{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:1999:W37TVZHK4I2RDUBN2UFXMOFS4X","short_pith_number":"pith:W37TVZHK","canonical_record":{"source":{"id":"hep-th/9905088","kind":"arxiv","version":3},"metadata":{"license":"","primary_cat":"hep-th","submitted_at":"1999-05-13T10:25:17Z","cross_cats_sorted":["cond-mat","gr-qc","hep-ph","math-ph","math.MP","nlin.PS","nlin.SI","patt-sol","solv-int"],"title_canon_sha256":"d9067be9b9f7b85e93f20995f791553d2cfadf7aa4c1fda3933b5f70a78643e4","abstract_canon_sha256":"9811b326585b78873849d97128cfc2d6e9b8acca0f82e186e201d9d5d64f9ae2"},"schema_version":"1.0"},"canonical_sha256":"b6ff3ae4eae23511d02dd50b7638b2e5fa2b31d8da44a7654d54196beb00fee4","source":{"kind":"arxiv","id":"hep-th/9905088","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"hep-th/9905088","created_at":"2026-05-18T01:05:54Z"},{"alias_kind":"arxiv_version","alias_value":"hep-th/9905088v3","created_at":"2026-05-18T01:05:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-th/9905088","created_at":"2026-05-18T01:05:54Z"},{"alias_kind":"pith_short_12","alias_value":"W37TVZHK4I2R","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_16","alias_value":"W37TVZHK4I2RDUBN","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_8","alias_value":"W37TVZHK","created_at":"2026-05-18T12:25:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:1999:W37TVZHK4I2RDUBN2UFXMOFS4X","target":"record","payload":{"canonical_record":{"source":{"id":"hep-th/9905088","kind":"arxiv","version":3},"metadata":{"license":"","primary_cat":"hep-th","submitted_at":"1999-05-13T10:25:17Z","cross_cats_sorted":["cond-mat","gr-qc","hep-ph","math-ph","math.MP","nlin.PS","nlin.SI","patt-sol","solv-int"],"title_canon_sha256":"d9067be9b9f7b85e93f20995f791553d2cfadf7aa4c1fda3933b5f70a78643e4","abstract_canon_sha256":"9811b326585b78873849d97128cfc2d6e9b8acca0f82e186e201d9d5d64f9ae2"},"schema_version":"1.0"},"canonical_sha256":"b6ff3ae4eae23511d02dd50b7638b2e5fa2b31d8da44a7654d54196beb00fee4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:05:54.985625Z","signature_b64":"C6Ou+qYHEnhYq/HTPbtOayU0DcW/wOeVPyyLOS6ViKkexoKRg8Tga9V13rjFJ7Q0P5s3zMT0Yc14dgL5JG3dBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b6ff3ae4eae23511d02dd50b7638b2e5fa2b31d8da44a7654d54196beb00fee4","last_reissued_at":"2026-05-18T01:05:54.985056Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:05:54.985056Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"hep-th/9905088","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:05:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IOEbSdqbmFAMbaSaspOjQ2imhNdRAHS3fX5nxvmh0c/bhQDeXbZyNoVpnjG1SawNGMcx55K8qvqqErbaLyZICQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T21:48:44.990566Z"},"content_sha256":"10d605535dca6b19e1cde05aac0dda9e34930b9013f11ea6503eb3c1eb04e019","schema_version":"1.0","event_id":"sha256:10d605535dca6b19e1cde05aac0dda9e34930b9013f11ea6503eb3c1eb04e019"},{"event_type":"graph_snapshot","subject_pith_number":"pith:1999:W37TVZHK4I2RDUBN2UFXMOFS4X","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Renormalization-group Method for Reduction of Evolution Equations; invariant manifolds and envelopes","license":"","headline":"","cross_cats":["cond-mat","gr-qc","hep-ph","math-ph","math.MP","nlin.PS","nlin.SI","patt-sol","solv-int"],"primary_cat":"hep-th","authors_text":"K. Fujii, S.-I. Ei, T. Kunihiro","submitted_at":"1999-05-13T10:25:17Z","abstract_excerpt":"The renormalization group (RG) method as a powerful tool for reduction of evolution equations is formulated in terms of the notion of invariant manifolds. We start with derivation of an exact RG equation which is analogous to the Wilsonian RG equations in statistical physics and quantum field theory. It is clarified that the perturbative RG method constructs invariant manifolds successively as the initial value of evolution equations, thereby the meaning to set $t_0=t$ is naturally understood where $t_0$ is the arbitrary initial time. We show that the integral constants in the unperturbative