{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:WGBC36YJFMMDCWETCRIPLHK2GW","short_pith_number":"pith:WGBC36YJ","canonical_record":{"source":{"id":"1403.8000","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-03-31T14:00:35Z","cross_cats_sorted":["math-ph","math.MP","math.SP"],"title_canon_sha256":"6ee346ae83fbc548ca90813059ae68a831c809063456f642a7d999f5d498d154","abstract_canon_sha256":"06b9241a9ab54ae9fced40e8c763bc290e4f6fadbd798db9e655c1480e9f9f04"},"schema_version":"1.0"},"canonical_sha256":"b1822dfb092b183158931450f59d5a3590273db8805fb8cde735104597b05c07","source":{"kind":"arxiv","id":"1403.8000","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.8000","created_at":"2026-05-18T02:20:49Z"},{"alias_kind":"arxiv_version","alias_value":"1403.8000v2","created_at":"2026-05-18T02:20:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.8000","created_at":"2026-05-18T02:20:49Z"},{"alias_kind":"pith_short_12","alias_value":"WGBC36YJFMMD","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_16","alias_value":"WGBC36YJFMMDCWET","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_8","alias_value":"WGBC36YJ","created_at":"2026-05-18T12:28:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:WGBC36YJFMMDCWETCRIPLHK2GW","target":"record","payload":{"canonical_record":{"source":{"id":"1403.8000","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-03-31T14:00:35Z","cross_cats_sorted":["math-ph","math.MP","math.SP"],"title_canon_sha256":"6ee346ae83fbc548ca90813059ae68a831c809063456f642a7d999f5d498d154","abstract_canon_sha256":"06b9241a9ab54ae9fced40e8c763bc290e4f6fadbd798db9e655c1480e9f9f04"},"schema_version":"1.0"},"canonical_sha256":"b1822dfb092b183158931450f59d5a3590273db8805fb8cde735104597b05c07","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:20:49.804831Z","signature_b64":"h8BdGTQsX5faUy9ZnpVgZ28ul21I/JHTPyNans7Bn6NQo/gpY7c6NEJrZr1h7eM+V2Wv5b97X0qMIj56dSuEAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b1822dfb092b183158931450f59d5a3590273db8805fb8cde735104597b05c07","last_reissued_at":"2026-05-18T02:20:49.804076Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:20:49.804076Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1403.8000","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:20:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4pYRJ1Vx7ACndt0nB/VFIhRC9d8aTKP2NdPksJoMo8KwIkW/5EtuzYsBuBUpk2zznRoY0OdL8iiN+LV4i0I6BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T21:25:58.515016Z"},"content_sha256":"4e5d367c9796855e455fffef28d7037ad7b8072ccb6d5fe2621102c6564b5e4d","schema_version":"1.0","event_id":"sha256:4e5d367c9796855e455fffef28d7037ad7b8072ccb6d5fe2621102c6564b5e4d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:WGBC36YJFMMDCWETCRIPLHK2GW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"One-dimensional projective structures, convex curves and the ovals of Benguria & Loss","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.SP"],"primary_cat":"math.DG","authors_text":"Jacob Bernstein, Thomas Mettler","submitted_at":"2014-03-31T14:00:35Z","abstract_excerpt":"Benguria and Loss have conjectured that, amongst all smooth closed curves of length $2\\pi$ in the plane, the lowest possible eigenvalue of the operator $L=-\\Delta+\\kappa^2$ was one. They observed that this value was achieved on a two-parameter family, $\\mathcal{O}$, of geometrically distinct ovals containing the round circle and collapsing to a multiplicity-two line segment. We characterize the curves in $\\mathcal{O}$ as absolute minima of two related geometric functionals. We also discuss a connection with projective differential geometry and use it to explain the natural symmetries of all th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.8000","kind":"arxiv","version":2},"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":"2026-05-18T02:20:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"S9/QGryMnMq+//SGkso5YJuszZ0izVMcNsSNVo4aMwynwQYAK7+1z95r3Dd0KZ7IPcPvEEAJidmz/Ca97QdtDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T21:25:58.515692Z"},"content_sha256":"b11d2f27abb5286a5302e801b8fcd965aa98a2a12c1ad0d77f824f27cbc02b6d","schema_version":"1.0","event_id":"sha256:b11d2f27abb5286a5302e801b8fcd965aa98a2a12c1ad0d77f824f27cbc02b6d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WGBC36YJFMMDCWETCRIPLHK2GW/bundle.json","state_url":"https://pith.science/pith