{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:X674EJSMGJD4METDEFQULIHAE4","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":"40f227fcc9086c733620426b156674066a9edecf42a9e331230748b0199c0120","cross_cats_sorted":["math.AP","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2025-05-08T14:32:24Z","title_canon_sha256":"f48ac700ef964ad80c3a30d4a5a217424bddf57f12cf730012b73891c9a1f19a"},"schema_version":"1.0","source":{"id":"2505.05293","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.05293","created_at":"2026-07-05T11:00:22Z"},{"alias_kind":"arxiv_version","alias_value":"2505.05293v1","created_at":"2026-07-05T11:00:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.05293","created_at":"2026-07-05T11:00:22Z"},{"alias_kind":"pith_short_12","alias_value":"X674EJSMGJD4","created_at":"2026-07-05T11:00:22Z"},{"alias_kind":"pith_short_16","alias_value":"X674EJSMGJD4METD","created_at":"2026-07-05T11:00:22Z"},{"alias_kind":"pith_short_8","alias_value":"X674EJSM","created_at":"2026-07-05T11:00:22Z"}],"graph_snapshots":[{"event_id":"sha256:81a3675f91e0164e928f5eb56032806272ccf52e502b4501164e3bba4950765b","target":"graph","created_at":"2026-07-05T11:00:22Z","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/2505.05293/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Building on seminal work of Nadirashvili and previous work of the authors, we prove the existence of metrics maximizing the area-normalized first eigenvalue of the Laplacian on every closed nonorientable surface, and give a simple new proof of existence in the orientable case complementing that of [Pet24b], thus resolving the long-standing existence problem for $\\lambda_1$-maximizing metrics on closed surfaces of any topology. Namely, we prove by contradiction that the supremum $\\Lambda_1(M)$ of the normalized first eigenvalue over all metrics on $M$ obeys the strict monotonicity $\\Lambda_1(M\\","authors_text":"Daniel Stern, Mikhail Karpukhin, Romain Petrides","cross_cats":["math.AP","math.SP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2025-05-08T14:32:24Z","title":"Existence of metrics maximizing the first Laplace eigenvalue on closed surfaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.05293","kind":"arxiv","version":1},"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:b9081c376cf36c9b714854c4ae5cbf39af09b2cadcc5683ddb9e0d6eb85298f1","target":"record","created_at":"2026-07-05T11:00:22Z","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":"40f227fcc9086c733620426b156674066a9edecf42a9e331230748b0199c0120","cross_cats_sorted":["math.AP","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2025-05-08T14:32:24Z","title_canon_sha256":"f48ac700ef964ad80c3a30d4a5a217424bddf57f12cf730012b73891c9a1f19a"},"schema_version":"1.0","source":{"id":"2505.05293","kind":"arxiv","version":1}},"canonical_sha256":"bfbfc2264c3247c61263216145a0e027238e7b47a30ba2fcec2bbc91d79341cc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bfbfc2264c3247c61263216145a0e027238e7b47a30ba2fcec2bbc91d79341cc","first_computed_at":"2026-07-05T11:00:22.322389Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:00:22.322389Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"eZQrt7ztkSgtjsoHnh0yAnFk7zzg8d01LuiGuowX5bAs/MrY9GnxcIGxxReGJfhs1vBYmL7Nxyl4a4Tp6DxaDw==","signature_status":"signed_v1","signed_at":"2026-07-05T11:00:22.322893Z","signed_message":"canonical_sha256_bytes"},"source_id":"2505.05293","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b9081c376cf36c9b714854c4ae5cbf39af09b2cadcc5683ddb9e0d6eb85298f1","sha256:81a3675f91e0164e928f5eb56032806272ccf52e502b4501164e3bba4950765b"],"state_sha256":"b204b306a744c13cebc4b563d25487f3f5885eee43c27885c7b353991dbb9540"}