{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:KQGIG6VOVS5TCJGPEIMFDODALR","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":"9f03fd60ea3207b71231f0d4fbfe561d64bdf9ffa6c4b957af01a74d851d8270","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-12-03T10:54:49Z","title_canon_sha256":"b86589c9a9de4f1d6da36916dac115ac17fba2cc58e10051694d4623b3c5b6d3"},"schema_version":"1.0","source":{"id":"1512.01031","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.01031","created_at":"2026-05-18T01:25:23Z"},{"alias_kind":"arxiv_version","alias_value":"1512.01031v1","created_at":"2026-05-18T01:25:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.01031","created_at":"2026-05-18T01:25:23Z"},{"alias_kind":"pith_short_12","alias_value":"KQGIG6VOVS5T","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_16","alias_value":"KQGIG6VOVS5TCJGP","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_8","alias_value":"KQGIG6VO","created_at":"2026-05-18T12:29:29Z"}],"graph_snapshots":[{"event_id":"sha256:af37f5fd900b11d31c5bddc029b4e80a8417026842d76096ab7819020caac545","target":"graph","created_at":"2026-05-18T01:25:23Z","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"},"paper":{"abstract_excerpt":"New lower bounds of the first nonzero eigenvalue of the weighted $p$-Laplacian are established on compact smooth metric measure spaces with or without boundaries. Under the assumption of positive lower bound for the $m$-Bakry--\\'{E}mery Ricci curvature, the Escober--Lichnerowicz--Reilly type estimates are proved; under the assumption of nonnegative $\\infty$-Bakry--\\'{E}mery Ricci curvature and the $m$-Bakry--\\'{E}mery Ricci curvature bounded from below by a non-positive constant, the Li--Yau type lower bound estimates are given. The weighted $p$-Bochner formula and the weighted $p$-Reilly form","authors_text":"Huaiqian Li, Yuzhao Wang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-12-03T10:54:49Z","title":"Lower Bound Estimates for The First Eigenvalue of The Weighted $p$-Laplacian on Smooth Metric Measure Spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.01031","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":"sha256:37864437c6e8025bcd769baa803e57c1574022597b9dd2779073d5b2535f17bb","target":"record","created_at":"2026-05-18T01:25:23Z","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":"9f03fd60ea3207b71231f0d4fbfe561d64bdf9ffa6c4b957af01a74d851d8270","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-12-03T10:54:49Z","title_canon_sha256":"b86589c9a9de4f1d6da36916dac115ac17fba2cc58e10051694d4623b3c5b6d3"},"schema_version":"1.0","source":{"id":"1512.01031","kind":"arxiv","version":1}},"canonical_sha256":"540c837aaeacbb3124cf221851b8605c4d21f4008ddfb6a872fc54c4865befa6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"540c837aaeacbb3124cf221851b8605c4d21f4008ddfb6a872fc54c4865befa6","first_computed_at":"2026-05-18T01:25:23.543325Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:25:23.543325Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PsVXKS8GDIiIs06gLE/DpBpyuPrcKr8bjtnxgIkeJcz7JcgJT0E+xC8gE+3sV3Z2kf1VEyJ5tsuDsXZ5uq8vAg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:25:23.543782Z","signed_message":"canonical_sha256_bytes"},"source_id":"1512.01031","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:37864437c6e8025bcd769baa803e57c1574022597b9dd2779073d5b2535f17bb","sha256:af37f5fd900b11d31c5bddc029b4e80a8417026842d76096ab7819020caac545"],"state_sha256":"2fbb917118d768ae1e0655f00f7574436f910b7d1848b5155224195c255ea5c4"}