{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:LMINCLIRRARNBOLLTRCILTFUBK","short_pith_number":"pith:LMINCLIR","schema_version":"1.0","canonical_sha256":"5b10d12d118822d0b96b9c4485ccb40a994d1b39dad9550a2516a1fd45d64971","source":{"kind":"arxiv","id":"1604.07142","version":1},"attestation_state":"computed","paper":{"title":"Normalization in Lie algebras via mould calculus and applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.DS","authors_text":"David Sauzin (IMCCE), Thierry Paul (CMLS)","submitted_at":"2016-04-25T06:41:37Z","abstract_excerpt":"We establish Ecalle's mould calculus in an abstract Lie-theoretic setting and use it to solve a normalization problem, which covers several formal normal form problems in the theory of dynamical systems. The mould formalism allows us to reduce the Lie-theoretic problem to a mould equation, the solutions of which are remarkably explicit and can be fully described by means of a gauge transformation group. The dynamical applications include the construction of Poincar{\\'e}-Dulac formal normal forms for a vector field around an equilibrium point, a formal infinite-order multiphase averaging proced"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1604.07142","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-04-25T06:41:37Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"c9fad6034bb1b565276913a96a77b729852c64b5a7fc05c847d3f4174a237775","abstract_canon_sha256":"8540cfc29776056c55f5131a1bc8b77012e504feae797d2d29b7342e3dd99473"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:26:02.203168Z","signature_b64":"DRbwfwcp5bcjxVphIlXfylXEv1Q+Mkktx20c7OgX5DUAHPa4AUQnEUMWWpG/t+u51BZq/osQ+m/Cj/ErBt6FBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5b10d12d118822d0b96b9c4485ccb40a994d1b39dad9550a2516a1fd45d64971","last_reissued_at":"2026-05-18T00:26:02.202559Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:26:02.202559Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Normalization in Lie algebras via mould calculus and applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.DS","authors_text":"David Sauzin (IMCCE), Thierry Paul (CMLS)","submitted_at":"2016-04-25T06:41:37Z","abstract_excerpt":"We establish Ecalle's mould calculus in an abstract Lie-theoretic setting and use it to solve a normalization problem, which covers several formal normal form problems in the theory of dynamical systems. The mould formalism allows us to reduce the Lie-theoretic problem to a mould equation, the solutions of which are remarkably explicit and can be fully described by means of a gauge transformation group. The dynamical applications include the construction of Poincar{\\'e}-Dulac formal normal forms for a vector field around an equilibrium point, a formal infinite-order multiphase averaging proced"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.07142","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1604.07142","created_at":"2026-05-18T00:26:02.202656+00:00"},{"alias_kind":"arxiv_version","alias_value":"1604.07142v1","created_at":"2026-05-18T00:26:02.202656+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.07142","created_at":"2026-05-18T00:26:02.202656+00:00"},{"alias_kind":"pith_short_12","alias_value":"LMINCLIRRARN","created_at":"2026-05-18T12:30:29.479603+00:00"},{"alias_kind":"pith_short_16","alias_value":"LMINCLIRRARNBOLL","created_at":"2026-05-18T12:30:29.479603+00:00"},{"alias_kind":"pith_short_8","alias_value":"LMINCLIR","created_at":"2026-05-18T12:30:29.479603+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/LMINCLIRRARNBOLLTRCILTFUBK","json":"https://pith.science/pith/LMINCLIRRARNBOLLTRCILTFUBK.json","graph_json":"https://pith.science/api/pith-number/LMINCLIRRARNBOLLTRCILTFUBK/graph.json","events_json":"https://pith.science/api/pith-number/LMINCLIRRARNBOLLTRCILTFUBK/events.json","paper":"https://pith.science/paper/LMINCLIR"},"agent_actions":{"view_html":"https://pith.science/pith/LMINCLIRRARNBOLLTRCILTFUBK","download_json":"https://pith.science/pith/LMINCLIRRARNBOLLTRCILTFUBK.json","view_paper":"https://pith.science/paper/LMINCLIR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1604.07142&json=true","fetch_graph":"https://pith.science/api/pith-number/LMINCLIRRARNBOLLTRCILTFUBK/graph.json","fetch_events":"https://pith.science/api/pith-number/LMINCLIRRARNBOLLTRCILTFUBK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LMINCLIRRARNBOLLTRCILTFUBK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LMINCLIRRARNBOLLTRCILTFUBK/action/storage_attestation","attest_author":"https://pith.science/pith/LMINCLIRRARNBOLLTRCILTFUBK/action/author_attestation","sign_citation":"https://pith.science/pith/LMINCLIRRARNBOLLTRCILTFUBK/action/citation_signature","submit_replication":"https://pith.science/pith/LMINCLIRRARNBOLLTRCILTFUBK/action/replication_record"}},"created_at":"2026-05-18T00:26:02.202656+00:00","updated_at":"2026-05-18T00:26:02.202656+00:00"}