{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:L5K5EMFNLTYC6EBFMCVMYPC4VW","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":"8ee7f9da1fcc84d9dbbd35984c65eafb75ffc84b05fcd2dcefd96d15eba3ec55","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-10-22T09:55:20Z","title_canon_sha256":"b5033eaf012771f2a9b02b6104925c480731d99e9befb526986b47802d331859"},"schema_version":"1.0","source":{"id":"1510.06561","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.06561","created_at":"2026-05-18T01:24:51Z"},{"alias_kind":"arxiv_version","alias_value":"1510.06561v1","created_at":"2026-05-18T01:24:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.06561","created_at":"2026-05-18T01:24:51Z"},{"alias_kind":"pith_short_12","alias_value":"L5K5EMFNLTYC","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_16","alias_value":"L5K5EMFNLTYC6EBF","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_8","alias_value":"L5K5EMFN","created_at":"2026-05-18T12:29:29Z"}],"graph_snapshots":[{"event_id":"sha256:685250bd63ba34d6fd28582a0fe9fb10c113feb1ac0682854494b614dc80c7bc","target":"graph","created_at":"2026-05-18T01:24:51Z","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 revisit the problem of introducing an a priori control for devices that can be modeled via a symplectic map in a neighborhood of an elliptic equilibrium. Using a technique based on Lie transform methods we produce a normal form algorithm that avoids the usual step of interpolating the map with a flow. The formal algorithm is completed with quantitative estimates that bring into evidence the asymptotic character of the normal form transformation. Then we perform an heuristic analysis of the dynamical behavior of the map using the invariant function for the normalized map. Finally, we discuss","authors_text":"A. Giorgilli, M. Sansottera, T. Carletti","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-10-22T09:55:20Z","title":"High-order control for symplectic maps"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.06561","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":"sha256:87f5fc19b504f146f47eb8ff1cd50e2af4568841157efb20ee4d035e92ba7140","target":"record","created_at":"2026-05-18T01:24:51Z","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":"8ee7f9da1fcc84d9dbbd35984c65eafb75ffc84b05fcd2dcefd96d15eba3ec55","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-10-22T09:55:20Z","title_canon_sha256":"b5033eaf012771f2a9b02b6104925c480731d99e9befb526986b47802d331859"},"schema_version":"1.0","source":{"id":"1510.06561","kind":"arxiv","version":1}},"canonical_sha256":"5f55d230ad5cf02f102560aacc3c5cad9c6393250e4a4e78515a52dbcff6bbf4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5f55d230ad5cf02f102560aacc3c5cad9c6393250e4a4e78515a52dbcff6bbf4","first_computed_at":"2026-05-18T01:24:51.421436Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:24:51.421436Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5AKtJ4hIVtoMGcB3OtHc1K1yVQEyzv2g/oO4YY4ey6TIhVt7C0XP4QRX6tT7ReEdWCthQkFHooFYr6vX8XSBAA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:24:51.422103Z","signed_message":"canonical_sha256_bytes"},"source_id":"1510.06561","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:87f5fc19b504f146f47eb8ff1cd50e2af4568841157efb20ee4d035e92ba7140","sha256:685250bd63ba34d6fd28582a0fe9fb10c113feb1ac0682854494b614dc80c7bc"],"state_sha256":"f5d71e6d75f1128c940a072c56d6c94d83c7c99fdf2708df51f29df329147412"}