{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:JDNSEMIU5GLCKZ3SCE7CAYASAH","short_pith_number":"pith:JDNSEMIU","canonical_record":{"source":{"id":"1107.4704","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-07-23T18:39:52Z","cross_cats_sorted":[],"title_canon_sha256":"47fcc960e13f04f5135dddbc6efb5446bd7db77d93049f4f0db77b7bed5a3941","abstract_canon_sha256":"d6ede2d1648aeb4f9fa1b0e4d465a773b94495979d8d8998ab4a4efbe9848601"},"schema_version":"1.0"},"canonical_sha256":"48db223114e996256772113e20601201c3b02582fc93579653b287a16da79e01","source":{"kind":"arxiv","id":"1107.4704","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.4704","created_at":"2026-05-18T04:07:52Z"},{"alias_kind":"arxiv_version","alias_value":"1107.4704v2","created_at":"2026-05-18T04:07:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.4704","created_at":"2026-05-18T04:07:52Z"},{"alias_kind":"pith_short_12","alias_value":"JDNSEMIU5GLC","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_16","alias_value":"JDNSEMIU5GLCKZ3S","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_8","alias_value":"JDNSEMIU","created_at":"2026-05-18T12:26:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:JDNSEMIU5GLCKZ3SCE7CAYASAH","target":"record","payload":{"canonical_record":{"source":{"id":"1107.4704","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-07-23T18:39:52Z","cross_cats_sorted":[],"title_canon_sha256":"47fcc960e13f04f5135dddbc6efb5446bd7db77d93049f4f0db77b7bed5a3941","abstract_canon_sha256":"d6ede2d1648aeb4f9fa1b0e4d465a773b94495979d8d8998ab4a4efbe9848601"},"schema_version":"1.0"},"canonical_sha256":"48db223114e996256772113e20601201c3b02582fc93579653b287a16da79e01","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:07:52.487075Z","signature_b64":"hMTLI0zTAkthoTYXEF96SfFfPYeFSmlMDZgETFR2eYPlonQ6DxIXXrN42cixWFspdzNJDz0MWSayjAxsP2YOBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"48db223114e996256772113e20601201c3b02582fc93579653b287a16da79e01","last_reissued_at":"2026-05-18T04:07:52.486622Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:07:52.486622Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1107.4704","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:07:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"o/G9WZMZmlGCo0NJjZBj/wH8rIZzuoK8Pg9qDawVLpML0Qr5jvecgn6sWWwB2uxeTIdfrNJzTWy7SUNrG5TDBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T09:21:23.441936Z"},"content_sha256":"3f24a4264f551dc32176b6c036d145dfeb27807e5a387d8d4a6001c073a9516c","schema_version":"1.0","event_id":"sha256:3f24a4264f551dc32176b6c036d145dfeb27807e5a387d8d4a6001c073a9516c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:JDNSEMIU5GLCKZ3SCE7CAYASAH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Reducibility of cocycles under a Brjuno-R\\\"ussmann arithmetical condition","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Claire Chavaudret (JAD), Stefano Marmi (SNS PISA)","submitted_at":"2011-07-23T18:39:52Z","abstract_excerpt":"The arithmetics of the frequency and of the rotation number play a fundamental role in the study of reducibility of analytic quasi-periodic cocycles which are sufficiently close to a constant. In this paper we show how to generalize previous works by L.H.Eliasson which deal with the diophantine case so as to implement a Brjuno-Russmann arithmetical condition both on the frequency and on the rotation number. Our approach adapts the Poschel-Russmann KAM method, which was previously used in the problem of linearization of vector fields, to the problem of reducing cocycles."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.4704","kind":"arxiv","version":2},"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":"2026-05-18T04:07:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"K5i8E4eF2MIKW4I3GqVpFaR319R+TP7hnELkSWaM9vN6slITmbSgiSAsD3MKJEbjGhJRAnisnSEbTwVnHJY5CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T09:21:23.442284Z"},"content_sha256":"285785dcff3265aaef21c97ebb5402758032df3dca56670a18edf10823d355da","schema_version":"1.0","event_id":"sha256:285785dcff3265aaef21c97ebb5402758032df3dca56670a18edf10823d355da"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JDNSEMIU5GLCKZ3SCE7CAYASAH/bundle.json","state_url":"https://pith.science/pith