{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2004:TJONMK5ALZBIR3OUYMYPSCPQ27","short_pith_number":"pith:TJONMK5A","canonical_record":{"source":{"id":"nlin/0410019","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"nlin.CD","submitted_at":"2004-10-14T18:46:25Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"afb805d61f6ac0c07ab6fbd61fb76ac3e6b5b114d6b54d6cfe86d29213819a3a","abstract_canon_sha256":"4a9e846183f44f73b92e50121e0db267f5264945d35362550f585f54cacffe43"},"schema_version":"1.0"},"canonical_sha256":"9a5cd62ba05e4288edd4c330f909f0d7f7590bafed155ca4e69c1b69c507bb49","source":{"kind":"arxiv","id":"nlin/0410019","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"nlin/0410019","created_at":"2026-07-04T14:42:01Z"},{"alias_kind":"arxiv_version","alias_value":"nlin/0410019v1","created_at":"2026-07-04T14:42:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.nlin/0410019","created_at":"2026-07-04T14:42:01Z"},{"alias_kind":"pith_short_12","alias_value":"TJONMK5ALZBI","created_at":"2026-07-04T14:42:01Z"},{"alias_kind":"pith_short_16","alias_value":"TJONMK5ALZBIR3OU","created_at":"2026-07-04T14:42:01Z"},{"alias_kind":"pith_short_8","alias_value":"TJONMK5A","created_at":"2026-07-04T14:42:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2004:TJONMK5ALZBIR3OUYMYPSCPQ27","target":"record","payload":{"canonical_record":{"source":{"id":"nlin/0410019","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"nlin.CD","submitted_at":"2004-10-14T18:46:25Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"afb805d61f6ac0c07ab6fbd61fb76ac3e6b5b114d6b54d6cfe86d29213819a3a","abstract_canon_sha256":"4a9e846183f44f73b92e50121e0db267f5264945d35362550f585f54cacffe43"},"schema_version":"1.0"},"canonical_sha256":"9a5cd62ba05e4288edd4c330f909f0d7f7590bafed155ca4e69c1b69c507bb49","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T14:42:01.142200Z","signature_b64":"xArjsTdixHufAmrvSDxE0SuujY7J+yicPR8Qqo5CW7FfEIVgaXpHSMUUENLKB3Q68uYIi0WNY9SvaEwmrZRrCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9a5cd62ba05e4288edd4c330f909f0d7f7590bafed155ca4e69c1b69c507bb49","last_reissued_at":"2026-07-04T14:42:01.141860Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T14:42:01.141860Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"nlin/0410019","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":"2026-07-04T14:42:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"okk5Kmc04r9jdF1rO4c09M8ext1UkRFGat4t2U2meeGTxMQ9Mx/Gjl8qRYGkZrowSPD+noRECXwti9wwYTmADg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-05T07:01:13.027251Z"},"content_sha256":"1c9a09c8326855ffcf66cc14c011707f63ff2147bc4b37a0a5d54e146ae55943","schema_version":"1.0","event_id":"sha256:1c9a09c8326855ffcf66cc14c011707f63ff2147bc4b37a0a5d54e146ae55943"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2004:TJONMK5ALZBIR3OUYMYPSCPQ27","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The First Birkhoff Coefficient and the Stability of 2-Periodic Orbits on Billiards","license":"","headline":"","cross_cats":["math.DS"],"primary_cat":"nlin.CD","authors_text":"Brasil), Sonia Pinto de Carvalho (Departamento de Matematica UFMG, Sylvie Oliffson Kamphorst","submitted_at":"2004-10-14T18:46:25Z","abstract_excerpt":"In this work we address the question of proving the stability of elliptic 2-periodic orbits for strictly convex billiards. Eventhough it is part of a widely accepted belief that ellipticity implies stability, classical theorems show that the certainty of stability relies upon more fine conditions. We present a review of the main results and general theorems and describe the procedure to fullfill the supplementary conditions for strictly convex billiards."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"nlin/0410019","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/nlin/0410019/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":"2026-07-04T14:42:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8YFKX5VLd7nyRHX3Ln9p6Xsz7QPWmVXi+1o3UudgtOFKq2bX4ONg0+9xLjzbNGIjflCl025+yKYC7B2tI3efCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-05T07:01:13.027625Z"},"content_sha256":"2ac57c344d319f7907b99e4a0984de7f073cbeeb5020226e2431f29f76c567f7","schema_version":"1.0","event_id":"sha256:2ac57c344d319f7907b99e4a0984de7f073cbeeb5020226e2431f29f76c567f7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TJONMK5ALZBIR3OUYMYPSCPQ27/bundle.json","state_url":"https://pith.