{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:AQWVZ6CIEQU6T6DKYRFYS6LOC2","short_pith_number":"pith:AQWVZ6CI","canonical_record":{"source":{"id":"1412.7404","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-12-23T15:24:21Z","cross_cats_sorted":[],"title_canon_sha256":"1a10516b2ee33d28d83ab8a6340714f1b351b867ff45bed3315184831b0c0bb5","abstract_canon_sha256":"05317f0269298a1953a96effa93eef709c2877f06e5500360f1067822ba4ed22"},"schema_version":"1.0"},"canonical_sha256":"042d5cf8482429e9f86ac44b89796e16b3b68a65ef782083e50d01ea9c67037b","source":{"kind":"arxiv","id":"1412.7404","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.7404","created_at":"2026-05-18T02:30:38Z"},{"alias_kind":"arxiv_version","alias_value":"1412.7404v1","created_at":"2026-05-18T02:30:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.7404","created_at":"2026-05-18T02:30:38Z"},{"alias_kind":"pith_short_12","alias_value":"AQWVZ6CIEQU6","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_16","alias_value":"AQWVZ6CIEQU6T6DK","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_8","alias_value":"AQWVZ6CI","created_at":"2026-05-18T12:28:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:AQWVZ6CIEQU6T6DKYRFYS6LOC2","target":"record","payload":{"canonical_record":{"source":{"id":"1412.7404","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-12-23T15:24:21Z","cross_cats_sorted":[],"title_canon_sha256":"1a10516b2ee33d28d83ab8a6340714f1b351b867ff45bed3315184831b0c0bb5","abstract_canon_sha256":"05317f0269298a1953a96effa93eef709c2877f06e5500360f1067822ba4ed22"},"schema_version":"1.0"},"canonical_sha256":"042d5cf8482429e9f86ac44b89796e16b3b68a65ef782083e50d01ea9c67037b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:30:38.950182Z","signature_b64":"WXOCLlqbv7XOPjDOIDiKmdKfgyTXjp/XIOFvZCEhUSq4TqKUUBDic39BGQkxF+Xj1MO+66LoRhO5PDifBn/FDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"042d5cf8482429e9f86ac44b89796e16b3b68a65ef782083e50d01ea9c67037b","last_reissued_at":"2026-05-18T02:30:38.949687Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:30:38.949687Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1412.7404","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":"2026-05-18T02:30:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"C+4DrWWlOQJjUNi/S0W0z0S38BxsGYczvnDItFVBCwZ8ZTmbX4HZEtu7bG3sX6CCQ36wi8nCQRK0KzqAaO3xDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T18:18:29.056208Z"},"content_sha256":"463ed943908eb9b38f13ffc4425fdf2e8ab7475ff21b0864aa16c7e04f98b270","schema_version":"1.0","event_id":"sha256:463ed943908eb9b38f13ffc4425fdf2e8ab7475ff21b0864aa16c7e04f98b270"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:AQWVZ6CIEQU6T6DKYRFYS6LOC2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Admissibility and nonuniformly hyperbolic sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Claudia Valls, Davor Dragicevic, Luis Barreira","submitted_at":"2014-12-23T15:24:21Z","abstract_excerpt":"We obtain a characterization of two classes of dynamics with nonuniformly hyperbolic behavior in terms of an admissibility property. Namely, we consider exponential dichotomies with respect to a sequence of norms and nonuniformly hyperbolic sets. We note that the approach to establishing exponential bounds along the stable and the unstable directions differs from the standard technique of substituting test sequences. Moreover, we obtain the bounds in a single step."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.7404","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":"2026-05-18T02:30:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"foUlo30WYBbkK6GELWNJ17co/hKX9g5gxN/FwoEVu+g9Y0YaeFDOuCat32UBStp1CBRG1uktrFuDkzh62ICgAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T18:18:29.056579Z"},"content_sha256":"8f961d3c29b130d4d178d93f204d72832d6bf0b2d2fd8701dfc3b21cc91e6afc","schema_version":"1.0","event_id":"sha256:8f961d3c29b130d4d178d93f204d72832d6bf0b2d2fd8701dfc3b21cc91e6afc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AQWVZ6CIEQU6T6DKYRFYS6LOC2/bundle.json","state_url":"https://pith.science/