{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:PVVCFSVFUB37LGGL3R6LO2YIXN","short_pith_number":"pith:PVVCFSVF","canonical_record":{"source":{"id":"1708.00487","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-08-01T19:48:37Z","cross_cats_sorted":[],"title_canon_sha256":"e512c7fe884f17e4f448c319cddfeb0e4db87329991b850f4a237bf545b5fc02","abstract_canon_sha256":"6534c1c45a6cef5b727cdb99781ca2f64b2db7a5379354c6f15914a971a6ff7c"},"schema_version":"1.0"},"canonical_sha256":"7d6a22caa5a077f598cbdc7cb76b08bb4c96a12a1888a65b86cbab8c32d96c0c","source":{"kind":"arxiv","id":"1708.00487","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.00487","created_at":"2026-05-17T23:45:24Z"},{"alias_kind":"arxiv_version","alias_value":"1708.00487v2","created_at":"2026-05-17T23:45:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.00487","created_at":"2026-05-17T23:45:24Z"},{"alias_kind":"pith_short_12","alias_value":"PVVCFSVFUB37","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_16","alias_value":"PVVCFSVFUB37LGGL","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_8","alias_value":"PVVCFSVF","created_at":"2026-05-18T12:31:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:PVVCFSVFUB37LGGL3R6LO2YIXN","target":"record","payload":{"canonical_record":{"source":{"id":"1708.00487","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-08-01T19:48:37Z","cross_cats_sorted":[],"title_canon_sha256":"e512c7fe884f17e4f448c319cddfeb0e4db87329991b850f4a237bf545b5fc02","abstract_canon_sha256":"6534c1c45a6cef5b727cdb99781ca2f64b2db7a5379354c6f15914a971a6ff7c"},"schema_version":"1.0"},"canonical_sha256":"7d6a22caa5a077f598cbdc7cb76b08bb4c96a12a1888a65b86cbab8c32d96c0c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:45:24.449868Z","signature_b64":"0CD3Segp8yYIziWXLlMM0MvIcipa5WH6w0tgbq0Yzl776QkwsANT/iyxQBdnpqw5/gjZy5m92ayLCJDyjW8WDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7d6a22caa5a077f598cbdc7cb76b08bb4c96a12a1888a65b86cbab8c32d96c0c","last_reissued_at":"2026-05-17T23:45:24.449511Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:45:24.449511Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1708.00487","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:45:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CuaBLCPhbrx+dah9AxrJ5ohfMPba6/FtHow/puueAa+Ia/9PDKp+Yt1jsd0BV5anEJsb4tGtXG3Eq6rKL4KUCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T06:06:18.181697Z"},"content_sha256":"7f57421bba5a82dacfa8ea00369c61dea2619940eaeb3262e4edb93f4ae346ac","schema_version":"1.0","event_id":"sha256:7f57421bba5a82dacfa8ea00369c61dea2619940eaeb3262e4edb93f4ae346ac"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:PVVCFSVFUB37LGGL3R6LO2YIXN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Periodic approximation of exceptional Lyapunov exponents for semi-invertible operator cocycles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Davor Dragicevic, Lucas Backes","submitted_at":"2017-08-01T19:48:37Z","abstract_excerpt":"We prove that for semi-invertible and H\\\"older continuous linear cocycles $A$ acting on an arbitrary Banach space and defined over a base space that satisfies the Anosov Closing Property, all exceptional Lyapunov exponents of $A$ with respect to an ergodic invariant measure for base dynamics can be approximated with Lyapunov exponents of $A$ with respect to ergodic measures supported on periodic orbits. Our result is applicable to a wide class of infinite-dimensional dynamical systems."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.00487","kind":"arxiv","version":2},"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":"2026-05-17T23:45:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7H6gsBKcxIDvRcmqC5o/zpsq9xt4PYI3rLywr/ERQMJdqkohlbqYR6HUM+VLkY7RrcmRQsG4GGQ0eColKOqNAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T06:06:18.182051Z"},"content_sha256":"4d0e907bcc88a8860486c6c8cb6aed965665ed163b215b7293203f24c93065cf","schema_version":"1.0","event_id":"sha256:4d0e907bcc88a8860486c6c8cb6aed965665ed163b215b7293203f24c93065cf"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PVVCFSVFUB37LGGL3R6LO2YIXN/bundle.json","state_url":"https://pith.science/pith