{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:3HAHALXPXRP42NZ5VGNJKOOJJG","short_pith_number":"pith:3HAHALXP","canonical_record":{"source":{"id":"1106.4053","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-06-20T21:56:46Z","cross_cats_sorted":[],"title_canon_sha256":"91c8fd813943b140be1ecd3249311be6945d459040af1aaea6f72ce530dcae5e","abstract_canon_sha256":"a1cbdd51cd112a12acda9845e9b6e45ef021225f35785d8f41062d5df07c6cbb"},"schema_version":"1.0"},"canonical_sha256":"d9c0702eefbc5fcd373da99a9539c949ba279a07af2268822ca1218289c32bca","source":{"kind":"arxiv","id":"1106.4053","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1106.4053","created_at":"2026-05-18T01:35:57Z"},{"alias_kind":"arxiv_version","alias_value":"1106.4053v4","created_at":"2026-05-18T01:35:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.4053","created_at":"2026-05-18T01:35:57Z"},{"alias_kind":"pith_short_12","alias_value":"3HAHALXPXRP4","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_16","alias_value":"3HAHALXPXRP42NZ5","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_8","alias_value":"3HAHALXP","created_at":"2026-05-18T12:26:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:3HAHALXPXRP42NZ5VGNJKOOJJG","target":"record","payload":{"canonical_record":{"source":{"id":"1106.4053","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-06-20T21:56:46Z","cross_cats_sorted":[],"title_canon_sha256":"91c8fd813943b140be1ecd3249311be6945d459040af1aaea6f72ce530dcae5e","abstract_canon_sha256":"a1cbdd51cd112a12acda9845e9b6e45ef021225f35785d8f41062d5df07c6cbb"},"schema_version":"1.0"},"canonical_sha256":"d9c0702eefbc5fcd373da99a9539c949ba279a07af2268822ca1218289c32bca","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:35:57.756143Z","signature_b64":"svgmEFpV0kf1nBWZvzWHrYA6t7ittu29M0PTeP4lOWvqKezEFkJVy2GCxfsRDAOKWiYiGbM6OnJqUVF326kIBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d9c0702eefbc5fcd373da99a9539c949ba279a07af2268822ca1218289c32bca","last_reissued_at":"2026-05-18T01:35:57.755710Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:35:57.755710Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1106.4053","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":"2026-05-18T01:35:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"d73fEgjvuvbl7DFgyosjMu2S9NFf1OZGtGf23KqMiEO6L7CqrsybGvv/07dVll8euZzeJ/+5jXzd5vvn4oCRAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T06:00:11.698341Z"},"content_sha256":"b2ff86771905f099121900a97a412bf1582ccbabca3f35509b438bd94131477c","schema_version":"1.0","event_id":"sha256:b2ff86771905f099121900a97a412bf1582ccbabca3f35509b438bd94131477c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:3HAHALXPXRP42NZ5VGNJKOOJJG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Holder Shadowing on Finite Intervals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Sergey Tikhomirov","submitted_at":"2011-06-20T21:56:46Z","abstract_excerpt":"For any $\\theta, \\omega > 1/2$ we prove that, if any $d$-pseudotrajectory of length $\\sim 1/d^{\\omega}$ of a diffeomorphism $f\\in C^2$ can be $d^{\\theta}$-shadowed by an exact trajectory, then $f$ is structurally stable. Previously it was conjectured by Hammel-Grebogi-Yorke that for $\\theta = \\omega = 1/2$ this property holds for a wide class of non-uniformly hyperbolic diffeomorphisms. In the proof we introduce the notion of sublinear growth property for inhomogenious linear equations and prove that it implies exponential dichotomy."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.4053","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":"2026-05-18T01:35:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2MxbUmZYCYr1m7sQbpnvuqG9lrmgTRNsuxiwtbXvXVR2OJAhJieKumN7rMutq8D0VrF175odSt8AwDfkxWAlBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T06:00:11.698921Z"},"content_sha256":"e69e22d674a33a12864d3c422f42093dc31a43a86c28d5cda0bf9264c1858855","schema_version":"1.0","event_id":"sha256:e69e22d674a33a12864d3c422f42093dc31a43a86c28d5cda0bf9264c1858855"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3HAHALXPXRP42NZ5VGNJKOOJJG/bundle.json","state_url":"https://pith.science