{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:1998:YHNEGYQPGP6WNOSHUFMUF65VHC","short_pith_number":"pith:YHNEGYQP","canonical_record":{"source":{"id":"chao-dyn/9810035","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"chao-dyn","submitted_at":"1998-10-29T09:14:47Z","cross_cats_sorted":["nlin.CD"],"title_canon_sha256":"bd88ba8d53cff9e569089ef7cfc24e98cba25234b2f30220f02f62e50de03763","abstract_canon_sha256":"6b5bb52bea544a76c2eb95a384d86bdfcadd0a5aff5d48b3e740417ddd1eb122"},"schema_version":"1.0"},"canonical_sha256":"c1da43620f33fd66ba47a15942fbb53880b6b2b091fce724f704c84109cbbbc3","source":{"kind":"arxiv","id":"chao-dyn/9810035","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"chao-dyn/9810035","created_at":"2026-07-04T14:17:29Z"},{"alias_kind":"arxiv_version","alias_value":"chao-dyn/9810035v1","created_at":"2026-07-04T14:17:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.chao-dyn/9810035","created_at":"2026-07-04T14:17:29Z"},{"alias_kind":"pith_short_12","alias_value":"YHNEGYQPGP6W","created_at":"2026-07-04T14:17:29Z"},{"alias_kind":"pith_short_16","alias_value":"YHNEGYQPGP6WNOSH","created_at":"2026-07-04T14:17:29Z"},{"alias_kind":"pith_short_8","alias_value":"YHNEGYQP","created_at":"2026-07-04T14:17:29Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:1998:YHNEGYQPGP6WNOSHUFMUF65VHC","target":"record","payload":{"canonical_record":{"source":{"id":"chao-dyn/9810035","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"chao-dyn","submitted_at":"1998-10-29T09:14:47Z","cross_cats_sorted":["nlin.CD"],"title_canon_sha256":"bd88ba8d53cff9e569089ef7cfc24e98cba25234b2f30220f02f62e50de03763","abstract_canon_sha256":"6b5bb52bea544a76c2eb95a384d86bdfcadd0a5aff5d48b3e740417ddd1eb122"},"schema_version":"1.0"},"canonical_sha256":"c1da43620f33fd66ba47a15942fbb53880b6b2b091fce724f704c84109cbbbc3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T14:17:29.969779Z","signature_b64":"JotaTV8IPrY9An5RqF+cgzfCZuvySfw/9k3/okIAtfPIF/pVgq2sNmdmRP7ZJTxMnDU56FrVd8bnImDho2FwAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c1da43620f33fd66ba47a15942fbb53880b6b2b091fce724f704c84109cbbbc3","last_reissued_at":"2026-07-04T14:17:29.969394Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T14:17:29.969394Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"chao-dyn/9810035","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":"2026-07-04T14:17:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zmBZbu3UX3pibwQuKaaczrxozhKjKwu3hfws2qHGjMu0OUlsK1ho+hfNSFDHEfOYldYrUqW3scS9FyTDkBLKAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-06T06:59:18.257725Z"},"content_sha256":"56155332eefcd966026a66b08f33997e42837c930bf77a9055903a6dd9347850","schema_version":"1.0","event_id":"sha256:56155332eefcd966026a66b08f33997e42837c930bf77a9055903a6dd9347850"},{"event_type":"graph_snapshot","subject_pith_number":"pith:1998:YHNEGYQPGP6WNOSHUFMUF65VHC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Bryuno Function and the Standard Map","license":"","headline":"","cross_cats":["nlin.CD"],"primary_cat":"chao-dyn","authors_text":"Alberto Berretti, Guido Gentile","submitted_at":"1998-10-29T09:14:47Z","abstract_excerpt":"For the standard map the homotopically non-trivial invariant curves of rotation number satisfying the Bryuno condition are shown to be analytic in the perturbative parameter, provided the latter is small enough. The radius of convergence of the Lindstedt series -- sometimes called critical function of the standard map -- is studied and the relation with the Bryuno function is derived: the logarithm of the radius of convergence plus twice the Bryuno function is proved to be bounded (from below and from above) uniformily in the rotation number."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"chao-dyn/9810035","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/chao-dyn/9810035/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-04T14:17:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dKm50FPoXsKNeS869tGb2MkWhaQSI35JSE71mroSyYLiGOiwVnegck7D2uFyu/1wUQaKs5MUlr9/DsGakhJrBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-06T06:59:18.258115Z"},"content_sha256":"c757dd3404ae6724a4a6e01ea2d43c11e78a9ce5953db42ff04065e59bd643b8","schema_version":"1.0","event_id":"sha256:c757dd3404ae6724a4a6e01ea2d43c11e78a9ce5953db42ff04065e59bd643b8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YHNEGYQPGP6WNOSHUFMUF65VHC/bundle.json","state_url":"https://pith