{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:7VA5JACULIPSRR2QA7VH6O3V4F","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":"fe84bcaca001fcdd1b9469f7e9cd7cc74b563d50ee82f2c0a1e7d24acdc0e4ca","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-11-14T07:22:42Z","title_canon_sha256":"ae66cf94e7377814970b35238cc8d4e007e0b1de31fc12026d5bd166dfb416a9"},"schema_version":"1.0","source":{"id":"1111.3115","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.3115","created_at":"2026-05-18T04:05:38Z"},{"alias_kind":"arxiv_version","alias_value":"1111.3115v2","created_at":"2026-05-18T04:05:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.3115","created_at":"2026-05-18T04:05:38Z"},{"alias_kind":"pith_short_12","alias_value":"7VA5JACULIPS","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_16","alias_value":"7VA5JACULIPSRR2Q","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_8","alias_value":"7VA5JACU","created_at":"2026-05-18T12:26:22Z"}],"graph_snapshots":[{"event_id":"sha256:30613ee6c04e51e8412101397d273d15ba37cddbfd511f5181999963b8698fb6","target":"graph","created_at":"2026-05-18T04:05:38Z","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":"In this paper, we study eigenvalues of the poly-Laplacian with arbitrary order on a bounded domain in an n-dimensional Euclidean space and obtain a lower bound for eigenvalues, which generalizes the results due to Cheng-Wei [5] and gives an improvement of results due to Cheng- Qi-Wei [3].","authors_text":"Guoxin Wei, Lingzhong Zeng","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-11-14T07:22:42Z","title":"Estimates for Eigenvalues of Poly-harmonic Operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.3115","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:f403f6d848f0f2bf124f295fac9b58084c3e513d9c9f16f6960602e3cdc14f91","target":"record","created_at":"2026-05-18T04:05:38Z","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":"fe84bcaca001fcdd1b9469f7e9cd7cc74b563d50ee82f2c0a1e7d24acdc0e4ca","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-11-14T07:22:42Z","title_canon_sha256":"ae66cf94e7377814970b35238cc8d4e007e0b1de31fc12026d5bd166dfb416a9"},"schema_version":"1.0","source":{"id":"1111.3115","kind":"arxiv","version":2}},"canonical_sha256":"fd41d480545a1f28c75007ea7f3b75e16775602fb813add1361f2097daf71c60","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fd41d480545a1f28c75007ea7f3b75e16775602fb813add1361f2097daf71c60","first_computed_at":"2026-05-18T04:05:38.066829Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:05:38.066829Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+BIHXR/PVCGOQM+DwnPXcW8uhRRERZiT2phR+cs9jQNlMHErcY9EXzH20qBshBRDIQyTeZMO9A+hygWZ86N7Cw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:05:38.067299Z","signed_message":"canonical_sha256_bytes"},"source_id":"1111.3115","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f403f6d848f0f2bf124f295fac9b58084c3e513d9c9f16f6960602e3cdc14f91","sha256:30613ee6c04e51e8412101397d273d15ba37cddbfd511f5181999963b8698fb6"],"state_sha256":"7423805e6e411ce3119bcfc759ca137c6dcf406e2e75e85b6efa9df7831e6bf5"}