{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:QMY235M5EKXSONB7JFZBEWRUOZ","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":"377346f2ecb3351329f3c1c3b6e3955602ab05ebbdd167e193b58f4380904823","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-06-02T14:07:49Z","title_canon_sha256":"21e01fa06181f08382779328538af2bcebcfa4cb71c1859838700c7afda93292"},"schema_version":"1.0","source":{"id":"2606.03684","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.03684","created_at":"2026-06-03T01:06:04Z"},{"alias_kind":"arxiv_version","alias_value":"2606.03684v1","created_at":"2026-06-03T01:06:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.03684","created_at":"2026-06-03T01:06:04Z"},{"alias_kind":"pith_short_12","alias_value":"QMY235M5EKXS","created_at":"2026-06-03T01:06:04Z"},{"alias_kind":"pith_short_16","alias_value":"QMY235M5EKXSONB7","created_at":"2026-06-03T01:06:04Z"},{"alias_kind":"pith_short_8","alias_value":"QMY235M5","created_at":"2026-06-03T01:06:04Z"}],"graph_snapshots":[{"event_id":"sha256:434b7912a6fb583bafbbb068abc8694972883ba130d6e840d475a0e6c7e99a96","target":"graph","created_at":"2026-06-03T01:06:04Z","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/2606.03684/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove that, on a bounded open convex domain $\\Omega\\subset\\mathbb{R}^n$, the first Dirichlet eigenfunction of the Laplacian or the Ornstein--Uhlenbeck operator is $\\alpha$-logconcave for every $\\alpha\\in(0,1/2]$. This extends the recent $1/2$-logconcavity theorem of Crasta--Fragal\\`{a} for the Laplacian to the weighted Gaussian setting and, simultaneously, to a broader range of exponents. More precisely, if $u$ denotes the first eigenfunction normalized by $\\|u\\|_\\infty=1$, then for every $\\alpha\\in(0,1/2]$, the function $-\\bigl(-\\log(\\kappa u(x))\\bigr)^{\\alpha}$ is concave in $\\Omega$ prov","authors_text":"Jin Sun, Kui Wang, Lei Qin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-06-02T14:07:49Z","title":"To $1/2$-logconcavity and beyond: Geometric properties of Dirichlet eigenfunctions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.03684","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":"sha256:0086d5d41d4fc3c89d973a4c0c007300d05ca26ff9a69092116a370963cdcd4b","target":"record","created_at":"2026-06-03T01:06:04Z","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":"377346f2ecb3351329f3c1c3b6e3955602ab05ebbdd167e193b58f4380904823","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-06-02T14:07:49Z","title_canon_sha256":"21e01fa06181f08382779328538af2bcebcfa4cb71c1859838700c7afda93292"},"schema_version":"1.0","source":{"id":"2606.03684","kind":"arxiv","version":1}},"canonical_sha256":"8331adf59d22af27343f4972125a34766d2f723593ee07e0eb9edc93aa5c84ee","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8331adf59d22af27343f4972125a34766d2f723593ee07e0eb9edc93aa5c84ee","first_computed_at":"2026-06-03T01:06:04.510111Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-03T01:06:04.510111Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CVRGCsKi6EAWSvuGDn7Q9lxZFw6MncvL2OlhapEaG8MFtzB5oZv4etKH4O4LulVOuOMa54tDhw7yPGaNjK57Cg==","signature_status":"signed_v1","signed_at":"2026-06-03T01:06:04.510572Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.03684","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0086d5d41d4fc3c89d973a4c0c007300d05ca26ff9a69092116a370963cdcd4b","sha256:434b7912a6fb583bafbbb068abc8694972883ba130d6e840d475a0e6c7e99a96"],"state_sha256":"edd2af4ab72477467be168eeb6393d108cbb969edf0bc7a435c3bde5378d487e"}