.science/pith/YHNEGYQPGP6WNOSHUFMUF65VHC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YHNEGYQPGP6WNOSHUFMUF65VHC/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":"2026-07-06T06:59:18Z","links":{"resolver":"https://pith.science/pith/YHNEGYQPGP6WNOSHUFMUF65VHC","bundle":"https://pith.science/pith/YHNEGYQPGP6WNOSHUFMUF65VHC/bundle.json","state":"https://pith.science/pith/YHNEGYQPGP6WNOSHUFMUF65VHC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YHNEGYQPGP6WNOSHUFMUF65VHC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1998:YHNEGYQPGP6WNOSHUFMUF65VHC","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":"6b5bb52bea544a76c2eb95a384d86bdfcadd0a5aff5d48b3e740417ddd1eb122","cross_cats_sorted":["nlin.CD"],"license":"","primary_cat":"chao-dyn","submitted_at":"1998-10-29T09:14:47Z","title_canon_sha256":"bd88ba8d53cff9e569089ef7cfc24e98cba25234b2f30220f02f62e50de03763"},"schema_version":"1.0","source":{"id":"chao-dyn/9810035","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"chao-dyn/9810035","created_at":"2026-07-04T14:17:29Z"},{"alias_kind":"arxiv_version","alias_value":"chao-dyn/9810035v1","created_at":"2026-07-04T14:17:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.chao-dyn/9810035","created_at":"2026-07-04T14:17:29Z"},{"alias_kind":"pith_short_12","alias_value":"YHNEGYQPGP6W","created_at":"2026-07-04T14:17:29Z"},{"alias_kind":"pith_short_16","alias_value":"YHNEGYQPGP6WNOSH","created_at":"2026-07-04T14:17:29Z"},{"alias_kind":"pith_short_8","alias_value":"YHNEGYQP","created_at":"2026-07-04T14:17:29Z"}],"graph_snapshots":[{"event_id":"sha256:c757dd3404ae6724a4a6e01ea2d43c11e78a9ce5953db42ff04065e59bd643b8","target":"graph","created_at":"2026-07-04T14:17:29Z","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/chao-dyn/9810035/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"For the standard map the homotopically non-trivial invariant curves of rotation number satisfying the Bryuno condition are shown to be analytic in the perturbative parameter, provided the latter is small enough. The radius of convergence of the Lindstedt series -- sometimes called critical function of the standard map -- is studied and the relation with the Bryuno function is derived: the logarithm of the radius of convergence plus twice the Bryuno function is proved to be bounded (from below and from above) uniformily in the rotation number.","authors_text":"Alberto Berretti, Guido Gentile","cross_cats":["nlin.CD"],"headline":"","license":"","primary_cat":"chao-dyn","submitted_at":"1998-10-29T09:14:47Z","title":"Bryuno Function and the Standard Map"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"chao-dyn/9810035","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":"sha256:56155332eefcd966026a66b08f33997e42837c930bf77a9055903a6dd9347850","target":"record","created_at":"2026-07-04T14:17:29Z","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":"6b5bb52bea544a76c2eb95a384d86bdfcadd0a5aff5d48b3e740417ddd1eb122","cross_cats_sorted":["nlin.CD"],"license":"","primary_cat":"chao-dyn","submitted_at":"1998-10-29T09:14:47Z","title_canon_sha256":"bd88ba8d53cff9e569089ef7cfc24e98cba25234b2f30220f02f62e50de03763"},"schema_version":"1.0","source":{"id":"chao-dyn/9810035","kind":"arxiv","version":1}},"canonical_sha256":"c1da43620f33fd66ba47a15942fbb53880b6b2b091fce724f704c84109cbbbc3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c1da43620f33fd66ba47a15942fbb53880b6b2b091fce724f704c84109cbbbc3","first_computed_at":"2026-07-04T14:17:29.969394Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T14:17:29.969394Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JotaTV8IPrY9An5RqF+cgzfCZuvySfw/9k3/okIAtfPIF/pVgq2sNmdmRP7ZJTxMnDU56FrVd8bnImDho2FwAw==","signature_status":"signed_v1","signed_at":"2026-07-04T14:17:29.969779Z","signed_message":"canonical_sha256_bytes"},"source_id":"chao-dyn/9810035","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:56155332eefcd966026a66b08f33997e42837c930bf77a9055903a6dd9347850","sha256:c757dd3404ae6724a4a6e01ea2d43c11e78a9ce5953db42ff04065e59bd643b8"],"state_sha256":"a0cf52b1e4e1c86167480980cc027c524faa1b134e270e392f39a2948864ee37"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"K3B4TlRBHj81y6YsLLWWf6sdC6ToKk7pDeAjdYF9ODez6HarJzMF6f8wky1FMGfrxz9P6HQg8w5hojs4oPxeAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-06T06:59:18.260012Z","bundle_sha256":"40efb48cc693839c0e5a614209eb0a862276225e34152d5dc09b68e703252e29"}}