science/pith/TJONMK5ALZBIR3OUYMYPSCPQ27/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TJONMK5ALZBIR3OUYMYPSCPQ27/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":"2026-07-05T07:01:13Z","links":{"resolver":"https://pith.science/pith/TJONMK5ALZBIR3OUYMYPSCPQ27","bundle":"https://pith.science/pith/TJONMK5ALZBIR3OUYMYPSCPQ27/bundle.json","state":"https://pith.science/pith/TJONMK5ALZBIR3OUYMYPSCPQ27/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TJONMK5ALZBIR3OUYMYPSCPQ27/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2004:TJONMK5ALZBIR3OUYMYPSCPQ27","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":"4a9e846183f44f73b92e50121e0db267f5264945d35362550f585f54cacffe43","cross_cats_sorted":["math.DS"],"license":"","primary_cat":"nlin.CD","submitted_at":"2004-10-14T18:46:25Z","title_canon_sha256":"afb805d61f6ac0c07ab6fbd61fb76ac3e6b5b114d6b54d6cfe86d29213819a3a"},"schema_version":"1.0","source":{"id":"nlin/0410019","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"nlin/0410019","created_at":"2026-07-04T14:42:01Z"},{"alias_kind":"arxiv_version","alias_value":"nlin/0410019v1","created_at":"2026-07-04T14:42:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.nlin/0410019","created_at":"2026-07-04T14:42:01Z"},{"alias_kind":"pith_short_12","alias_value":"TJONMK5ALZBI","created_at":"2026-07-04T14:42:01Z"},{"alias_kind":"pith_short_16","alias_value":"TJONMK5ALZBIR3OU","created_at":"2026-07-04T14:42:01Z"},{"alias_kind":"pith_short_8","alias_value":"TJONMK5A","created_at":"2026-07-04T14:42:01Z"}],"graph_snapshots":[{"event_id":"sha256:2ac57c344d319f7907b99e4a0984de7f073cbeeb5020226e2431f29f76c567f7","target":"graph","created_at":"2026-07-04T14:42:01Z","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/nlin/0410019/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this work we address the question of proving the stability of elliptic 2-periodic orbits for strictly convex billiards. Eventhough it is part of a widely accepted belief that ellipticity implies stability, classical theorems show that the certainty of stability relies upon more fine conditions. We present a review of the main results and general theorems and describe the procedure to fullfill the supplementary conditions for strictly convex billiards.","authors_text":"Brasil), Sonia Pinto de Carvalho (Departamento de Matematica UFMG, Sylvie Oliffson Kamphorst","cross_cats":["math.DS"],"headline":"","license":"","primary_cat":"nlin.CD","submitted_at":"2004-10-14T18:46:25Z","title":"The First Birkhoff Coefficient and the Stability of 2-Periodic Orbits on Billiards"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"nlin/0410019","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":"sha256:1c9a09c8326855ffcf66cc14c011707f63ff2147bc4b37a0a5d54e146ae55943","target":"record","created_at":"2026-07-04T14:42:01Z","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":"4a9e846183f44f73b92e50121e0db267f5264945d35362550f585f54cacffe43","cross_cats_sorted":["math.DS"],"license":"","primary_cat":"nlin.CD","submitted_at":"2004-10-14T18:46:25Z","title_canon_sha256":"afb805d61f6ac0c07ab6fbd61fb76ac3e6b5b114d6b54d6cfe86d29213819a3a"},"schema_version":"1.0","source":{"id":"nlin/0410019","kind":"arxiv","version":1}},"canonical_sha256":"9a5cd62ba05e4288edd4c330f909f0d7f7590bafed155ca4e69c1b69c507bb49","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9a5cd62ba05e4288edd4c330f909f0d7f7590bafed155ca4e69c1b69c507bb49","first_computed_at":"2026-07-04T14:42:01.141860Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T14:42:01.141860Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xArjsTdixHufAmrvSDxE0SuujY7J+yicPR8Qqo5CW7FfEIVgaXpHSMUUENLKB3Q68uYIi0WNY9SvaEwmrZRrCg==","signature_status":"signed_v1","signed_at":"2026-07-04T14:42:01.142200Z","signed_message":"canonical_sha256_bytes"},"source_id":"nlin/0410019","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1c9a09c8326855ffcf66cc14c011707f63ff2147bc4b37a0a5d54e146ae55943","sha256:2ac57c344d319f7907b99e4a0984de7f073cbeeb5020226e2431f29f76c567f7"],"state_sha256":"642329bda5fd17f5299981e519714a8631de4a2f71348cfe8f48ae4779c481f8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"E+E+21Rn17jigGeaeroJNz07HB3Rg6mO6ckdcuPdzcJEV3d8Ydcrf3TzH/ZPneI1wOJ7jzqtF1h6f0OJ3lLZBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-05T07:01:13.029491Z","bundle_sha256":"7d71e7865397eac47c7f37052392de4a09a6410fd82bd9cd672ae77f5d69a5dc"}}