{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:1998:K7PQ3OUGNLYT6Z2YRDX74FIPTH","short_pith_number":"pith:K7PQ3OUG","canonical_record":{"source":{"id":"chao-dyn/9805019","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"chao-dyn","submitted_at":"1998-05-22T14:40:33Z","cross_cats_sorted":["nlin.CD"],"title_canon_sha256":"910d79151645f6a6956d48519adffcdea25b19f02ab4eedb39e773faf946334f","abstract_canon_sha256":"bf524858d4ccba7b8fe3b0afa799f13d1851914da735396bbf564ee32b8d107a"},"schema_version":"1.0"},"canonical_sha256":"57df0dba866af13f675888effe150f99d7789db4b7b4811f211cf111f31f7c34","source":{"kind":"arxiv","id":"chao-dyn/9805019","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"chao-dyn/9805019","created_at":"2026-05-18T01:40:11Z"},{"alias_kind":"arxiv_version","alias_value":"chao-dyn/9805019v1","created_at":"2026-05-18T01:40:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.chao-dyn/9805019","created_at":"2026-05-18T01:40:11Z"},{"alias_kind":"pith_short_12","alias_value":"K7PQ3OUGNLYT","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_16","alias_value":"K7PQ3OUGNLYT6Z2Y","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_8","alias_value":"K7PQ3OUG","created_at":"2026-05-18T12:25:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:1998:K7PQ3OUGNLYT6Z2YRDX74FIPTH","target":"record","payload":{"canonical_record":{"source":{"id":"chao-dyn/9805019","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"chao-dyn","submitted_at":"1998-05-22T14:40:33Z","cross_cats_sorted":["nlin.CD"],"title_canon_sha256":"910d79151645f6a6956d48519adffcdea25b19f02ab4eedb39e773faf946334f","abstract_canon_sha256":"bf524858d4ccba7b8fe3b0afa799f13d1851914da735396bbf564ee32b8d107a"},"schema_version":"1.0"},"canonical_sha256":"57df0dba866af13f675888effe150f99d7789db4b7b4811f211cf111f31f7c34","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:40:11.653298Z","signature_b64":"jxCBjE/ZPocgCJqRzQGHwoJF2AkLtHSRd89hLn400C2xkt3ovFm3SvjIpwgJrYjM4q6CdbpTjvqpjypn+OkkCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"57df0dba866af13f675888effe150f99d7789db4b7b4811f211cf111f31f7c34","last_reissued_at":"2026-05-18T01:40:11.652599Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:40:11.652599Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"chao-dyn/9805019","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:40:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mv40I/pta3EK76OBX5XxM8/ZkzFN/zyxbvQEwx0TpsLNwkmDjhAM7F98Ao20GqeYbdYmoNJ76AQBtGkN5w9gDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T20:13:31.011107Z"},"content_sha256":"396d30d14948d7d6454de6c6b818945a0db059b7fb48e2b5e0a03a3fcd3d15d9","schema_version":"1.0","event_id":"sha256:396d30d14948d7d6454de6c6b818945a0db059b7fb48e2b5e0a03a3fcd3d15d9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:1998:K7PQ3OUGNLYT6Z2YRDX74FIPTH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"An Approximate KAM-Renormalization-Group Scheme for Hamiltonian Systems","license":"","headline":"","cross_cats":["nlin.CD"],"primary_cat":"chao-dyn","authors_text":"C. Chandre, G. Benfatto, H. R. Jauslin","submitted_at":"1998-05-22T14:40:33Z","abstract_excerpt":"We construct an approximate renormalization scheme for Hamiltonian systems with two degrees of freedom. This scheme is a combination of Kolmogorov-Arnold-Moser (KAM) theory and renormalization-group techniques. It makes the connection between the approximate renormalization procedure derived by Escande and Doveil, and a systematic expansion of the transformation. In particular, we show that the two main approximations, consisting in keeping only the quadratic terms in the actions and the two main resonances, keep the essential information on the threshold of the breakup of invariant tori."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"chao-dyn/9805019","kind":"arxiv","version":1},"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":"2026-05-18T01:40:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"h7y+XwQE4IvaQH04WDlwJoBmYhpaeEpHcmBJdX+0qhThenNHpZvLVE7Q96bKcSUjSO6wD62MwzHEvzFxDVEXAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T20:13:31.011528Z"},"content_sha256":"1a00e6837bae3279fcef5cde5e3dc6928f5efdcb3cc94fdcea3013a38fcf6e33","schema_version":"1.0","event_id":"sha256:1a00e6837bae3279fcef5cde5e3dc6928f5efdcb3cc94fdcea3013a38fcf6e33"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/K7PQ3OUGNLYT6Z2YRDX74FIPTH/bundle.json","state_url":