{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:AN4YIMMKU2IAAYIV2PHC7Q6TUF","short_pith_number":"pith:AN4YIMMK","canonical_record":{"source":{"id":"1206.7102","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-06-29T18:55:22Z","cross_cats_sorted":[],"title_canon_sha256":"67fdceab4760dd7c7d9f5e5f3a071fa96cda31b96b7094945c452317cfe438bd","abstract_canon_sha256":"da3976ec15f2edec5428e51a3bd8fcf5965251020bb23b683a9fcfadbffcd6db"},"schema_version":"1.0"},"canonical_sha256":"037984318aa690006115d3ce2fc3d3a15b2a1992df7614830f7ae956f7e31fc8","source":{"kind":"arxiv","id":"1206.7102","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1206.7102","created_at":"2026-05-18T03:52:13Z"},{"alias_kind":"arxiv_version","alias_value":"1206.7102v1","created_at":"2026-05-18T03:52:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.7102","created_at":"2026-05-18T03:52:13Z"},{"alias_kind":"pith_short_12","alias_value":"AN4YIMMKU2IA","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_16","alias_value":"AN4YIMMKU2IAAYIV","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_8","alias_value":"AN4YIMMK","created_at":"2026-05-18T12:26:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:AN4YIMMKU2IAAYIV2PHC7Q6TUF","target":"record","payload":{"canonical_record":{"source":{"id":"1206.7102","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-06-29T18:55:22Z","cross_cats_sorted":[],"title_canon_sha256":"67fdceab4760dd7c7d9f5e5f3a071fa96cda31b96b7094945c452317cfe438bd","abstract_canon_sha256":"da3976ec15f2edec5428e51a3bd8fcf5965251020bb23b683a9fcfadbffcd6db"},"schema_version":"1.0"},"canonical_sha256":"037984318aa690006115d3ce2fc3d3a15b2a1992df7614830f7ae956f7e31fc8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:52:13.018446Z","signature_b64":"mK0sSF9uT+GWA6wlyhnXNJEPqyBDMxjJwYrZLU6ld9ryyFKy4GiIqoY1DAmclueb2At6RkPYi9MAujEwlniQDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"037984318aa690006115d3ce2fc3d3a15b2a1992df7614830f7ae956f7e31fc8","last_reissued_at":"2026-05-18T03:52:13.017608Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:52:13.017608Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1206.7102","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:52:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QVidxGWhaO6LuVFfVIm1oB61LGgikbFmlSyJCDF1bN9UQ8tnZIKpUMb5wOPDWiV9byHEYQdrx3Obw0erZrUjBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T17:15:23.758175Z"},"content_sha256":"50d828852da54e59be615d33435c37d4649cbd7dc5425dc92dd85af8f3b06f54","schema_version":"1.0","event_id":"sha256:50d828852da54e59be615d33435c37d4649cbd7dc5425dc92dd85af8f3b06f54"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:AN4YIMMKU2IAAYIV2PHC7Q6TUF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Sharp bounds for the first eigenvalue of a fourth order Steklov problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Alessandro Savo (MeMoMat), Simon Raulot (LMRS)","submitted_at":"2012-06-29T18:55:22Z","abstract_excerpt":"We study the biharmonic Steklov eigenvalue problem on a compact Riemannian manifold $\\Omega$ with smooth boundary. We give a computable, sharp lower bound of the first eigenvalue of this problem, which depends only on the dimension, a lower bound of the Ricci curvature of the domain, a lower bound of the mean curvature of its boundary and the inner radius. The proof is obtained by estimating the isoperimetric ratio of non-negative subharmonic functions on $\\Omega$, which is of independent interest. We also give a comparison theorem for geodesic balls."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.7102","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:52:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eP+UKMufJ9SgK0kyKN71WKIjNOuT8rd+kyTQr7HhHk+VmkTCpXupKPDFpUF8e8z1epYu55fdAZ15Qp5UYzTBAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T17:15:23.758531Z"},"content_sha256":"0d4988c27a54c1fb09b84ef501fb86016947065c4ec16a989aba3b93490fe54e","schema_version":"1.0","event_id":"sha256:0d4988c27a54c1fb09b84ef501fb86016947065c4ec16a989aba3b93490fe54e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AN4YIMMKU2IAAYIV2PHC7Q6TUF/bundle.json","state_url":"https://pith.science/pith/AN4YIMMKU2IAAYIV2PHC7Q6TUF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AN4YIMMKU2IAAYIV2PHC7Q6TUF/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-23T17:15:23Z","links":{"resolver":"https://pith.science/pith/AN4YIMMKU2IAAYIV2PHC7Q6TUF","bundle":"https://pith.science/pith/AN4YIMMKU2IAAYIV2PHC7Q6TUF/bundle.json","state":"https://pith.science/pith/AN4YIMMKU2IAAYIV2PHC7Q6TUF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AN4YIMMKU2IAAYIV2PHC7Q6TUF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:AN4YIMMKU2IAAYIV2PHC7Q6TUF","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":"da3976ec15f2edec5428e51a3bd8fcf5965251020bb23b683a9fcfadbffcd6db","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-06-29T18:55:22Z","title_canon_sha256":"67fdceab4760dd7c7d9f5e5f3a071fa96cda31b96b7094945c452317cfe438bd"},"schema_version":"1.0","source":{"id":"1206.7102","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1206.7102","created_at":"2026-05-18T03:52:13Z"},{"alias_kind":"arxiv_version","alias_value":"1206.7102v1","created_at":"2026-05-18T03:52:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.7102","created_at":"2026-05-18T03:52:13Z"},{"alias_kind":"pith_short_12","alias_value":"AN4YIMMKU2IA","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_16","alias_value":"AN4YIMMKU2IAAYIV","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_8","alias_value":"AN4YIMMK","created_at":"2026-05-18T12:26:58Z"}],"graph_snapshots":[{"event_id":"sha256:0d4988c27a54c1fb09b84ef501fb86016947065c4ec16a989aba3b93490fe54e","target":"graph","created_at":"2026-05-18T03:52:13Z","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":"We study the biharmonic Steklov eigenvalue problem on a compact Riemannian manifold $\\Omega$ with smooth boundary. We give a computable, sharp lower bound of the first eigenvalue of this problem, which depends only on the dimension, a lower bound of the Ricci curvature of the domain, a lower bound of the mean curvature of its boundary and the inner radius. The proof is obtained by estimating the isoperimetric ratio of non-negative subharmonic functions on $\\Omega$, which is of independent interest. We also give a comparison theorem for geodesic balls.","authors_text":"Alessandro Savo (MeMoMat), Simon Raulot (LMRS)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-06-29T18:55:22Z","title":"Sharp bounds for the first eigenvalue of a fourth order Steklov problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.7102","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":"sha256:50d828852da54e59be615d33435c37d4649cbd7dc5425dc92dd85af8f3b06f54","target":"record","created_at":"2026-05-18T03:52:13Z","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":"da3976ec15f2edec5428e51a3bd8fcf5965251020bb23b683a9fcfadbffcd6db","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-06-29T18:55:22Z","title_canon_sha256":"67fdceab4760dd7c7d9f5e5f3a071fa96cda31b96b7094945c452317cfe438bd"},"schema_version":"1.0","source":{"id":"1206.7102","kind":"arxiv","version":1}},"canonical_sha256":"037984318aa690006115d3ce2fc3d3a15b2a1992df7614830f7ae956f7e31fc8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"037984318aa690006115d3ce2fc3d3a15b2a1992df7614830f7ae956f7e31fc8","first_computed_at":"2026-05-18T03:52:13.017608Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:52:13.017608Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mK0sSF9uT+GWA6wlyhnXNJEPqyBDMxjJwYrZLU6ld9ryyFKy4GiIqoY1DAmclueb2At6RkPYi9MAujEwlniQDw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:52:13.018446Z","signed_message":"canonical_sha256_bytes"},"source_id":"1206.7102","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:50d828852da54e59be615d33435c37d4649cbd7dc5425dc92dd85af8f3b06f54","sha256:0d4988c27a54c1fb09b84ef501fb86016947065c4ec16a989aba3b93490fe54e"],"state_sha256":"282d1fc896af4c8aaacd3bdadb5d6d90a4f113908f32955d21ecd9fde76875cc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"m+AwAaLp018kMCpjGVsqzW8ONDQaSBF9/OW0dw+L5a/jVLAszTFI58fndBIL05zxapo4rz15Ic5//3WGZE2oDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T17:15:23.760384Z","bundle_sha256":"f078127d6b11ac24d8d0a5968d6b2f9ce54e0c004b76da63a5c6bfcba4dab8ed"}}