{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:MDWET67TW6XTEI4RCTSDHZKU2V","short_pith_number":"pith:MDWET67T","canonical_record":{"source":{"id":"1510.03722","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-10-13T14:55:14Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"a32cb653f7cb8753dadcb60d45aef6d5c09ec91a6a1ff70277d208e63e6eb580","abstract_canon_sha256":"ab9677116530408dd4c3555a72505746ef093085f7ebcc96b8071a0b124ae363"},"schema_version":"1.0"},"canonical_sha256":"60ec49fbf3b7af32239114e433e554d57403bcc3608c881c54dcc686e32ddea1","source":{"kind":"arxiv","id":"1510.03722","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.03722","created_at":"2026-05-18T00:41:46Z"},{"alias_kind":"arxiv_version","alias_value":"1510.03722v1","created_at":"2026-05-18T00:41:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.03722","created_at":"2026-05-18T00:41:46Z"},{"alias_kind":"pith_short_12","alias_value":"MDWET67TW6XT","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_16","alias_value":"MDWET67TW6XTEI4R","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_8","alias_value":"MDWET67T","created_at":"2026-05-18T12:29:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:MDWET67TW6XTEI4RCTSDHZKU2V","target":"record","payload":{"canonical_record":{"source":{"id":"1510.03722","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-10-13T14:55:14Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"a32cb653f7cb8753dadcb60d45aef6d5c09ec91a6a1ff70277d208e63e6eb580","abstract_canon_sha256":"ab9677116530408dd4c3555a72505746ef093085f7ebcc96b8071a0b124ae363"},"schema_version":"1.0"},"canonical_sha256":"60ec49fbf3b7af32239114e433e554d57403bcc3608c881c54dcc686e32ddea1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:41:46.661819Z","signature_b64":"ksg7tf0zT+bpiRrLrIqYuFCuLQe7DN81SDzd0nnLG9Cg+8ucKju/StrmSHj+6CNbd2gNnoCKudkfkl5+VDShDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"60ec49fbf3b7af32239114e433e554d57403bcc3608c881c54dcc686e32ddea1","last_reissued_at":"2026-05-18T00:41:46.661094Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:41:46.661094Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1510.03722","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":"2026-05-18T00:41:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"92NgLxwwnngxrAkUW7FoRT9aRe2njn17kEKJ4B9dqarArk640YzyM0FppfxH7ALDe6zbQket2TP85FtSeoOLBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T15:45:12.205244Z"},"content_sha256":"b32237c7195064ad4c460a178fde79bfcb4021bdb465a3bfe9c6e6cc27184467","schema_version":"1.0","event_id":"sha256:b32237c7195064ad4c460a178fde79bfcb4021bdb465a3bfe9c6e6cc27184467"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:MDWET67TW6XTEI4RCTSDHZKU2V","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Pinching of the first eigenvalue for second order operators on hypersurfaces of the Euclidean space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Julian Scheuer, Julien Roth","submitted_at":"2015-10-13T14:55:14Z","abstract_excerpt":"We prove stability results associated with upper bounds for the first eigenvalue of certain second order differential operators of divergence-type on hypersurfaces of the Euclidean space. We deduce some applications to $r$-stability as well as to almost-Einstein hypersurfaces."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.03722","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":"2026-05-18T00:41:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZbUJyB5Wd9Kp2simjlo5ETwLo5LSH+U5R8uZ4GKJ+FQFzZhihj+wDzV9E7N2XgpdExL14UH0wbdva+2UuZbeAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T15:45:12.205589Z"},"content_sha256":"84bad66ed96529bd0c2cd7edc8c63e11b12ba33737ed7643d2d9c8a7833214b2","schema_version":"1.0","event_id":"sha256:84bad66ed96529bd0c2cd7edc8c63e11b12ba33737ed7643d2d9c8a7833214b2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MDWET67TW6XTEI4RCTSDHZKU2V/bundle.json","state_url":"https