{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:UBPOSXW6GGJ73M2GVJ3CY7GNXI","short_pith_number":"pith:UBPOSXW6","schema_version":"1.0","canonical_sha256":"a05ee95ede3193fdb346aa762c7ccdba33fbdea91ff4112e86a0f914f5b70d82","source":{"kind":"arxiv","id":"1802.05700","version":1},"attestation_state":"computed","paper":{"title":"Chang Palais-Smale condition and global inversion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Olivia Gut\\'u","submitted_at":"2018-02-15T18:49:38Z","abstract_excerpt":"Let f be local diffeomorphism between real Banach spaces. We prove that if the locally Lipschitz functional F(x)=1/2|f(x)-y|^2 satisfies the Chang Palais-Smale condition for all y in the target space of f, then f is a norm-coercive global diffeomorphism. We also give a version of this fact for a weighted Chang Palais-Smale condition. Finally, we study the relationship of this criterion to some classical global inversion conditions."},"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":"1802.05700","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-02-15T18:49:38Z","cross_cats_sorted":[],"title_canon_sha256":"0451060e14b7350e73128a5e101d4b11ac55030a9c2b6559e0b75ff67b4ddca9","abstract_canon_sha256":"325a50159d12d02abb5f6531af67c7e3fcdb395e3eadadffe4e28b0dbd3195f9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:01:16.565661Z","signature_b64":"E+4yU2pUGwVwmeXiSVorsvtmi1k/bTVaWVEdLuFt2gKgouipllGDAK2sWJjbUj6CYVbEcnmC8N8pHO+quUABDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a05ee95ede3193fdb346aa762c7ccdba33fbdea91ff4112e86a0f914f5b70d82","last_reissued_at":"2026-05-18T00:01:16.565066Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:01:16.565066Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Chang Palais-Smale condition and global inversion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Olivia Gut\\'u","submitted_at":"2018-02-15T18:49:38Z","abstract_excerpt":"Let f be local diffeomorphism between real Banach spaces. We prove that if the locally Lipschitz functional F(x)=1/2|f(x)-y|^2 satisfies the Chang Palais-Smale condition for all y in the target space of f, then f is a norm-coercive global diffeomorphism. We also give a version of this fact for a weighted Chang Palais-Smale condition. Finally, we study the relationship of this criterion to some classical global inversion conditions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.05700","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":"1802.05700","created_at":"2026-05-18T00:01:16.565158+00:00"},{"alias_kind":"arxiv_version","alias_value":"1802.05700v1","created_at":"2026-05-18T00:01:16.565158+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.05700","created_at":"2026-05-18T00:01:16.565158+00:00"},{"alias_kind":"pith_short_12","alias_value":"UBPOSXW6GGJ7","created_at":"2026-05-18T12:32:56.356000+00:00"},{"alias_kind":"pith_short_16","alias_value":"UBPOSXW6GGJ73M2G","created_at":"2026-05-18T12:32:56.356000+00:00"},{"alias_kind":"pith_short_8","alias_value":"UBPOSXW6","created_at":"2026-05-18T12:32:56.356000+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/UBPOSXW6GGJ73M2GVJ3CY7GNXI","json":"https://pith.science/pith/UBPOSXW6GGJ73M2GVJ3CY7GNXI.json","graph_json":"https://pith.science/api/pith-number/UBPOSXW6GGJ73M2GVJ3CY7GNXI/graph.json","events_json":"https://pith.science/api/pith-number/UBPOSXW6GGJ73M2GVJ3CY7GNXI/events.json","paper":"https://pith.science/paper/UBPOSXW6"},"agent_actions":{"view_html":"https://pith.science/pith/UBPOSXW6GGJ73M2GVJ3CY7GNXI","download_json":"https://pith.science/pith/UBPOSXW6GGJ73M2GVJ3CY7GNXI.json","view_paper":"https://pith.science/paper/UBPOSXW6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1802.05700&json=true","fetch_graph":"https://pith.science/api/pith-number/UBPOSXW6GGJ73M2GVJ3CY7GNXI/graph.json","fetch_events":"https://pith.science/api/pith-number/UBPOSXW6GGJ73M2GVJ3CY7GNXI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UBPOSXW6GGJ73M2GVJ3CY7GNXI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UBPOSXW6GGJ73M2GVJ3CY7GNXI/action/storage_attestation","attest_author":"https://pith.science/pith/UBPOSXW6GGJ73M2GVJ3CY7GNXI/action/author_attestation","sign_citation":"https://pith.science/pith/UBPOSXW6GGJ73M2GVJ3CY7GNXI/action/citation_signature","submit_replication":"https://pith.science/pith/UBPOSXW6GGJ73M2GVJ3CY7GNXI/action/replication_record"}},"created_at":"2026-05-18T00:01:16.565158+00:00","updated_at":"2026-05-18T00:01:16.565158+00:00"}