{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:OYPN3WVQ7SFFFM7YQGLCRQXFVV","short_pith_number":"pith:OYPN3WVQ","schema_version":"1.0","canonical_sha256":"761edddab0fc8a52b3f8819628c2e5ad60eafc8234dc86fefa52016bb28a693b","source":{"kind":"arxiv","id":"1311.6943","version":1},"attestation_state":"computed","paper":{"title":"An abstract Nash-Moser theorem and quasi-periodic solutions for NLW and NLS on compact Lie groups and homogeneous manifold","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.AP","authors_text":"Livia Corsi, Massimiliano Berti, Michela Procesi","submitted_at":"2013-11-27T11:55:52Z","abstract_excerpt":"We prove an abstract Implicit Function Theorem with parameters for smooth operators defined on sequence scales, modeled for the search of quasi-periodic solutions of PDEs. The tame estimates required for the inverse linearised operators at each step of the iterative scheme are deduced via a multiscale inductive argument. The Cantor like set of parameters where the solution exists is defined in a non inductive way. This formulation completely decouples the iterative scheme from the measure theoretical analysis of the parameters where the small divisors non-resonance conditions are verified. As "},"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":"1311.6943","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-11-27T11:55:52Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"8b4eebef6276e768ed3d6b16bec689e667166b1531f81d8e869b87bf4d55dfe9","abstract_canon_sha256":"421f3c6a8e1e59010908008674540f1a6a9cc6fbad0929cf141febc00cfea4ff"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:46:05.725941Z","signature_b64":"RwyTGqlA1b7BnB+AThCr93cPz+kD4zdnMsEuQMIv6bOYv5Fuma4qS7vyyoVOgyJzAiyjzyT/pRHMWmtSc2OxCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"761edddab0fc8a52b3f8819628c2e5ad60eafc8234dc86fefa52016bb28a693b","last_reissued_at":"2026-05-18T01:46:05.725250Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:46:05.725250Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"An abstract Nash-Moser theorem and quasi-periodic solutions for NLW and NLS on compact Lie groups and homogeneous manifold","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.AP","authors_text":"Livia Corsi, Massimiliano Berti, Michela Procesi","submitted_at":"2013-11-27T11:55:52Z","abstract_excerpt":"We prove an abstract Implicit Function Theorem with parameters for smooth operators defined on sequence scales, modeled for the search of quasi-periodic solutions of PDEs. The tame estimates required for the inverse linearised operators at each step of the iterative scheme are deduced via a multiscale inductive argument. The Cantor like set of parameters where the solution exists is defined in a non inductive way. This formulation completely decouples the iterative scheme from the measure theoretical analysis of the parameters where the small divisors non-resonance conditions are verified. As "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.6943","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":"1311.6943","created_at":"2026-05-18T01:46:05.725358+00:00"},{"alias_kind":"arxiv_version","alias_value":"1311.6943v1","created_at":"2026-05-18T01:46:05.725358+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.6943","created_at":"2026-05-18T01:46:05.725358+00:00"},{"alias_kind":"pith_short_12","alias_value":"OYPN3WVQ7SFF","created_at":"2026-05-18T12:27:54.935989+00:00"},{"alias_kind":"pith_short_16","alias_value":"OYPN3WVQ7SFFFM7Y","created_at":"2026-05-18T12:27:54.935989+00:00"},{"alias_kind":"pith_short_8","alias_value":"OYPN3WVQ","created_at":"2026-05-18T12:27:54.935989+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/OYPN3WVQ7SFFFM7YQGLCRQXFVV","json":"https://pith.science/pith/OYPN3WVQ7SFFFM7YQGLCRQXFVV.json","graph_json":"https://pith.science/api/pith-number/OYPN3WVQ7SFFFM7YQGLCRQXFVV/graph.json","events_json":"https://pith.science/api/pith-number/OYPN3WVQ7SFFFM7YQGLCRQXFVV/events.json","paper":"https://pith.science/paper/OYPN3WVQ"},"agent_actions":{"view_html":"https://pith.science/pith/OYPN3WVQ7SFFFM7YQGLCRQXFVV","download_json":"https://pith.science/pith/OYPN3WVQ7SFFFM7YQGLCRQXFVV.json","view_paper":"https://pith.science/paper/OYPN3WVQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1311.6943&json=true","fetch_graph":"https://pith.science/api/pith-number/OYPN3WVQ7SFFFM7YQGLCRQXFVV/graph.json","fetch_events":"https://pith.science/api/pith-number/OYPN3WVQ7SFFFM7YQGLCRQXFVV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OYPN3WVQ7SFFFM7YQGLCRQXFVV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OYPN3WVQ7SFFFM7YQGLCRQXFVV/action/storage_attestation","attest_author":"https://pith.science/pith/OYPN3WVQ7SFFFM7YQGLCRQXFVV/action/author_attestation","sign_citation":"https://pith.science/pith/OYPN3WVQ7SFFFM7YQGLCRQXFVV/action/citation_signature","submit_replication":"https://pith.science/pith/OYPN3WVQ7SFFFM7YQGLCRQXFVV/action/replication_record"}},"created_at":"2026-05-18T01:46:05.725358+00:00","updated_at":"2026-05-18T01:46:05.725358+00:00"}