{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:VJGVCPXICDYKXUSMU5ZEHSMRE3","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":"0050e49af5f7af646bbbbda673339711fd548546db699d8f4bf3f0fa76c90a7d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-11-24T15:51:31Z","title_canon_sha256":"524be55d50dce57ba217f5a49aeb14ae8b171e931fda9fbfee5064b0b0168a5c"},"schema_version":"1.0","source":{"id":"2411.15887","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2411.15887","created_at":"2026-07-05T09:45:16Z"},{"alias_kind":"arxiv_version","alias_value":"2411.15887v2","created_at":"2026-07-05T09:45:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.15887","created_at":"2026-07-05T09:45:16Z"},{"alias_kind":"pith_short_12","alias_value":"VJGVCPXICDYK","created_at":"2026-07-05T09:45:16Z"},{"alias_kind":"pith_short_16","alias_value":"VJGVCPXICDYKXUSM","created_at":"2026-07-05T09:45:16Z"},{"alias_kind":"pith_short_8","alias_value":"VJGVCPXI","created_at":"2026-07-05T09:45:16Z"}],"graph_snapshots":[{"event_id":"sha256:b42e9e2cc16d25f89e38070d4dd0bd337105fcff34c5e3a68b7ba26e7bb0d3ec","target":"graph","created_at":"2026-07-05T09:45:16Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2411.15887/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We develop novel variational methods for solving scaled equations that do not have the mountain pass geometry, classical linking geometry based on linear subspaces, or $\\mathbb Z_2$ symmetry, and therefore cannot be solved using classical variational arguments. Our contributions here include new critical group estimates for scaled functionals, nonlinear saddle point and linking geometries based on scaling, a notion of local linking based on scaling, and scaling-based multiplicity results for symmetric functionals. We develop these methods in an abstract setting involving scaled operators and s","authors_text":"Carlo Mercuri, Kanishka Perera","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-11-24T15:51:31Z","title":"Variational methods for scaled functionals with applications to the Schr\\\"{o}dinger-Poisson-Slater equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.15887","kind":"arxiv","version":2},"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":"sha256:9ec4b036ee478f344cfeeb8f2842307e0ab3b459fd576be4e3ffa384d981096d","target":"record","created_at":"2026-07-05T09:45:16Z","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":"0050e49af5f7af646bbbbda673339711fd548546db699d8f4bf3f0fa76c90a7d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-11-24T15:51:31Z","title_canon_sha256":"524be55d50dce57ba217f5a49aeb14ae8b171e931fda9fbfee5064b0b0168a5c"},"schema_version":"1.0","source":{"id":"2411.15887","kind":"arxiv","version":2}},"canonical_sha256":"aa4d513ee810f0abd24ca77243c99126e897802cfefa07a950be9a90a09915be","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"aa4d513ee810f0abd24ca77243c99126e897802cfefa07a950be9a90a09915be","first_computed_at":"2026-07-05T09:45:16.566867Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:45:16.566867Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zr8lIS+4Okeg1YPiLX7YDNP4+v/UNr01Ds4N1t/wZKjP6tWtIYo7WWj24mz38JJF2kOKGTM41L67eJjR1qf9DQ==","signature_status":"signed_v1","signed_at":"2026-07-05T09:45:16.567268Z","signed_message":"canonical_sha256_bytes"},"source_id":"2411.15887","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9ec4b036ee478f344cfeeb8f2842307e0ab3b459fd576be4e3ffa384d981096d","sha256:b42e9e2cc16d25f89e38070d4dd0bd337105fcff34c5e3a68b7ba26e7bb0d3ec"],"state_sha256":"01e84546727b9ade3a4351ea026fd033cb312d4d75754c0f2523c03b0b40723a"}