/JDNSEMIU5GLCKZ3SCE7CAYASAH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JDNSEMIU5GLCKZ3SCE7CAYASAH/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":"2026-06-21T09:21:23Z","links":{"resolver":"https://pith.science/pith/JDNSEMIU5GLCKZ3SCE7CAYASAH","bundle":"https://pith.science/pith/JDNSEMIU5GLCKZ3SCE7CAYASAH/bundle.json","state":"https://pith.science/pith/JDNSEMIU5GLCKZ3SCE7CAYASAH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JDNSEMIU5GLCKZ3SCE7CAYASAH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:JDNSEMIU5GLCKZ3SCE7CAYASAH","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":"d6ede2d1648aeb4f9fa1b0e4d465a773b94495979d8d8998ab4a4efbe9848601","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-07-23T18:39:52Z","title_canon_sha256":"47fcc960e13f04f5135dddbc6efb5446bd7db77d93049f4f0db77b7bed5a3941"},"schema_version":"1.0","source":{"id":"1107.4704","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.4704","created_at":"2026-05-18T04:07:52Z"},{"alias_kind":"arxiv_version","alias_value":"1107.4704v2","created_at":"2026-05-18T04:07:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.4704","created_at":"2026-05-18T04:07:52Z"},{"alias_kind":"pith_short_12","alias_value":"JDNSEMIU5GLC","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_16","alias_value":"JDNSEMIU5GLCKZ3S","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_8","alias_value":"JDNSEMIU","created_at":"2026-05-18T12:26:32Z"}],"graph_snapshots":[{"event_id":"sha256:285785dcff3265aaef21c97ebb5402758032df3dca56670a18edf10823d355da","target":"graph","created_at":"2026-05-18T04:07:52Z","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 arithmetics of the frequency and of the rotation number play a fundamental role in the study of reducibility of analytic quasi-periodic cocycles which are sufficiently close to a constant. In this paper we show how to generalize previous works by L.H.Eliasson which deal with the diophantine case so as to implement a Brjuno-Russmann arithmetical condition both on the frequency and on the rotation number. Our approach adapts the Poschel-Russmann KAM method, which was previously used in the problem of linearization of vector fields, to the problem of reducing cocycles.","authors_text":"Claire Chavaudret (JAD), Stefano Marmi (SNS PISA)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-07-23T18:39:52Z","title":"Reducibility of cocycles under a Brjuno-R\\\"ussmann arithmetical condition"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.4704","kind":"arxiv","version":2},"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":"sha256:3f24a4264f551dc32176b6c036d145dfeb27807e5a387d8d4a6001c073a9516c","target":"record","created_at":"2026-05-18T04:07:52Z","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":"d6ede2d1648aeb4f9fa1b0e4d465a773b94495979d8d8998ab4a4efbe9848601","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-07-23T18:39:52Z","title_canon_sha256":"47fcc960e13f04f5135dddbc6efb5446bd7db77d93049f4f0db77b7bed5a3941"},"schema_version":"1.0","source":{"id":"1107.4704","kind":"arxiv","version":2}},"canonical_sha256":"48db223114e996256772113e20601201c3b02582fc93579653b287a16da79e01","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"48db223114e996256772113e20601201c3b02582fc93579653b287a16da79e01","first_computed_at":"2026-05-18T04:07:52.486622Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:07:52.486622Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hMTLI0zTAkthoTYXEF96SfFfPYeFSmlMDZgETFR2eYPlonQ6DxIXXrN42cixWFspdzNJDz0MWSayjAxsP2YOBg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:07:52.487075Z","signed_message":"canonical_sha256_bytes"},"source_id":"1107.4704","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3f24a4264f551dc32176b6c036d145dfeb27807e5a387d8d4a6001c073a9516c","sha256:285785dcff3265aaef21c97ebb5402758032df3dca56670a18edf10823d355da"],"state_sha256":"5f637eafa0641096a302740a8a80a9dd5505bd4e8b208e3cbf180a1cd908070a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5gVzuCLRIYFGvIfMGiwzrI5MCNVXa5kkf+ZsM0u98AFT+kMEnEk/BvXSIaPMNT+MuM5ZvDDOhuAz33Hr+1mpBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-21T09:21:23.444234Z","bundle_sha256":"0bfb26af03e5ae3370c4e2a25715cb4ca28997b82a72d9b84516fd3d53136505"}}