{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:3YPREGKEMKY5QYEGVACB2VESVN","short_pith_number":"pith:3YPREGKE","schema_version":"1.0","canonical_sha256":"de1f12194462b1d86086a8041d5492ab428c50ae5b7e692cfe0adf2d08ac26c0","source":{"kind":"arxiv","id":"1508.07388","version":2},"attestation_state":"computed","paper":{"title":"Shy shadows of infinite-dimensional partially hyperbolic invariant sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.CA","math.FA"],"primary_cat":"math.DS","authors_text":"Daniel Smania","submitted_at":"2015-08-29T02:50:31Z","abstract_excerpt":"Let $\\mathcal{R}$ be a strongly compact $C^2$ map defined in an open subset of an infinite-dimensional Banach space such that the image of its derivative $D_F \\mathcal{R}$ is dense for every $F$. Let $\\Omega$ be a compact, forward invariant and partially hyperbolic set of $\\mathcal{R}$ such that $\\mathcal{R}\\colon \\Omega\\rightarrow \\Omega$ is onto. The $\\delta$-shadow $W^s_\\delta(\\Omega)$ of $\\Omega$ is the union of the sets $$W^s_\\delta(G)= \\{F\\colon dist(\\mathcal{R}^iF, \\mathcal{R}^iG) \\leq \\delta, \\ for \\ every \\ i\\geq 0 \\},$$ where $G \\in \\Omega$. Suppose that $W^s_\\delta(\\Omega)$ has tran"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1508.07388","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-08-29T02:50:31Z","cross_cats_sorted":["math.AP","math.CA","math.FA"],"title_canon_sha256":"4ba0b042dbc9330c855f709342ce56434ee8815cbf69219cc9123d7bc72ff302","abstract_canon_sha256":"0a4a327d6d435fb9474f85d815e015e150f9ed3c9977951b161d674fc8fe63dc"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:50:16.696124Z","signature_b64":"oHECy7rlera/rsL6RQ9F6QSwIbDcZ5bE3VhrVoNYBlhXgMPx4ZsFZrWuUlDzhYM6NYEwhv6PS/AtcAxxv27mCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"de1f12194462b1d86086a8041d5492ab428c50ae5b7e692cfe0adf2d08ac26c0","last_reissued_at":"2026-05-17T23:50:16.695454Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:50:16.695454Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Shy shadows of infinite-dimensional partially hyperbolic invariant sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.CA","math.FA"],"primary_cat":"math.DS","authors_text":"Daniel Smania","submitted_at":"2015-08-29T02:50:31Z","abstract_excerpt":"Let $\\mathcal{R}$ be a strongly compact $C^2$ map defined in an open subset of an infinite-dimensional Banach space such that the image of its derivative $D_F \\mathcal{R}$ is dense for every $F$. Let $\\Omega$ be a compact, forward invariant and partially hyperbolic set of $\\mathcal{R}$ such that $\\mathcal{R}\\colon \\Omega\\rightarrow \\Omega$ is onto. The $\\delta$-shadow $W^s_\\delta(\\Omega)$ of $\\Omega$ is the union of the sets $$W^s_\\delta(G)= \\{F\\colon dist(\\mathcal{R}^iF, \\mathcal{R}^iG) \\leq \\delta, \\ for \\ every \\ i\\geq 0 \\},$$ where $G \\in \\Omega$. Suppose that $W^s_\\delta(\\Omega)$ has tran"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.07388","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1508.07388","created_at":"2026-05-17T23:50:16.695533+00:00"},{"alias_kind":"arxiv_version","alias_value":"1508.07388v2","created_at":"2026-05-17T23:50:16.695533+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.07388","created_at":"2026-05-17T23:50:16.695533+00:00"},{"alias_kind":"pith_short_12","alias_value":"3YPREGKEMKY5","created_at":"2026-05-18T12:29:02.477457+00:00"},{"alias_kind":"pith_short_16","alias_value":"3YPREGKEMKY5QYEG","created_at":"2026-05-18T12:29:02.477457+00:00"},{"alias_kind":"pith_short_8","alias_value":"3YPREGKE","created_at":"2026-05-18T12:29:02.477457+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/3YPREGKEMKY5QYEGVACB2VESVN","json":"https://pith.science/pith/3YPREGKEMKY5QYEGVACB2VESVN.json","graph_json":"https://pith.science/api/pith-number/3YPREGKEMKY5QYEGVACB2VESVN/graph.json","events_json":"https://pith.science/api/pith-number/3YPREGKEMKY5QYEGVACB2VESVN/events.json","paper":"https://pith.science/paper/3YPREGKE"},"agent_actions":{"view_html":"https://pith.science/pith/3YPREGKEMKY5QYEGVACB2VESVN","download_json":"https://pith.science/pith/3YPREGKEMKY5QYEGVACB2VESVN.json","view_paper":"https://pith.science/paper/3YPREGKE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1508.07388&json=true","fetch_graph":"https://pith.science/api/pith-number/3YPREGKEMKY5QYEGVACB2VESVN/graph.json","fetch_events":"https://pith.science/api/pith-number/3YPREGKEMKY5QYEGVACB2VESVN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3YPREGKEMKY5QYEGVACB2VESVN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3YPREGKEMKY5QYEGVACB2VESVN/action/storage_attestation","attest_author":"https://pith.science/pith/3YPREGKEMKY5QYEGVACB2VESVN/action/author_attestation","sign_citation":"https://pith.science/pith/3YPREGKEMKY5QYEGVACB2VESVN/action/citation_signature","submit_replication":"https://pith.science/pith/3YPREGKEMKY5QYEGVACB2VESVN/action/replication_record"}},"created_at":"2026-05-17T23:50:16.695533+00:00","updated_at":"2026-05-17T23:50:16.695533+00:00"}