/pith/3HAHALXPXRP42NZ5VGNJKOOJJG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3HAHALXPXRP42NZ5VGNJKOOJJG/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":"2026-06-07T06:00:11Z","links":{"resolver":"https://pith.science/pith/3HAHALXPXRP42NZ5VGNJKOOJJG","bundle":"https://pith.science/pith/3HAHALXPXRP42NZ5VGNJKOOJJG/bundle.json","state":"https://pith.science/pith/3HAHALXPXRP42NZ5VGNJKOOJJG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3HAHALXPXRP42NZ5VGNJKOOJJG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:3HAHALXPXRP42NZ5VGNJKOOJJG","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":"a1cbdd51cd112a12acda9845e9b6e45ef021225f35785d8f41062d5df07c6cbb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-06-20T21:56:46Z","title_canon_sha256":"91c8fd813943b140be1ecd3249311be6945d459040af1aaea6f72ce530dcae5e"},"schema_version":"1.0","source":{"id":"1106.4053","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1106.4053","created_at":"2026-05-18T01:35:57Z"},{"alias_kind":"arxiv_version","alias_value":"1106.4053v4","created_at":"2026-05-18T01:35:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.4053","created_at":"2026-05-18T01:35:57Z"},{"alias_kind":"pith_short_12","alias_value":"3HAHALXPXRP4","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_16","alias_value":"3HAHALXPXRP42NZ5","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_8","alias_value":"3HAHALXP","created_at":"2026-05-18T12:26:18Z"}],"graph_snapshots":[{"event_id":"sha256:e69e22d674a33a12864d3c422f42093dc31a43a86c28d5cda0bf9264c1858855","target":"graph","created_at":"2026-05-18T01:35:57Z","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":"For any $\\theta, \\omega > 1/2$ we prove that, if any $d$-pseudotrajectory of length $\\sim 1/d^{\\omega}$ of a diffeomorphism $f\\in C^2$ can be $d^{\\theta}$-shadowed by an exact trajectory, then $f$ is structurally stable. Previously it was conjectured by Hammel-Grebogi-Yorke that for $\\theta = \\omega = 1/2$ this property holds for a wide class of non-uniformly hyperbolic diffeomorphisms. In the proof we introduce the notion of sublinear growth property for inhomogenious linear equations and prove that it implies exponential dichotomy.","authors_text":"Sergey Tikhomirov","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-06-20T21:56:46Z","title":"Holder Shadowing on Finite Intervals"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.4053","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:b2ff86771905f099121900a97a412bf1582ccbabca3f35509b438bd94131477c","target":"record","created_at":"2026-05-18T01:35:57Z","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":"a1cbdd51cd112a12acda9845e9b6e45ef021225f35785d8f41062d5df07c6cbb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-06-20T21:56:46Z","title_canon_sha256":"91c8fd813943b140be1ecd3249311be6945d459040af1aaea6f72ce530dcae5e"},"schema_version":"1.0","source":{"id":"1106.4053","kind":"arxiv","version":4}},"canonical_sha256":"d9c0702eefbc5fcd373da99a9539c949ba279a07af2268822ca1218289c32bca","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d9c0702eefbc5fcd373da99a9539c949ba279a07af2268822ca1218289c32bca","first_computed_at":"2026-05-18T01:35:57.755710Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:35:57.755710Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"svgmEFpV0kf1nBWZvzWHrYA6t7ittu29M0PTeP4lOWvqKezEFkJVy2GCxfsRDAOKWiYiGbM6OnJqUVF326kIBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:35:57.756143Z","signed_message":"canonical_sha256_bytes"},"source_id":"1106.4053","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b2ff86771905f099121900a97a412bf1582ccbabca3f35509b438bd94131477c","sha256:e69e22d674a33a12864d3c422f42093dc31a43a86c28d5cda0bf9264c1858855"],"state_sha256":"d508eafae8bc6105deed1f711c7d78cc787e7c924577f585d18e30cc3c3d4299"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PdX4ZDZRy8CbO7gTOtYzxDb6tRI50r+p7vcbGC/2aSfPTkDiIQZ/SL/hSxjGa98jvr4WOfN3IRnKl/DM7kvLBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T06:00:11.702122Z","bundle_sha256":"393c34335471ae6e4765c5093559b0963f7afd04defd491a84e9203cad0e9008"}}