{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1995:5H5JTOFGJXBX2M42UZS7TM44BB","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":"c9948a516622fb6fe253f91b8152697d6cf46a6313961060768e4d62aace7978","cross_cats_sorted":["cond-mat","gr-qc"],"license":"","primary_cat":"hep-th","submitted_at":"1995-06-23T22:28:52Z","title_canon_sha256":"40cafafbefb7bbae529323fd8e59bde226734faa170bc1b90f5c9c677fa011dd"},"schema_version":"1.0","source":{"id":"hep-th/9506161","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"hep-th/9506161","created_at":"2026-07-04T15:32:29Z"},{"alias_kind":"arxiv_version","alias_value":"hep-th/9506161v1","created_at":"2026-07-04T15:32:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-th/9506161","created_at":"2026-07-04T15:32:29Z"},{"alias_kind":"pith_short_12","alias_value":"5H5JTOFGJXBX","created_at":"2026-07-04T15:32:29Z"},{"alias_kind":"pith_short_16","alias_value":"5H5JTOFGJXBX2M42","created_at":"2026-07-04T15:32:29Z"},{"alias_kind":"pith_short_8","alias_value":"5H5JTOFG","created_at":"2026-07-04T15:32:29Z"}],"graph_snapshots":[{"event_id":"sha256:a2b4833c2520a7844e38662ee4e6092e3c4ce291e1c09586996a2d862313b0f4","target":"graph","created_at":"2026-07-04T15:32:29Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/hep-th/9506161/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Perturbative renormalization group theory is developed as a unified tool for global asymptotic analysis. With numerous examples, we illustrate its application to ordinary differential equation problems involving multiple scales, boundary layers with technically difficult asymptotic matching, and WKB analysis. In contrast to conventional methods, the renormalization group approach requires neither {\\it ad hoc\\/} assumptions about the structure of perturbation series nor the use of asymptotic matching. Our renormalization group approach provides approximate solutions which are practically superi","authors_text":"Lin-Yuan Chen, Nigel Goldenfeld, Y. Oono","cross_cats":["cond-mat","gr-qc"],"headline":"","license":"","primary_cat":"hep-th","submitted_at":"1995-06-23T22:28:52Z","title":"The Renormalization Group and Singular Perturbations: Multiple-Scales, Boundary Layers and Reductive Perturbation Theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/9506161","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":"sha256:9a5684d318759c87deacca5fa793536859a9ebc22bcc699e7625363ccf254e6d","target":"record","created_at":"2026-07-04T15:32:29Z","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":"c9948a516622fb6fe253f91b8152697d6cf46a6313961060768e4d62aace7978","cross_cats_sorted":["cond-mat","gr-qc"],"license":"","primary_cat":"hep-th","submitted_at":"1995-06-23T22:28:52Z","title_canon_sha256":"40cafafbefb7bbae529323fd8e59bde226734faa170bc1b90f5c9c677fa011dd"},"schema_version":"1.0","source":{"id":"hep-th/9506161","kind":"arxiv","version":1}},"canonical_sha256":"e9fa99b8a64dc37d339aa665f9b39c08571883428f65a85c6e55bfa97e99f981","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e9fa99b8a64dc37d339aa665f9b39c08571883428f65a85c6e55bfa97e99f981","first_computed_at":"2026-07-04T15:32:29.250688Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T15:32:29.250688Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"i7Gw3qNEJ/7Usgmbsikq0v9bGukoXyx4E4qgH/ysqnyvB1NsgCoxXRGrPUj6RqFWrun3fEuz6okLdjcsaLPtAQ==","signature_status":"signed_v1","signed_at":"2026-07-04T15:32:29.251083Z","signed_message":"canonical_sha256_bytes"},"source_id":"hep-th/9506161","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9a5684d318759c87deacca5fa793536859a9ebc22bcc699e7625363ccf254e6d","sha256:a2b4833c2520a7844e38662ee4e6092e3c4ce291e1c09586996a2d862313b0f4"],"state_sha256":"2988669f3c93207cb2e94e0f5bf1a045df0c26f0e2b8af7917403005d2094b4d"}