{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:EG6QEEJTJRJUSR66Q7ODLRRYHY","short_pith_number":"pith:EG6QEEJT","schema_version":"1.0","canonical_sha256":"21bd0211334c534947de87dc35c6383e109daf9083fb07144415f1f47e8602d4","source":{"kind":"arxiv","id":"2506.08754","version":1},"attestation_state":"computed","paper":{"title":"Introduction to Nonlinear Spectral Analysis","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["math.AP","math.OC"],"primary_cat":"math.SP","authors_text":"Leon Bungert, Yury Korolev","submitted_at":"2025-06-10T12:47:17Z","abstract_excerpt":"These notes are meant as an introduction to the theory of nonlinear spectral theory. We will discuss the variational form of nonlninear eigenvalue problems and the corresponding non-linear Euler--Lagrange equations, as well as connections with gradient flows. For the latter ones, we will give precise conditions for finite time extinction and discuss convergence rates. We will use this theory to study asymptotic behaviour of nonlinear PDEs and present applications in $L^\\infty$ variational problems. Finally we will discuss numerical methods for solving gradient flows and computing nonlinear eig"},"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":"2506.08754","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.SP","submitted_at":"2025-06-10T12:47:17Z","cross_cats_sorted":["math.AP","math.OC"],"title_canon_sha256":"a47829a6c172b83f7abadfbe35f76a895b8bd31576da0f464feca88f5a5d69e7","abstract_canon_sha256":"7e7c6148c6995eb19ebdf9476fdb9262d57c9625f3654732b3f2b503b66db63f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:19:12.769711Z","signature_b64":"HFNUlCth22q9RiTLfbstvV9beru+ercNy0X3HaRVK8zpPknVeqnv3dLXnHvujcHdwuXMEYdxj/jLcd/tjrIaDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"21bd0211334c534947de87dc35c6383e109daf9083fb07144415f1f47e8602d4","last_reissued_at":"2026-07-05T11:19:12.769274Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:19:12.769274Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Introduction to Nonlinear Spectral Analysis","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["math.AP","math.OC"],"primary_cat":"math.SP","authors_text":"Leon Bungert, Yury Korolev","submitted_at":"2025-06-10T12:47:17Z","abstract_excerpt":"These notes are meant as an introduction to the theory of nonlinear spectral theory. We will discuss the variational form of nonlninear eigenvalue problems and the corresponding non-linear Euler--Lagrange equations, as well as connections with gradient flows. For the latter ones, we will give precise conditions for finite time extinction and discuss convergence rates. We will use this theory to study asymptotic behaviour of nonlinear PDEs and present applications in $L^\\infty$ variational problems. Finally we will discuss numerical methods for solving gradient flows and computing nonlinear eig"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.08754","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2506.08754/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2506.08754","created_at":"2026-07-05T11:19:12.769338+00:00"},{"alias_kind":"arxiv_version","alias_value":"2506.08754v1","created_at":"2026-07-05T11:19:12.769338+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.08754","created_at":"2026-07-05T11:19:12.769338+00:00"},{"alias_kind":"pith_short_12","alias_value":"EG6QEEJTJRJU","created_at":"2026-07-05T11:19:12.769338+00:00"},{"alias_kind":"pith_short_16","alias_value":"EG6QEEJTJRJUSR66","created_at":"2026-07-05T11:19:12.769338+00:00"},{"alias_kind":"pith_short_8","alias_value":"EG6QEEJT","created_at":"2026-07-05T11:19:12.769338+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2605.12301","citing_title":"Approximation of Maximally Monotone Operators : A Graph Convergence Perspective","ref_index":18,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/EG6QEEJTJRJUSR66Q7ODLRRYHY","json":"https://pith.science/pith/EG6QEEJTJRJUSR66Q7ODLRRYHY.json","graph_json":"https://pith.science/api/pith-number/EG6QEEJTJRJUSR66Q7ODLRRYHY/graph.json","events_json":"https://pith.science/api/pith-number/EG6QEEJTJRJUSR66Q7ODLRRYHY/events.json","paper":"https://pith.science/paper/EG6QEEJT"},"agent_actions":{"view_html":"https://pith.science/pith/EG6QEEJTJRJUSR66Q7ODLRRYHY","download_json":"https://pith.science/pith/EG6QEEJTJRJUSR66Q7ODLRRYHY.json","view_paper":"https://pith.science/paper/EG6QEEJT","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2506.08754&json=true","fetch_graph":"https://pith.science/api/pith-number/EG6QEEJTJRJUSR66Q7ODLRRYHY/graph.json","fetch_events":"https://pith.science/api/pith-number/EG6QEEJTJRJUSR66Q7ODLRRYHY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/EG6QEEJTJRJUSR66Q7ODLRRYHY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/EG6QEEJTJRJUSR66Q7ODLRRYHY/action/storage_attestation","attest_author":"https://pith.science/pith/EG6QEEJTJRJUSR66Q7ODLRRYHY/action/author_attestation","sign_citation":"https://pith.science/pith/EG6QEEJTJRJUSR66Q7ODLRRYHY/action/citation_signature","submit_replication":"https://pith.science/pith/EG6QEEJTJRJUSR66Q7ODLRRYHY/action/replication_record"}},"created_at":"2026-07-05T11:19:12.769338+00:00","updated_at":"2026-07-05T11:19:12.769338+00:00"}