{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:ACEYXVXITYKHXEZPPBURGNIKQU","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":"5e6938b428b8567399ac14b1d46b1f0bd0aa6cbf91dd2ebf768545af8fe06797","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-11-25T13:37:39Z","title_canon_sha256":"0b81866525f83bf617ed319997581de6b4ffcd4819d050cfaf37bf36a0b32ebc"},"schema_version":"1.0","source":{"id":"2411.16377","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2411.16377","created_at":"2026-07-05T09:40:08Z"},{"alias_kind":"arxiv_version","alias_value":"2411.16377v1","created_at":"2026-07-05T09:40:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.16377","created_at":"2026-07-05T09:40:08Z"},{"alias_kind":"pith_short_12","alias_value":"ACEYXVXITYKH","created_at":"2026-07-05T09:40:08Z"},{"alias_kind":"pith_short_16","alias_value":"ACEYXVXITYKHXEZP","created_at":"2026-07-05T09:40:08Z"},{"alias_kind":"pith_short_8","alias_value":"ACEYXVXI","created_at":"2026-07-05T09:40:08Z"}],"graph_snapshots":[{"event_id":"sha256:09beb5f9669ee5bf9c73b5a54d77d9948de98d2d12e4d49c07a15ea0b43605fe","target":"graph","created_at":"2026-07-05T09:40:08Z","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/2411.16377/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we investigate the log-concavity property of the first eigenfunction to the weighted $p$-Laplace operator in class of bounded, convex and smooth domain. Moreover, we prove a Brunn-Minkowski-type inequality for the first eigenvalue to the weighted $p$-Laplace operator in the class of $C^2$ convex bodies in $\\R^n$","authors_text":"Lei Qin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-11-25T13:37:39Z","title":"log-concavity of eigenfunction and Brunn-Minkowski inequality of eigenvalue for weighted p-Laplace operator"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.16377","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:d265d1055c49f7665a336467e2f96b005c30dcb1e360701f091238334ec1421c","target":"record","created_at":"2026-07-05T09:40:08Z","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":"5e6938b428b8567399ac14b1d46b1f0bd0aa6cbf91dd2ebf768545af8fe06797","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-11-25T13:37:39Z","title_canon_sha256":"0b81866525f83bf617ed319997581de6b4ffcd4819d050cfaf37bf36a0b32ebc"},"schema_version":"1.0","source":{"id":"2411.16377","kind":"arxiv","version":1}},"canonical_sha256":"00898bd6e89e147b932f786913350a8508b063f5d0df709a81f82ad61cf54cab","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"00898bd6e89e147b932f786913350a8508b063f5d0df709a81f82ad61cf54cab","first_computed_at":"2026-07-05T09:40:08.360442Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:40:08.360442Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mldt3B5BIi6tQAhCeG1LHu044wMSEq3qiKwPixoILmrvfrSYaRtrAtZ56Hk0L7tn+1Tg7wcqs8zht3aqyyOmAw==","signature_status":"signed_v1","signed_at":"2026-07-05T09:40:08.360890Z","signed_message":"canonical_sha256_bytes"},"source_id":"2411.16377","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d265d1055c49f7665a336467e2f96b005c30dcb1e360701f091238334ec1421c","sha256:09beb5f9669ee5bf9c73b5a54d77d9948de98d2d12e4d49c07a15ea0b43605fe"],"state_sha256":"5eb2eadb404d0e51668e631a81edd95ca410f44ec43ee34798eaef9ef69c4fa2"}