{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:VCLZLI6XTNGOLSKJUGSPECURCG","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":"5a38d186da45b371e4d9e64ed4ae8308c3cc098a661d46eddd2d9186cf68f48d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2009-11-26T00:50:38Z","title_canon_sha256":"d3a61bd6f245542aac6170f1a59b4c2cd9217446bf827da7013b7fe48b1c9e73"},"schema_version":"1.0","source":{"id":"0911.4990","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0911.4990","created_at":"2026-05-18T02:10:36Z"},{"alias_kind":"arxiv_version","alias_value":"0911.4990v1","created_at":"2026-05-18T02:10:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0911.4990","created_at":"2026-05-18T02:10:36Z"},{"alias_kind":"pith_short_12","alias_value":"VCLZLI6XTNGO","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_16","alias_value":"VCLZLI6XTNGOLSKJ","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_8","alias_value":"VCLZLI6X","created_at":"2026-05-18T12:26:02Z"}],"graph_snapshots":[{"event_id":"sha256:36ff977b47adf4f2e2e110590bad29d6c2e881d8d283cda4602bf915ff936504","target":"graph","created_at":"2026-05-18T02:10:36Z","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":"The renormalization group (RG) method is one of the singular perturbation methods which is used in search for asymptotic behavior of solutions of differential equations. In this article, time-independent vector fields and time (almost) periodic vector fields are considered. Theorems on error estimates for approximate solutions, existence of approximate invariant manifolds and their stability, inheritance of symmetries from those for the original equation to those for the RG equation, are proved. Further it is proved that the RG method unifies traditional singular perturbation methods, such as ","authors_text":"Hayato Chiba","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2009-11-26T00:50:38Z","title":"Extension and Unification of Singular Perturbation Methods for ODEs Based on the Renormalization Group Method"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0911.4990","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":"sha256:34a04669c46f4acbbe2f75ba8a0d2b588e73e495e5095acc38d1646d48d00ee8","target":"record","created_at":"2026-05-18T02:10:36Z","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":"5a38d186da45b371e4d9e64ed4ae8308c3cc098a661d46eddd2d9186cf68f48d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2009-11-26T00:50:38Z","title_canon_sha256":"d3a61bd6f245542aac6170f1a59b4c2cd9217446bf827da7013b7fe48b1c9e73"},"schema_version":"1.0","source":{"id":"0911.4990","kind":"arxiv","version":1}},"canonical_sha256":"a89795a3d79b4ce5c949a1a4f20a911182f038880b8003a8c59393f949d548f2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a89795a3d79b4ce5c949a1a4f20a911182f038880b8003a8c59393f949d548f2","first_computed_at":"2026-05-18T02:10:36.606390Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:10:36.606390Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"oGVaR+orkd+t9MO25tcWi+xlxbQzKzvbUu6JbFbrfg9+CNSfQNinT5jXif+6BbgLp0IjdhSFAcwz1ItLXPR3Cw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:10:36.607181Z","signed_message":"canonical_sha256_bytes"},"source_id":"0911.4990","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:34a04669c46f4acbbe2f75ba8a0d2b588e73e495e5095acc38d1646d48d00ee8","sha256:36ff977b47adf4f2e2e110590bad29d6c2e881d8d283cda4602bf915ff936504"],"state_sha256":"5ac64a4c357681fea826c9bb46f8907c80a83cf7b09052128583fb412b6d693c"}