{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:E4LKFCZC4G2OTKTMLOB6FYT6JU","short_pith_number":"pith:E4LKFCZC","canonical_record":{"source":{"id":"1506.07017","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-06-23T14:11:13Z","cross_cats_sorted":[],"title_canon_sha256":"3a1666274f2a3c0d79b587fc10ed89483e75158fef4c20b1daab0a7fa46e1bf1","abstract_canon_sha256":"04e029b2a8bb076cf2f212e4ea3768030551d62312eedeb0b13b0166788ad2e5"},"schema_version":"1.0"},"canonical_sha256":"2716a28b22e1b4e9aa6c5b83e2e27e4d1a33e137a2e9074ec9e4a0b18f4f02ee","source":{"kind":"arxiv","id":"1506.07017","version":5},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.07017","created_at":"2026-05-18T01:08:29Z"},{"alias_kind":"arxiv_version","alias_value":"1506.07017v5","created_at":"2026-05-18T01:08:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.07017","created_at":"2026-05-18T01:08:29Z"},{"alias_kind":"pith_short_12","alias_value":"E4LKFCZC4G2O","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_16","alias_value":"E4LKFCZC4G2OTKTM","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_8","alias_value":"E4LKFCZC","created_at":"2026-05-18T12:29:17Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:E4LKFCZC4G2OTKTMLOB6FYT6JU","target":"record","payload":{"canonical_record":{"source":{"id":"1506.07017","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-06-23T14:11:13Z","cross_cats_sorted":[],"title_canon_sha256":"3a1666274f2a3c0d79b587fc10ed89483e75158fef4c20b1daab0a7fa46e1bf1","abstract_canon_sha256":"04e029b2a8bb076cf2f212e4ea3768030551d62312eedeb0b13b0166788ad2e5"},"schema_version":"1.0"},"canonical_sha256":"2716a28b22e1b4e9aa6c5b83e2e27e4d1a33e137a2e9074ec9e4a0b18f4f02ee","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:08:29.083543Z","signature_b64":"k3cznBuwzM2u1LqnE0pzNnh9atVg0bp6WNh6PKaKU3wDCqX3iEyzgVLZAMsjXAYbRRI0omy6vMiXy3GMsO+bDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2716a28b22e1b4e9aa6c5b83e2e27e4d1a33e137a2e9074ec9e4a0b18f4f02ee","last_reissued_at":"2026-05-18T01:08:29.082923Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:08:29.082923Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1506.07017","source_version":5,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:08:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eCzH7qQqLnJY/tBP4lLeQCvPVmgIFftSGhQ/RF83q/YAiDxvxgLC/RQ00bn7pXOhwN4DWgXXjMqkJaGONpTSAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T08:36:50.947246Z"},"content_sha256":"fc768b76b3298c2b750f5cc5776535b27799a861de26549745087a0f46b05a22","schema_version":"1.0","event_id":"sha256:fc768b76b3298c2b750f5cc5776535b27799a861de26549745087a0f46b05a22"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:E4LKFCZC4G2OTKTMLOB6FYT6JU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Isoperimetric inequality for the third eigenvalue of the Laplace-Beltrami operator on $\\mathbb S^2$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Nikolai Nadirashvili, Yannick Sire","submitted_at":"2015-06-23T14:11:13Z","abstract_excerpt":"We prove an Hersch's type isoperimetric inequality for the third positive eigenvalue on $\\mathbb S^2$. Our method builds on the theory we developped to construct extremal metrics on Riemannian surfaces in conformal classes for any eigenvalue."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.07017","kind":"arxiv","version":5},"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":"2026-05-18T01:08:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ao2LyANC8XpFtJNu878E5nOK1g3/x9FmW8u5vJLOqeT5ta3rxPifbPcfVbUb1S8NwcG/63vAzpQA8Blhm6ZXDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T08:36:50.947607Z"},"content_sha256":"f1feb2cc846faa1e54ca440de8e618909189136c9c46e4b1cdd28a40eb12f830","schema_version":"1.0","event_id":"sha256:f1feb2cc846faa1e54ca440de8e618909189136c9c46e4b1cdd28a40eb12f830"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/E4LKFCZC4G2OTKTMLOB6FYT6JU/bundle.json","state_url":"https