4932v4","created_at":"2026-05-18T01:02:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.4932","created_at":"2026-05-18T01:02:14Z"},{"alias_kind":"pith_short_12","alias_value":"CT4Z6XKBB5KC","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_16","alias_value":"CT4Z6XKBB5KCSOME","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_8","alias_value":"CT4Z6XKB","created_at":"2026-05-18T12:27:40Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:CT4Z6XKBB5KCSOMEWDT2UIO4JR","target":"record","payload":{"canonical_record":{"source":{"id":"1311.4932","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-11-20T01:03:45Z","cross_cats_sorted":[],"title_canon_sha256":"5cf658cab01fc5f24f553198e4de66982fde1b94538f4d93e29457a1992f92f2","abstract_canon_sha256":"e40c1990673cfcc3d813de9ecba9bd5bc906689abe2219848fbe44d716c6e17b"},"schema_version":"1.0"},"canonical_sha256":"14f99f5d410f54293984b0e7aa21dc4c4b895a1331891dbcb4e67b278a743b35","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:02:14.293373Z","signature_b64":"Eu2X24emy3H3ve97m07DXmroEndBy5Rkd6BAlZCLCPPtxazYRJKG/70ztqbZBQUrDV6pkbrbqu5WlHnIzSVuCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"14f99f5d410f54293984b0e7aa21dc4c4b895a1331891dbcb4e67b278a743b35","last_reissued_at":"2026-05-18T01:02:14.292601Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:02:14.292601Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1311.4932","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:02:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8TDSj1E/JjIooS184MNRl+BxFqHLKxJr079hiXqknlEDqi5GhT2+ndx0JNYLTMUG3QdM+3vfEQD2mTAZRxAWCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T23:17:57.630421Z"},"content_sha256":"b8ac4031aeb90d7a0fbda796070a14229557e9ec92689f573f9e9754894e014b","schema_version":"1.0","event_id":"sha256:b8ac4031aeb90d7a0fbda796070a14229557e9ec92689f573f9e9754894e014b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:CT4Z6XKBB5KCSOMEWDT2UIO4JR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The semiclassical zeta function for geodesic flows on negatively curved manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Fr\\'ed\\'eric Faure, Masato Tsujii","submitted_at":"2013-11-20T01:03:45Z","abstract_excerpt":"We consider the semi-classical (or Gutzwiller-Voros) zeta function for $C^\\infty$ contact Anosov flows. Analyzing the spectrum of transfer operators associated to the flow, we prove, for any $\\tau>0$, that its zeros are contained in the union of the $\\tau$-neighborhood of the imaginary axis, $|\\Re(s)|<\\tau$, and the region $\\Re(s)<-\\chi_0+\\tau$, up to finitely many exceptions, where $\\chi_0>0$ is the hyperbolicity exponent of the flow. Further we show that the zeros in the neighborhood of the imaginary axis satisfy an analogue of the Weyl law."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.4932","kind":"arxiv","version":4},"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":"2026-05-18T01:02:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oGylYI/uVa0RwQR46BtLMB4TOcCbjRMnzyaXDVTIvgayvaU+lkTugCnUufivqM/cq/o1FScPzsJBm193gd1dAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T23:17:57.630771Z"},"content_sha256":"1a68f9d834cf247fb2917769522341a49b377d6276d06c0cbf56a832f557b407","schema_version":"1.0","event_id":"sha256:1a68f9d834cf247fb2917769522341a49b377d6276d06c0cbf56a832f557b407"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CT4Z6XKBB5KCSOMEWDT2UIO4JR/bundle.json","state_url":"https://pith.science/pith/CT4Z6XKBB5KCSOMEWDT2UIO4JR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CT4Z6XKBB5KCSOMEWDT2UIO4JR/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":"2026-06-22T23:17:57Z","links":{"resolver":"https://pith.science/pith/CT4Z6XKBB5KCSOMEWDT2UIO4JR","bundle":"https://pith.science/pith/CT4Z6XKBB5KCSOMEWDT2UIO4JR/bundle.json","state":"https://pith.science/pith