s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/9905088","kind":"arxiv","version":3},"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":"2026-05-18T01:05:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"w+LPrxyRqXcjNbQd818877tu3T5bib3WXsIKcW39RtqInxK0RZ52SD5fnsX8QJLoDmpQ/1vt8SBDTpzFhSN4Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T21:48:44.990906Z"},"content_sha256":"b334838d296e85a3d98e378762b4eb717f32cdbe19bab5a58b3d0444ef42641f","schema_version":"1.0","event_id":"sha256:b334838d296e85a3d98e378762b4eb717f32cdbe19bab5a58b3d0444ef42641f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/W37TVZHK4I2RDUBN2UFXMOFS4X/bundle.json","state_url":"https://pith.science/pith/W37TVZHK4I2RDUBN2UFXMOFS4X/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/W37TVZHK4I2RDUBN2UFXMOFS4X/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":"2026-06-03T21:48:44Z","links":{"resolver":"https://pith.science/pith/W37TVZHK4I2RDUBN2UFXMOFS4X","bundle":"https://pith.science/pith/W37TVZHK4I2RDUBN2UFXMOFS4X/bundle.json","state":"https://pith.science/pith/W37TVZHK4I2RDUBN2UFXMOFS4X/state.json","well_known_bundle":"https://pith.science/.well-known/pith/W37TVZHK4I2RDUBN2UFXMOFS4X/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1999:W37TVZHK4I2RDUBN2UFXMOFS4X","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":"9811b326585b78873849d97128cfc2d6e9b8acca0f82e186e201d9d5d64f9ae2","cross_cats_sorted":["cond-mat","gr-qc","hep-ph","math-ph","math.MP","nlin.PS","nlin.SI","patt-sol","solv-int"],"license":"","primary_cat":"hep-th","submitted_at":"1999-05-13T10:25:17Z","title_canon_sha256":"d9067be9b9f7b85e93f20995f791553d2cfadf7aa4c1fda3933b5f70a78643e4"},"schema_version":"1.0","source":{"id":"hep-th/9905088","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"hep-th/9905088","created_at":"2026-05-18T01:05:54Z"},{"alias_kind":"arxiv_version","alias_value":"hep-th/9905088v3","created_at":"2026-05-18T01:05:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-th/9905088","created_at":"2026-05-18T01:05:54Z"},{"alias_kind":"pith_short_12","alias_value":"W37TVZHK4I2R","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_16","alias_value":"W37TVZHK4I2RDUBN","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_8","alias_value":"W37TVZHK","created_at":"2026-05-18T12:25:49Z"}],"graph_snapshots":[{"event_id":"sha256:b334838d296e85a3d98e378762b4eb717f32cdbe19bab5a58b3d0444ef42641f","target":"graph","created_at":"2026-05-18T01:05:54Z","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 as a powerful tool for reduction of evolution equations is formulated in terms of the notion of invariant manifolds. We start with derivation of an exact RG equation which is analogous to the Wilsonian RG equations in statistical physics and quantum field theory. It is clarified that the perturbative RG method constructs invariant manifolds successively as the initial value of evolution equations, thereby the meaning to set $t_0=t$ is naturally understood where $t_0$ is the arbitrary initial time. We show that the integral constants in the unperturbative s","authors_text":"K. Fujii, S.-I. Ei, T. Kunihiro","cross_cats":["cond-mat","gr-qc","hep-ph","math-ph","math.MP","nlin.PS","nlin.SI","patt-sol","solv-int"],"headline":"","license":"","primary_cat":"hep-th","submitted_at":"1999-05-13T10:25:17Z","title":"Renormalization-group Method for Reduction of Evolution Equations; invariant manifolds and envelopes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/9905088","kind":"arxiv","version":3},"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":"sha256:10d605535dca6b19e1cde05aac0dda9e34930b9013f11ea6503eb3c1eb04e019","target":"record","created_at":"2026-05-18T01:05:54Z","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":"9811b326585b78873849d97128cfc2d6e9b8acca0f82e186e201d9d5d64f9ae2","cross_cats_sorted":["cond-mat","gr-qc","hep-ph","math-ph","math.MP","nlin.PS","nlin.SI","patt-sol","solv-int"],"license":"","primary_cat":"hep-th","submitted_at":"1999-05-13T10:25:17Z","title_canon_sha256":"d9067be9b9f7b85e93f20995f791553d2cfadf7aa4c1fda3933b5f70a78643e4"},"schema_version":"1.0","source":{"id":"hep-th/9905088","kind":"arxiv","version":3}},"canonical_sha256":"b6ff3ae4eae23511d02dd50b7638b2e5fa2b31d8da44a7654d54196beb00fee4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b6ff3ae4eae23511d02dd50b7638b2e5fa2b31d8da44a7654d54196beb00fee4","first_computed_at":"2026-05-18T01:05:54.985056Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:05:54.985056Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"C6Ou+qYHEnhYq/HTPbtOayU0DcW/wOeVPyyLOS6ViKkexoKRg8Tga9V13rjFJ7Q0P5s3zMT0Yc14dgL5JG3dBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:05:54.985625Z","signed_message":"canonical_sha256_bytes"},"source_id":"hep-th/9905088","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:10d605535dca6b19e1cde05aac0dda9e34930b9013f11ea6503eb3c1eb04e019","sha256:b334838d296e85a3d98e378762b4eb717f32cdbe19bab5a58b3d0444ef42641f"],"state_sha256":"634a9f624095688a40f5cf7b961d77951e6f2e2c3d8acb5d58e25917c613032f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"D+pWtKVaZv9Rr5vtxgY/WtWyPCfVhx7d7WbPqkqDBI2I8cyWaPm6k05sjE5zJv38zVckxb3hqsbW5DVNIdI7Cw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T21:48:44.992891Z","bundle_sha256":"d0b90e517c569b4872c0af1761616ac8fdb623e4ef09a8c19ba935a08298167a"}}