://pith.science/pith/MDWET67TW6XTEI4RCTSDHZKU2V/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MDWET67TW6XTEI4RCTSDHZKU2V/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":"2026-05-30T15:45:12Z","links":{"resolver":"https://pith.science/pith/MDWET67TW6XTEI4RCTSDHZKU2V","bundle":"https://pith.science/pith/MDWET67TW6XTEI4RCTSDHZKU2V/bundle.json","state":"https://pith.science/pith/MDWET67TW6XTEI4RCTSDHZKU2V/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MDWET67TW6XTEI4RCTSDHZKU2V/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:MDWET67TW6XTEI4RCTSDHZKU2V","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":"ab9677116530408dd4c3555a72505746ef093085f7ebcc96b8071a0b124ae363","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-10-13T14:55:14Z","title_canon_sha256":"a32cb653f7cb8753dadcb60d45aef6d5c09ec91a6a1ff70277d208e63e6eb580"},"schema_version":"1.0","source":{"id":"1510.03722","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.03722","created_at":"2026-05-18T00:41:46Z"},{"alias_kind":"arxiv_version","alias_value":"1510.03722v1","created_at":"2026-05-18T00:41:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.03722","created_at":"2026-05-18T00:41:46Z"},{"alias_kind":"pith_short_12","alias_value":"MDWET67TW6XT","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_16","alias_value":"MDWET67TW6XTEI4R","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_8","alias_value":"MDWET67T","created_at":"2026-05-18T12:29:32Z"}],"graph_snapshots":[{"event_id":"sha256:84bad66ed96529bd0c2cd7edc8c63e11b12ba33737ed7643d2d9c8a7833214b2","target":"graph","created_at":"2026-05-18T00:41:46Z","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 stability results associated with upper bounds for the first eigenvalue of certain second order differential operators of divergence-type on hypersurfaces of the Euclidean space. We deduce some applications to $r$-stability as well as to almost-Einstein hypersurfaces.","authors_text":"Julian Scheuer, Julien Roth","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-10-13T14:55:14Z","title":"Pinching of the first eigenvalue for second order operators on hypersurfaces of the Euclidean space"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.03722","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:b32237c7195064ad4c460a178fde79bfcb4021bdb465a3bfe9c6e6cc27184467","target":"record","created_at":"2026-05-18T00:41:46Z","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":"ab9677116530408dd4c3555a72505746ef093085f7ebcc96b8071a0b124ae363","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-10-13T14:55:14Z","title_canon_sha256":"a32cb653f7cb8753dadcb60d45aef6d5c09ec91a6a1ff70277d208e63e6eb580"},"schema_version":"1.0","source":{"id":"1510.03722","kind":"arxiv","version":1}},"canonical_sha256":"60ec49fbf3b7af32239114e433e554d57403bcc3608c881c54dcc686e32ddea1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"60ec49fbf3b7af32239114e433e554d57403bcc3608c881c54dcc686e32ddea1","first_computed_at":"2026-05-18T00:41:46.661094Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:41:46.661094Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ksg7tf0zT+bpiRrLrIqYuFCuLQe7DN81SDzd0nnLG9Cg+8ucKju/StrmSHj+6CNbd2gNnoCKudkfkl5+VDShDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:41:46.661819Z","signed_message":"canonical_sha256_bytes"},"source_id":"1510.03722","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b32237c7195064ad4c460a178fde79bfcb4021bdb465a3bfe9c6e6cc27184467","sha256:84bad66ed96529bd0c2cd7edc8c63e11b12ba33737ed7643d2d9c8a7833214b2"],"state_sha256":"76b95a86cff0119ca521a4f30b7c6847d251a2bc318eb1e3683458efd85ac9c9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DGwojf1f/EBtfqY9d6+e74I+3ZLTjkroSnixetQLIs9R513bon7CPwUBWV6a3mzAAmw7n7XiTTscJW/Ap7c1AA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T15:45:12.208121Z","bundle_sha256":"aa99db4d185e00905ed281780ae38eca9e0a163364ee3c616fe828710627361e"}}