"https://pith.science/pith/K7PQ3OUGNLYT6Z2YRDX74FIPTH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/K7PQ3OUGNLYT6Z2YRDX74FIPTH/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":"2026-05-27T20:13:31Z","links":{"resolver":"https://pith.science/pith/K7PQ3OUGNLYT6Z2YRDX74FIPTH","bundle":"https://pith.science/pith/K7PQ3OUGNLYT6Z2YRDX74FIPTH/bundle.json","state":"https://pith.science/pith/K7PQ3OUGNLYT6Z2YRDX74FIPTH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/K7PQ3OUGNLYT6Z2YRDX74FIPTH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1998:K7PQ3OUGNLYT6Z2YRDX74FIPTH","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":"bf524858d4ccba7b8fe3b0afa799f13d1851914da735396bbf564ee32b8d107a","cross_cats_sorted":["nlin.CD"],"license":"","primary_cat":"chao-dyn","submitted_at":"1998-05-22T14:40:33Z","title_canon_sha256":"910d79151645f6a6956d48519adffcdea25b19f02ab4eedb39e773faf946334f"},"schema_version":"1.0","source":{"id":"chao-dyn/9805019","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"chao-dyn/9805019","created_at":"2026-05-18T01:40:11Z"},{"alias_kind":"arxiv_version","alias_value":"chao-dyn/9805019v1","created_at":"2026-05-18T01:40:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.chao-dyn/9805019","created_at":"2026-05-18T01:40:11Z"},{"alias_kind":"pith_short_12","alias_value":"K7PQ3OUGNLYT","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_16","alias_value":"K7PQ3OUGNLYT6Z2Y","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_8","alias_value":"K7PQ3OUG","created_at":"2026-05-18T12:25:49Z"}],"graph_snapshots":[{"event_id":"sha256:1a00e6837bae3279fcef5cde5e3dc6928f5efdcb3cc94fdcea3013a38fcf6e33","target":"graph","created_at":"2026-05-18T01:40:11Z","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 construct an approximate renormalization scheme for Hamiltonian systems with two degrees of freedom. This scheme is a combination of Kolmogorov-Arnold-Moser (KAM) theory and renormalization-group techniques. It makes the connection between the approximate renormalization procedure derived by Escande and Doveil, and a systematic expansion of the transformation. In particular, we show that the two main approximations, consisting in keeping only the quadratic terms in the actions and the two main resonances, keep the essential information on the threshold of the breakup of invariant tori.","authors_text":"C. Chandre, G. Benfatto, H. R. Jauslin","cross_cats":["nlin.CD"],"headline":"","license":"","primary_cat":"chao-dyn","submitted_at":"1998-05-22T14:40:33Z","title":"An Approximate KAM-Renormalization-Group Scheme for Hamiltonian Systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"chao-dyn/9805019","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":"sha256:396d30d14948d7d6454de6c6b818945a0db059b7fb48e2b5e0a03a3fcd3d15d9","target":"record","created_at":"2026-05-18T01:40:11Z","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":"bf524858d4ccba7b8fe3b0afa799f13d1851914da735396bbf564ee32b8d107a","cross_cats_sorted":["nlin.CD"],"license":"","primary_cat":"chao-dyn","submitted_at":"1998-05-22T14:40:33Z","title_canon_sha256":"910d79151645f6a6956d48519adffcdea25b19f02ab4eedb39e773faf946334f"},"schema_version":"1.0","source":{"id":"chao-dyn/9805019","kind":"arxiv","version":1}},"canonical_sha256":"57df0dba866af13f675888effe150f99d7789db4b7b4811f211cf111f31f7c34","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"57df0dba866af13f675888effe150f99d7789db4b7b4811f211cf111f31f7c34","first_computed_at":"2026-05-18T01:40:11.652599Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:40:11.652599Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jxCBjE/ZPocgCJqRzQGHwoJF2AkLtHSRd89hLn400C2xkt3ovFm3SvjIpwgJrYjM4q6CdbpTjvqpjypn+OkkCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:40:11.653298Z","signed_message":"canonical_sha256_bytes"},"source_id":"chao-dyn/9805019","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:396d30d14948d7d6454de6c6b818945a0db059b7fb48e2b5e0a03a3fcd3d15d9","sha256:1a00e6837bae3279fcef5cde5e3dc6928f5efdcb3cc94fdcea3013a38fcf6e33"],"state_sha256":"21c05eb36943623badaeed83a8e98a9048e5f20f65968023829a8517e15fdf15"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Fo0YL7lgUU4LpZJXcBScDqO+WNL/6OES1YySSWMKOR3Cf2Q7yIXME2fd1i+p8sk/jg7R9DkLxNVwevjXJ1i+Dw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T20:13:31.013664Z","bundle_sha256":"8570279e5d10aee3f97e6aad23b98092c36f8a1f5c3ac40b3b6a47f23451945d"}}