{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:VB3OXSRBMJSK2W2OCT6Z6YFKHI","short_pith_number":"pith:VB3OXSRB","canonical_record":{"source":{"id":"1703.01748","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-03-06T07:22:48Z","cross_cats_sorted":[],"title_canon_sha256":"df4c741aca6c60fa5fcbde7ff4285b154c76aa2e1c9a4325f078318e450469c5","abstract_canon_sha256":"be5138c056573dadef27d2c77efdaadf482914ca5d91225cb56f804c86f0e43f"},"schema_version":"1.0"},"canonical_sha256":"a876ebca216264ad5b4e14fd9f60aa3a2c4cb9ec476b93edcf3b1d58f59076a9","source":{"kind":"arxiv","id":"1703.01748","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.01748","created_at":"2026-05-18T00:49:29Z"},{"alias_kind":"arxiv_version","alias_value":"1703.01748v1","created_at":"2026-05-18T00:49:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.01748","created_at":"2026-05-18T00:49:29Z"},{"alias_kind":"pith_short_12","alias_value":"VB3OXSRBMJSK","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_16","alias_value":"VB3OXSRBMJSK2W2O","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_8","alias_value":"VB3OXSRB","created_at":"2026-05-18T12:31:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:VB3OXSRBMJSK2W2OCT6Z6YFKHI","target":"record","payload":{"canonical_record":{"source":{"id":"1703.01748","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-03-06T07:22:48Z","cross_cats_sorted":[],"title_canon_sha256":"df4c741aca6c60fa5fcbde7ff4285b154c76aa2e1c9a4325f078318e450469c5","abstract_canon_sha256":"be5138c056573dadef27d2c77efdaadf482914ca5d91225cb56f804c86f0e43f"},"schema_version":"1.0"},"canonical_sha256":"a876ebca216264ad5b4e14fd9f60aa3a2c4cb9ec476b93edcf3b1d58f59076a9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:49:29.775998Z","signature_b64":"9uJGxRZ7kmt83muCeahsCSF6REHsYC31MvF1v9Bk194NwwCsq2P1DNFt8AWW2OMCGbYqHcKoCGdV7eqUXSsaBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a876ebca216264ad5b4e14fd9f60aa3a2c4cb9ec476b93edcf3b1d58f59076a9","last_reissued_at":"2026-05-18T00:49:29.775381Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:49:29.775381Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1703.01748","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":"2026-05-18T00:49:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"taS8CMYxpkx97Ek49i0f3d07q7uUsJyvS6OP2r6qw5x3KlCf6S4TenKVbCbPSnG6u1GMSgG0URWQQnw1DggGCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T15:31:42.585059Z"},"content_sha256":"795dc52596af55171662c9c3ba49d909c0e2ef66e91849aed76cd9009bb8f883","schema_version":"1.0","event_id":"sha256:795dc52596af55171662c9c3ba49d909c0e2ef66e91849aed76cd9009bb8f883"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:VB3OXSRBMJSK2W2OCT6Z6YFKHI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Lagrange and Markov spectra from the dynamical point of view","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Carlos Matheus","submitted_at":"2017-03-06T07:22:48Z","abstract_excerpt":"This text grew out of my lecture notes for a 4-hours minicourse delivered on October 17 \\& 19, 2016 during the research school \"Applications of Ergodic Theory in Number Theory\" -- an activity related to the Jean-Molet Chair project of Mariusz Lema\\'nczyk and S\\'ebastien Ferenczi -- realized at CIRM, Marseille, France. The subject of this text is the same of my minicourse, namely, the structure of the so-called Lagrange and Markov spectra (with an special emphasis on a recent theorem of C. G. Moreira)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.01748","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":"2026-05-18T00:49:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/miV0dZCqLwPptqi7xkonIyPF84fgnx5fgkXg/aw7AVhrt0NncB75nPNjMQaO1n3xZYWNqXHt0Qb24dccSOTDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T15:31:42.585418Z"},"content_sha256":"e8d5c9c8fd315772acf23b78ef2c369855ef81b935f1f12b0eeb5fd0a971fbf2","schema_version":"1.0","event_id":"sha256:e8d5c9c8fd315772acf23b78ef2c369855ef81b935f1f12b0eeb5fd0a971fbf2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VB3OXSRBMJSK2W2OCT6Z6YFKHI/bundle.json","state_url":"https://pith.science/pith/VB3OXSRBMJSK2W2OCT6Z6YFKHI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VB3OXSRBMJSK2W2OCT6Z6YFKHI/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":"2026-05-30T15:31:42Z","links":{"resolver":"https://pith.science/pith/VB3OXSRBMJSK2W2OCT6Z6YFKHI","bundle":"https://pith.science/pith/VB3OXSRBMJSK2W2OCT6Z6YFKHI/bundle.json","state":"https://pith.science/pith/VB3OXSRBMJSK2W2OCT6Z6YFKHI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VB3OXSRBMJSK2W2OCT6Z6YFKHI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:VB3OXSRBMJSK2W2OCT6Z6YFKHI","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":"be5138c056573dadef27d2c77efdaadf482914ca5d91225cb56f804c86f0e43f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-03-06T07:22:48Z","title_canon_sha256":"df4c741aca6c60fa5fcbde7ff4285b154c76aa2e1c9a4325f078318e450469c5"},"schema_version":"1.0","source":{"id":"1703.01748","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.01748","created_at":"2026-05-18T00:49:29Z"},{"alias_kind":"arxiv_version","alias_value":"1703.01748v1","created_at":"2026-05-18T00:49:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.01748","created_at":"2026-05-18T00:49:29Z"},{"alias_kind":"pith_short_12","alias_value":"VB3OXSRBMJSK","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_16","alias_value":"VB3OXSRBMJSK2W2O","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_8","alias_value":"VB3OXSRB","created_at":"2026-05-18T12:31:49Z"}],"graph_snapshots":[{"event_id":"sha256:e8d5c9c8fd315772acf23b78ef2c369855ef81b935f1f12b0eeb5fd0a971fbf2","target":"graph","created_at":"2026-05-18T00:49:29Z","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"},"paper":{"abstract_excerpt":"This text grew out of my lecture notes for a 4-hours minicourse delivered on October 17 \\& 19, 2016 during the research school \"Applications of Ergodic Theory in Number Theory\" -- an activity related to the Jean-Molet Chair project of Mariusz Lema\\'nczyk and S\\'ebastien Ferenczi -- realized at CIRM, Marseille, France. The subject of this text is the same of my minicourse, namely, the structure of the so-called Lagrange and Markov spectra (with an special emphasis on a recent theorem of C. G. Moreira).","authors_text":"Carlos Matheus","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-03-06T07:22:48Z","title":"The Lagrange and Markov spectra from the dynamical point of view"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.01748","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":"sha256:795dc52596af55171662c9c3ba49d909c0e2ef66e91849aed76cd9009bb8f883","target":"record","created_at":"2026-05-18T00:49:29Z","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":"be5138c056573dadef27d2c77efdaadf482914ca5d91225cb56f804c86f0e43f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-03-06T07:22:48Z","title_canon_sha256":"df4c741aca6c60fa5fcbde7ff4285b154c76aa2e1c9a4325f078318e450469c5"},"schema_version":"1.0","source":{"id":"1703.01748","kind":"arxiv","version":1}},"canonical_sha256":"a876ebca216264ad5b4e14fd9f60aa3a2c4cb9ec476b93edcf3b1d58f59076a9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a876ebca216264ad5b4e14fd9f60aa3a2c4cb9ec476b93edcf3b1d58f59076a9","first_computed_at":"2026-05-18T00:49:29.775381Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:49:29.775381Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9uJGxRZ7kmt83muCeahsCSF6REHsYC31MvF1v9Bk194NwwCsq2P1DNFt8AWW2OMCGbYqHcKoCGdV7eqUXSsaBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:49:29.775998Z","signed_message":"canonical_sha256_bytes"},"source_id":"1703.01748","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:795dc52596af55171662c9c3ba49d909c0e2ef66e91849aed76cd9009bb8f883","sha256:e8d5c9c8fd315772acf23b78ef2c369855ef81b935f1f12b0eeb5fd0a971fbf2"],"state_sha256":"fcfee14742f1f1b770e5569af9d8a503388755fd95e552e1e0cf35135052bf6b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"f5mjRNtLL2x0JLwN4ijCp1K4oDFSjSsfdOtz7BOsL4LzZDq2wn/lHSp4LaUfrwhvZ9iYHgzkQSZnn0k4edTkAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T15:31:42.588237Z","bundle_sha256":"f7b391c96b10dabbca9690d985a0e40c036e61b953070fd2214473323da82f25"}}