/WGBC36YJFMMDCWETCRIPLHK2GW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WGBC36YJFMMDCWETCRIPLHK2GW/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":"2026-05-26T21:25:58Z","links":{"resolver":"https://pith.science/pith/WGBC36YJFMMDCWETCRIPLHK2GW","bundle":"https://pith.science/pith/WGBC36YJFMMDCWETCRIPLHK2GW/bundle.json","state":"https://pith.science/pith/WGBC36YJFMMDCWETCRIPLHK2GW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WGBC36YJFMMDCWETCRIPLHK2GW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:WGBC36YJFMMDCWETCRIPLHK2GW","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":"06b9241a9ab54ae9fced40e8c763bc290e4f6fadbd798db9e655c1480e9f9f04","cross_cats_sorted":["math-ph","math.MP","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-03-31T14:00:35Z","title_canon_sha256":"6ee346ae83fbc548ca90813059ae68a831c809063456f642a7d999f5d498d154"},"schema_version":"1.0","source":{"id":"1403.8000","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.8000","created_at":"2026-05-18T02:20:49Z"},{"alias_kind":"arxiv_version","alias_value":"1403.8000v2","created_at":"2026-05-18T02:20:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.8000","created_at":"2026-05-18T02:20:49Z"},{"alias_kind":"pith_short_12","alias_value":"WGBC36YJFMMD","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_16","alias_value":"WGBC36YJFMMDCWET","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_8","alias_value":"WGBC36YJ","created_at":"2026-05-18T12:28:54Z"}],"graph_snapshots":[{"event_id":"sha256:b11d2f27abb5286a5302e801b8fcd965aa98a2a12c1ad0d77f824f27cbc02b6d","target":"graph","created_at":"2026-05-18T02:20:49Z","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":"Benguria and Loss have conjectured that, amongst all smooth closed curves of length $2\\pi$ in the plane, the lowest possible eigenvalue of the operator $L=-\\Delta+\\kappa^2$ was one. They observed that this value was achieved on a two-parameter family, $\\mathcal{O}$, of geometrically distinct ovals containing the round circle and collapsing to a multiplicity-two line segment. We characterize the curves in $\\mathcal{O}$ as absolute minima of two related geometric functionals. We also discuss a connection with projective differential geometry and use it to explain the natural symmetries of all th","authors_text":"Jacob Bernstein, Thomas Mettler","cross_cats":["math-ph","math.MP","math.SP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-03-31T14:00:35Z","title":"One-dimensional projective structures, convex curves and the ovals of Benguria & Loss"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.8000","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":"sha256:4e5d367c9796855e455fffef28d7037ad7b8072ccb6d5fe2621102c6564b5e4d","target":"record","created_at":"2026-05-18T02:20:49Z","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":"06b9241a9ab54ae9fced40e8c763bc290e4f6fadbd798db9e655c1480e9f9f04","cross_cats_sorted":["math-ph","math.MP","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-03-31T14:00:35Z","title_canon_sha256":"6ee346ae83fbc548ca90813059ae68a831c809063456f642a7d999f5d498d154"},"schema_version":"1.0","source":{"id":"1403.8000","kind":"arxiv","version":2}},"canonical_sha256":"b1822dfb092b183158931450f59d5a3590273db8805fb8cde735104597b05c07","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b1822dfb092b183158931450f59d5a3590273db8805fb8cde735104597b05c07","first_computed_at":"2026-05-18T02:20:49.804076Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:20:49.804076Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"h8BdGTQsX5faUy9ZnpVgZ28ul21I/JHTPyNans7Bn6NQo/gpY7c6NEJrZr1h7eM+V2Wv5b97X0qMIj56dSuEAw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:20:49.804831Z","signed_message":"canonical_sha256_bytes"},"source_id":"1403.8000","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4e5d367c9796855e455fffef28d7037ad7b8072ccb6d5fe2621102c6564b5e4d","sha256:b11d2f27abb5286a5302e801b8fcd965aa98a2a12c1ad0d77f824f27cbc02b6d"],"state_sha256":"54753459118f95c8327907a9a1eafc642986b92a81cb5d3a077ee60495326148"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+WwGyR0D1xNdUE9Q+ufsiUXoFCeJxvBhVQBOzseDidDR+biatgGdN9z7HNY40S7ws8fu+vfasqqL81PL+u8jDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T21:25:58.519084Z","bundle_sha256":"019e281274a17e2ac638ab08d7aca2ac793e93c1c8dcecbe9f2f19e32dad9013"}}