{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:ZV3W6PJPF57BIAQC6452JZ3XBI","short_pith_number":"pith:ZV3W6PJP","canonical_record":{"source":{"id":"1705.06909","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-05-19T09:45:52Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"16a0216162fd18d1ca3a251c8c04449cc46b7e25dc9441b9c01f32adfe12417e","abstract_canon_sha256":"cf6487cebf5cf9b8802f65bca47a1b653628f1899d7d24efecead4b4da2d3910"},"schema_version":"1.0"},"canonical_sha256":"cd776f3d2f2f7e140202f73ba4e7770a3d443a8dbde9cc6cba992797f96d3508","source":{"kind":"arxiv","id":"1705.06909","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.06909","created_at":"2026-05-18T00:41:44Z"},{"alias_kind":"arxiv_version","alias_value":"1705.06909v2","created_at":"2026-05-18T00:41:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.06909","created_at":"2026-05-18T00:41:44Z"},{"alias_kind":"pith_short_12","alias_value":"ZV3W6PJPF57B","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_16","alias_value":"ZV3W6PJPF57BIAQC","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_8","alias_value":"ZV3W6PJP","created_at":"2026-05-18T12:31:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:ZV3W6PJPF57BIAQC6452JZ3XBI","target":"record","payload":{"canonical_record":{"source":{"id":"1705.06909","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-05-19T09:45:52Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"16a0216162fd18d1ca3a251c8c04449cc46b7e25dc9441b9c01f32adfe12417e","abstract_canon_sha256":"cf6487cebf5cf9b8802f65bca47a1b653628f1899d7d24efecead4b4da2d3910"},"schema_version":"1.0"},"canonical_sha256":"cd776f3d2f2f7e140202f73ba4e7770a3d443a8dbde9cc6cba992797f96d3508","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:41:44.066306Z","signature_b64":"x2M7q8pIRmoz8mfyx130KcAvWowQC4vkmzMewZZ2ud4MIIOaKtFeQdHAOIvyBH+AoyVyazcWZuCDTBTWYXEbAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cd776f3d2f2f7e140202f73ba4e7770a3d443a8dbde9cc6cba992797f96d3508","last_reissued_at":"2026-05-18T00:41:44.065632Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:41:44.065632Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1705.06909","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":"2026-05-18T00:41:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3URzdrsJjrGmzO3g5YW/moSjU8NKW97FX/KSJiurzsaR9Dx2St2RSdLL95HlriFWMVAqF/QK/Ms55a5Q7tL4Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T03:13:59.235075Z"},"content_sha256":"c4ee92e2a32f6daa4c8c3c090f175085b0de5034126767567753ec8857b616c8","schema_version":"1.0","event_id":"sha256:c4ee92e2a32f6daa4c8c3c090f175085b0de5034126767567753ec8857b616c8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:ZV3W6PJPF57BIAQC6452JZ3XBI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"KAM, $\\alpha$-Gevrey regularity and the $\\alpha$-Bruno-R\\\"ussmann condition","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.DS","authors_text":"Abed Bounemoura (CEREMADE, Imcce), Jacques F\\'ejoz (CEREMADE","submitted_at":"2017-05-19T09:45:52Z","abstract_excerpt":"We prove a new invariant torus theorem, for $\\alpha$-Gevrey smooth Hamiltonian systems, under an arithmetic assumption which we call the $\\alpha$-Bruno-R\\\"ussmann condition, and which reduces to the classical Bruno-R\\\"ussmann condition in the analytic category. Our proof is direct in the sense that, for analytic Hamiltonians, we avoid the use of complex extensions and, for non-analytic Hamiltonians, we do not use analytic approximation nor smoothing operators. Following Bessi, we also show that if a slightly weaker arithmetic condition is not satisfied, the invariant torus may be destroyed. Cr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.06909","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":"2026-05-18T00:41:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yYYw3wWTkbrzvp8YNA3+R32580ykq2PoDFPo3VRzT7DYxbKkt0l4PQowVgn37fYHqGKdoJK9Z7pYoD98VFJ+Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T03:13:59.235427Z"},"content_sha256":"600ee44db1e89d314ded94cbe058ea5281eee6516bfcb00e181e0be935f1dfa8","schema_version":"1.0","event_id":"sha256:600ee44db1e89d314ded94cbe058ea5281eee6516bfcb00e181e0be935f1dfa8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZV3W6PJPF57BIAQC6452JZ3XBI/bundle.json","state_url":"https://pith.science/pith/ZV3W6PJPF57BIAQC6452JZ3XBI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZV3W6PJPF57BIAQC6452JZ3XBI/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":"2026-06-28T03:13:59Z","links":{"resolver":"https://pith.science/pith/ZV3W6PJPF57BIAQC6452JZ3XBI","bundle":"https://pith.science/pith/ZV3W6PJPF57BIAQC6452JZ3XBI/bundle.json","state":"https://pith.science/pith/ZV3W6PJPF57BIAQC6452JZ3XBI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZV3W6PJPF57BIAQC6452JZ3XBI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:ZV3W6PJPF57BIAQC6452JZ3XBI","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":"cf6487cebf5cf9b8802f65bca47a1b653628f1899d7d24efecead4b4da2d3910","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-05-19T09:45:52Z","title_canon_sha256":"16a0216162fd18d1ca3a251c8c04449cc46b7e25dc9441b9c01f32adfe12417e"},"schema_version":"1.0","source":{"id":"1705.06909","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.06909","created_at":"2026-05-18T00:41:44Z"},{"alias_kind":"arxiv_version","alias_value":"1705.06909v2","created_at":"2026-05-18T00:41:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.06909","created_at":"2026-05-18T00:41:44Z"},{"alias_kind":"pith_short_12","alias_value":"ZV3W6PJPF57B","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_16","alias_value":"ZV3W6PJPF57BIAQC","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_8","alias_value":"ZV3W6PJP","created_at":"2026-05-18T12:31:59Z"}],"graph_snapshots":[{"event_id":"sha256:600ee44db1e89d314ded94cbe058ea5281eee6516bfcb00e181e0be935f1dfa8","target":"graph","created_at":"2026-05-18T00:41:44Z","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 prove a new invariant torus theorem, for $\\alpha$-Gevrey smooth Hamiltonian systems, under an arithmetic assumption which we call the $\\alpha$-Bruno-R\\\"ussmann condition, and which reduces to the classical Bruno-R\\\"ussmann condition in the analytic category. Our proof is direct in the sense that, for analytic Hamiltonians, we avoid the use of complex extensions and, for non-analytic Hamiltonians, we do not use analytic approximation nor smoothing operators. Following Bessi, we also show that if a slightly weaker arithmetic condition is not satisfied, the invariant torus may be destroyed. Cr","authors_text":"Abed Bounemoura (CEREMADE, Imcce), Jacques F\\'ejoz (CEREMADE","cross_cats":["math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-05-19T09:45:52Z","title":"KAM, $\\alpha$-Gevrey regularity and the $\\alpha$-Bruno-R\\\"ussmann condition"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.06909","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:c4ee92e2a32f6daa4c8c3c090f175085b0de5034126767567753ec8857b616c8","target":"record","created_at":"2026-05-18T00:41:44Z","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":"cf6487cebf5cf9b8802f65bca47a1b653628f1899d7d24efecead4b4da2d3910","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-05-19T09:45:52Z","title_canon_sha256":"16a0216162fd18d1ca3a251c8c04449cc46b7e25dc9441b9c01f32adfe12417e"},"schema_version":"1.0","source":{"id":"1705.06909","kind":"arxiv","version":2}},"canonical_sha256":"cd776f3d2f2f7e140202f73ba4e7770a3d443a8dbde9cc6cba992797f96d3508","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cd776f3d2f2f7e140202f73ba4e7770a3d443a8dbde9cc6cba992797f96d3508","first_computed_at":"2026-05-18T00:41:44.065632Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:41:44.065632Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"x2M7q8pIRmoz8mfyx130KcAvWowQC4vkmzMewZZ2ud4MIIOaKtFeQdHAOIvyBH+AoyVyazcWZuCDTBTWYXEbAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:41:44.066306Z","signed_message":"canonical_sha256_bytes"},"source_id":"1705.06909","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c4ee92e2a32f6daa4c8c3c090f175085b0de5034126767567753ec8857b616c8","sha256:600ee44db1e89d314ded94cbe058ea5281eee6516bfcb00e181e0be935f1dfa8"],"state_sha256":"34acbeb6cb2abdf8bc3a5a238dc032c06eb53f5ed9eb6f886738c6deef127053"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"REjviy8P5yF8KrPRyG/Xi4sY0eBEsBsr923UnKly9zaBHTSWV0t5nsR4Z40yybgnJM32e/vgxISbpluJbkXhCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-28T03:13:59.237298Z","bundle_sha256":"a02d7f0f1d78a6b3a64e427693286896606ebe957c19c16332c05a38e78c31a0"}}