/CT4Z6XKBB5KCSOMEWDT2UIO4JR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CT4Z6XKBB5KCSOMEWDT2UIO4JR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:CT4Z6XKBB5KCSOMEWDT2UIO4JR","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":"e40c1990673cfcc3d813de9ecba9bd5bc906689abe2219848fbe44d716c6e17b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-11-20T01:03:45Z","title_canon_sha256":"5cf658cab01fc5f24f553198e4de66982fde1b94538f4d93e29457a1992f92f2"},"schema_version":"1.0","source":{"id":"1311.4932","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1311.4932","created_at":"2026-05-18T01:02:14Z"},{"alias_kind":"arxiv_version","alias_value":"1311.4932v4","created_at":"2026-05-18T01:02:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.4932","created_at":"2026-05-18T01:02:14Z"},{"alias_kind":"pith_short_12","alias_value":"CT4Z6XKBB5KC","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_16","alias_value":"CT4Z6XKBB5KCSOME","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_8","alias_value":"CT4Z6XKB","created_at":"2026-05-18T12:27:40Z"}],"graph_snapshots":[{"event_id":"sha256:1a68f9d834cf247fb2917769522341a49b377d6276d06c0cbf56a832f557b407","target":"graph","created_at":"2026-05-18T01:02:14Z","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":"We consider the semi-classical (or Gutzwiller-Voros) zeta function for $C^\\infty$ contact Anosov flows. Analyzing the spectrum of transfer operators associated to the flow, we prove, for any $\\tau>0$, that its zeros are contained in the union of the $\\tau$-neighborhood of the imaginary axis, $|\\Re(s)|<\\tau$, and the region $\\Re(s)<-\\chi_0+\\tau$, up to finitely many exceptions, where $\\chi_0>0$ is the hyperbolicity exponent of the flow. Further we show that the zeros in the neighborhood of the imaginary axis satisfy an analogue of the Weyl law.","authors_text":"Fr\\'ed\\'eric Faure, Masato Tsujii","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-11-20T01:03:45Z","title":"The semiclassical zeta function for geodesic flows on negatively curved manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.4932","kind":"arxiv","version":4},"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:b8ac4031aeb90d7a0fbda796070a14229557e9ec92689f573f9e9754894e014b","target":"record","created_at":"2026-05-18T01:02:14Z","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":"e40c1990673cfcc3d813de9ecba9bd5bc906689abe2219848fbe44d716c6e17b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-11-20T01:03:45Z","title_canon_sha256":"5cf658cab01fc5f24f553198e4de66982fde1b94538f4d93e29457a1992f92f2"},"schema_version":"1.0","source":{"id":"1311.4932","kind":"arxiv","version":4}},"canonical_sha256":"14f99f5d410f54293984b0e7aa21dc4c4b895a1331891dbcb4e67b278a743b35","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"14f99f5d410f54293984b0e7aa21dc4c4b895a1331891dbcb4e67b278a743b35","first_computed_at":"2026-05-18T01:02:14.292601Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:02:14.292601Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Eu2X24emy3H3ve97m07DXmroEndBy5Rkd6BAlZCLCPPtxazYRJKG/70ztqbZBQUrDV6pkbrbqu5WlHnIzSVuCw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:02:14.293373Z","signed_message":"canonical_sha256_bytes"},"source_id":"1311.4932","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b8ac4031aeb90d7a0fbda796070a14229557e9ec92689f573f9e9754894e014b","sha256:1a68f9d834cf247fb2917769522341a49b377d6276d06c0cbf56a832f557b407"],"state_sha256":"1264d45066224d243044837f53a151c5e3bfa55801cd53e2378f0347739e5482"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dVACd+Kwuxl5Qc5hBCt4vM8EKEUYtQN6CIELBSaR39XOHu+E3dn/Ztpcx/FblgZkZ3/DvJPpIUtck2LnSRIvAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T23:17:57.632816Z","bundle_sha256":"d1561b2b97004c1cf8c4a5318dea32172705c83d144ec7f2a19da40f0edaa202"}}