pith/AQWVZ6CIEQU6T6DKYRFYS6LOC2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AQWVZ6CIEQU6T6DKYRFYS6LOC2/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":"2026-06-24T18:18:29Z","links":{"resolver":"https://pith.science/pith/AQWVZ6CIEQU6T6DKYRFYS6LOC2","bundle":"https://pith.science/pith/AQWVZ6CIEQU6T6DKYRFYS6LOC2/bundle.json","state":"https://pith.science/pith/AQWVZ6CIEQU6T6DKYRFYS6LOC2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AQWVZ6CIEQU6T6DKYRFYS6LOC2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:AQWVZ6CIEQU6T6DKYRFYS6LOC2","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":"05317f0269298a1953a96effa93eef709c2877f06e5500360f1067822ba4ed22","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-12-23T15:24:21Z","title_canon_sha256":"1a10516b2ee33d28d83ab8a6340714f1b351b867ff45bed3315184831b0c0bb5"},"schema_version":"1.0","source":{"id":"1412.7404","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.7404","created_at":"2026-05-18T02:30:38Z"},{"alias_kind":"arxiv_version","alias_value":"1412.7404v1","created_at":"2026-05-18T02:30:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.7404","created_at":"2026-05-18T02:30:38Z"},{"alias_kind":"pith_short_12","alias_value":"AQWVZ6CIEQU6","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_16","alias_value":"AQWVZ6CIEQU6T6DK","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_8","alias_value":"AQWVZ6CI","created_at":"2026-05-18T12:28:19Z"}],"graph_snapshots":[{"event_id":"sha256:8f961d3c29b130d4d178d93f204d72832d6bf0b2d2fd8701dfc3b21cc91e6afc","target":"graph","created_at":"2026-05-18T02:30:38Z","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 obtain a characterization of two classes of dynamics with nonuniformly hyperbolic behavior in terms of an admissibility property. Namely, we consider exponential dichotomies with respect to a sequence of norms and nonuniformly hyperbolic sets. We note that the approach to establishing exponential bounds along the stable and the unstable directions differs from the standard technique of substituting test sequences. Moreover, we obtain the bounds in a single step.","authors_text":"Claudia Valls, Davor Dragicevic, Luis Barreira","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-12-23T15:24:21Z","title":"Admissibility and nonuniformly hyperbolic sets"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.7404","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":"sha256:463ed943908eb9b38f13ffc4425fdf2e8ab7475ff21b0864aa16c7e04f98b270","target":"record","created_at":"2026-05-18T02:30:38Z","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":"05317f0269298a1953a96effa93eef709c2877f06e5500360f1067822ba4ed22","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-12-23T15:24:21Z","title_canon_sha256":"1a10516b2ee33d28d83ab8a6340714f1b351b867ff45bed3315184831b0c0bb5"},"schema_version":"1.0","source":{"id":"1412.7404","kind":"arxiv","version":1}},"canonical_sha256":"042d5cf8482429e9f86ac44b89796e16b3b68a65ef782083e50d01ea9c67037b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"042d5cf8482429e9f86ac44b89796e16b3b68a65ef782083e50d01ea9c67037b","first_computed_at":"2026-05-18T02:30:38.949687Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:30:38.949687Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WXOCLlqbv7XOPjDOIDiKmdKfgyTXjp/XIOFvZCEhUSq4TqKUUBDic39BGQkxF+Xj1MO+66LoRhO5PDifBn/FDw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:30:38.950182Z","signed_message":"canonical_sha256_bytes"},"source_id":"1412.7404","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:463ed943908eb9b38f13ffc4425fdf2e8ab7475ff21b0864aa16c7e04f98b270","sha256:8f961d3c29b130d4d178d93f204d72832d6bf0b2d2fd8701dfc3b21cc91e6afc"],"state_sha256":"0986612469c974ff5bad95f6c9c1cab6230cc003983e6649a2ac710c8da08842"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YryMz25q2LtZD0O6EMZubmg/BZyPCOfe+2wXgmqhEDHHnpKFHYwzZFZl7eLdWpwqpW/0Yalr6z7qxYA0255aAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T18:18:29.058497Z","bundle_sha256":"db69b481102e91eca32fd94ff5a8925213d2ab8eaf65783c8a2362ce14813cd6"}}