://pith.science/pith/E4LKFCZC4G2OTKTMLOB6FYT6JU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/E4LKFCZC4G2OTKTMLOB6FYT6JU/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":"2026-05-28T08:36:50Z","links":{"resolver":"https://pith.science/pith/E4LKFCZC4G2OTKTMLOB6FYT6JU","bundle":"https://pith.science/pith/E4LKFCZC4G2OTKTMLOB6FYT6JU/bundle.json","state":"https://pith.science/pith/E4LKFCZC4G2OTKTMLOB6FYT6JU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/E4LKFCZC4G2OTKTMLOB6FYT6JU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:E4LKFCZC4G2OTKTMLOB6FYT6JU","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":"04e029b2a8bb076cf2f212e4ea3768030551d62312eedeb0b13b0166788ad2e5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-06-23T14:11:13Z","title_canon_sha256":"3a1666274f2a3c0d79b587fc10ed89483e75158fef4c20b1daab0a7fa46e1bf1"},"schema_version":"1.0","source":{"id":"1506.07017","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.07017","created_at":"2026-05-18T01:08:29Z"},{"alias_kind":"arxiv_version","alias_value":"1506.07017v5","created_at":"2026-05-18T01:08:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.07017","created_at":"2026-05-18T01:08:29Z"},{"alias_kind":"pith_short_12","alias_value":"E4LKFCZC4G2O","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_16","alias_value":"E4LKFCZC4G2OTKTM","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_8","alias_value":"E4LKFCZC","created_at":"2026-05-18T12:29:17Z"}],"graph_snapshots":[{"event_id":"sha256:f1feb2cc846faa1e54ca440de8e618909189136c9c46e4b1cdd28a40eb12f830","target":"graph","created_at":"2026-05-18T01:08:29Z","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 prove an Hersch's type isoperimetric inequality for the third positive eigenvalue on $\\mathbb S^2$. Our method builds on the theory we developped to construct extremal metrics on Riemannian surfaces in conformal classes for any eigenvalue.","authors_text":"Nikolai Nadirashvili, Yannick Sire","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-06-23T14:11:13Z","title":"Isoperimetric inequality for the third eigenvalue of the Laplace-Beltrami operator on $\\mathbb S^2$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.07017","kind":"arxiv","version":5},"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:fc768b76b3298c2b750f5cc5776535b27799a861de26549745087a0f46b05a22","target":"record","created_at":"2026-05-18T01:08:29Z","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":"04e029b2a8bb076cf2f212e4ea3768030551d62312eedeb0b13b0166788ad2e5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-06-23T14:11:13Z","title_canon_sha256":"3a1666274f2a3c0d79b587fc10ed89483e75158fef4c20b1daab0a7fa46e1bf1"},"schema_version":"1.0","source":{"id":"1506.07017","kind":"arxiv","version":5}},"canonical_sha256":"2716a28b22e1b4e9aa6c5b83e2e27e4d1a33e137a2e9074ec9e4a0b18f4f02ee","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2716a28b22e1b4e9aa6c5b83e2e27e4d1a33e137a2e9074ec9e4a0b18f4f02ee","first_computed_at":"2026-05-18T01:08:29.082923Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:08:29.082923Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"k3cznBuwzM2u1LqnE0pzNnh9atVg0bp6WNh6PKaKU3wDCqX3iEyzgVLZAMsjXAYbRRI0omy6vMiXy3GMsO+bDg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:08:29.083543Z","signed_message":"canonical_sha256_bytes"},"source_id":"1506.07017","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fc768b76b3298c2b750f5cc5776535b27799a861de26549745087a0f46b05a22","sha256:f1feb2cc846faa1e54ca440de8e618909189136c9c46e4b1cdd28a40eb12f830"],"state_sha256":"b5532ecf92bb5c4322df55719423bfb1c71bac7e895af10b9f1d91058a2894c3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Bq4qaNZ1kfAj+aAudc9i15CXTXOHLx4fI1fTB6aNnO3Y039uDyiy/DECZl+UyfxMX0WWHmDLg1Tmn3pqu78RAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T08:36:50.949575Z","bundle_sha256":"0716196d8b771509266bc7361e9ebdb07595f2c3f6eadff9a31925260362d05e"}}