{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:FNRPYLXKN5EDMWUVGI6CYERVXW","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":"e3439a40e0dc95a7848290fa960158e14073c6543e55dcbfdfb582925c78119b","cross_cats_sorted":["math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-12-07T09:30:30Z","title_canon_sha256":"40dcd834f175d01c7a8fafd4647551216a850ae174cac3eae791118f355698f2"},"schema_version":"1.0","source":{"id":"1612.02162","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.02162","created_at":"2026-05-18T00:18:32Z"},{"alias_kind":"arxiv_version","alias_value":"1612.02162v2","created_at":"2026-05-18T00:18:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.02162","created_at":"2026-05-18T00:18:32Z"},{"alias_kind":"pith_short_12","alias_value":"FNRPYLXKN5ED","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_16","alias_value":"FNRPYLXKN5EDMWUV","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_8","alias_value":"FNRPYLXK","created_at":"2026-05-18T12:30:15Z"}],"graph_snapshots":[{"event_id":"sha256:a47fc621f418861fa586c0c83f71f07d40242880e66ab54c4caee93145792924","target":"graph","created_at":"2026-05-18T00:18:32Z","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 provide a rigorous numerical computation method to validate tubular neighborhoods of normally hyperbolic slow manifolds with the explicit radii for the fast-slow system \\begin{equation*} \\begin{cases} x' = f(x,y,\\epsilon), and y' =\\epsilon g(x,y,\\epsilon). & \\end{cases} \\end{equation*} Our main focus is the validation of the continuous family of eigenpairs $\\{\\lambda_i(y;\\epsilon), u_i(y;\\epsilon)\\}_{i=1}^n$ of $f_x(h_\\epsilon(y),y,\\epsilon)$ over the slow manifold $S_\\epsilon = \\{x = h_\\epsilon(y)\\}$ admitting the graph representation. In order to obtain such a family, we apply the interva","authors_text":"Kaname Matsue","cross_cats":["math.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-12-07T09:30:30Z","title":"Rigorous numerics of tubular, conic, star-shaped neighborhoods of slow manifolds for fast-slow systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.02162","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:bca6fef2d1914c7ac4a47886fe39c4f1efd8adbb97f3898ff15b4de17f3cf58d","target":"record","created_at":"2026-05-18T00:18:32Z","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":"e3439a40e0dc95a7848290fa960158e14073c6543e55dcbfdfb582925c78119b","cross_cats_sorted":["math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-12-07T09:30:30Z","title_canon_sha256":"40dcd834f175d01c7a8fafd4647551216a850ae174cac3eae791118f355698f2"},"schema_version":"1.0","source":{"id":"1612.02162","kind":"arxiv","version":2}},"canonical_sha256":"2b62fc2eea6f48365a95323c2c1235bda52a11cbdb2b52766e7c7fa5f95f9f27","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2b62fc2eea6f48365a95323c2c1235bda52a11cbdb2b52766e7c7fa5f95f9f27","first_computed_at":"2026-05-18T00:18:32.041928Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:18:32.041928Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ifc3kg2t8S3CIhwBizCJSqdF/Dp2vAmX+syLrDac1laWHIZo1Zp0GkuCIdLlChH1jQPMwENv8uUNjyabuCJODQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:18:32.042352Z","signed_message":"canonical_sha256_bytes"},"source_id":"1612.02162","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bca6fef2d1914c7ac4a47886fe39c4f1efd8adbb97f3898ff15b4de17f3cf58d","sha256:a47fc621f418861fa586c0c83f71f07d40242880e66ab54c4caee93145792924"],"state_sha256":"9ce1211a487ce90c142fdf4e69299558eeb0f29ae88bd893a813088d15722e4e"}