/PVVCFSVFUB37LGGL3R6LO2YIXN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PVVCFSVFUB37LGGL3R6LO2YIXN/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":"2026-05-31T06:06:18Z","links":{"resolver":"https://pith.science/pith/PVVCFSVFUB37LGGL3R6LO2YIXN","bundle":"https://pith.science/pith/PVVCFSVFUB37LGGL3R6LO2YIXN/bundle.json","state":"https://pith.science/pith/PVVCFSVFUB37LGGL3R6LO2YIXN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PVVCFSVFUB37LGGL3R6LO2YIXN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:PVVCFSVFUB37LGGL3R6LO2YIXN","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":"6534c1c45a6cef5b727cdb99781ca2f64b2db7a5379354c6f15914a971a6ff7c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-08-01T19:48:37Z","title_canon_sha256":"e512c7fe884f17e4f448c319cddfeb0e4db87329991b850f4a237bf545b5fc02"},"schema_version":"1.0","source":{"id":"1708.00487","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.00487","created_at":"2026-05-17T23:45:24Z"},{"alias_kind":"arxiv_version","alias_value":"1708.00487v2","created_at":"2026-05-17T23:45:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.00487","created_at":"2026-05-17T23:45:24Z"},{"alias_kind":"pith_short_12","alias_value":"PVVCFSVFUB37","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_16","alias_value":"PVVCFSVFUB37LGGL","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_8","alias_value":"PVVCFSVF","created_at":"2026-05-18T12:31:37Z"}],"graph_snapshots":[{"event_id":"sha256:4d0e907bcc88a8860486c6c8cb6aed965665ed163b215b7293203f24c93065cf","target":"graph","created_at":"2026-05-17T23:45:24Z","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 prove that for semi-invertible and H\\\"older continuous linear cocycles $A$ acting on an arbitrary Banach space and defined over a base space that satisfies the Anosov Closing Property, all exceptional Lyapunov exponents of $A$ with respect to an ergodic invariant measure for base dynamics can be approximated with Lyapunov exponents of $A$ with respect to ergodic measures supported on periodic orbits. Our result is applicable to a wide class of infinite-dimensional dynamical systems.","authors_text":"Davor Dragicevic, Lucas Backes","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-08-01T19:48:37Z","title":"Periodic approximation of exceptional Lyapunov exponents for semi-invertible operator cocycles"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.00487","kind":"arxiv","version":2},"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":"sha256:7f57421bba5a82dacfa8ea00369c61dea2619940eaeb3262e4edb93f4ae346ac","target":"record","created_at":"2026-05-17T23:45:24Z","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":"6534c1c45a6cef5b727cdb99781ca2f64b2db7a5379354c6f15914a971a6ff7c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-08-01T19:48:37Z","title_canon_sha256":"e512c7fe884f17e4f448c319cddfeb0e4db87329991b850f4a237bf545b5fc02"},"schema_version":"1.0","source":{"id":"1708.00487","kind":"arxiv","version":2}},"canonical_sha256":"7d6a22caa5a077f598cbdc7cb76b08bb4c96a12a1888a65b86cbab8c32d96c0c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7d6a22caa5a077f598cbdc7cb76b08bb4c96a12a1888a65b86cbab8c32d96c0c","first_computed_at":"2026-05-17T23:45:24.449511Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:45:24.449511Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0CD3Segp8yYIziWXLlMM0MvIcipa5WH6w0tgbq0Yzl776QkwsANT/iyxQBdnpqw5/gjZy5m92ayLCJDyjW8WDw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:45:24.449868Z","signed_message":"canonical_sha256_bytes"},"source_id":"1708.00487","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7f57421bba5a82dacfa8ea00369c61dea2619940eaeb3262e4edb93f4ae346ac","sha256:4d0e907bcc88a8860486c6c8cb6aed965665ed163b215b7293203f24c93065cf"],"state_sha256":"6cf8e1f151e78baa784e4ec2b516f11849663d9d02e47dfa0b1f816a9897dfb5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WiEdRcwhqb3afdacSgijuHyT9XyVWekSnbSlVQ2O/glchh949OO3iL+Ux0r2tiWTEK+jnUT8JgUh2zm6HjF0Bg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T06:06:18.184174Z","bundle_sha256":"ca72f014b3020d3b773741724aa507240d5518814d2bbd178270b67c23719c64"}}