{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:RRPIBSLQQFBL4NQ3BVUFALLZL6","short_pith_number":"pith:RRPIBSLQ","canonical_record":{"source":{"id":"1812.05022","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-12-12T16:48:01Z","cross_cats_sorted":["math.AP","math.MG"],"title_canon_sha256":"1bfdead373e445ad3ce0310ba1d9006d76b9408bb308adb29e96c9d1060acec4","abstract_canon_sha256":"28a201f7edd82b88d4897b57e6feeb25890692d54af08b05425230cc73771ff7"},"schema_version":"1.0"},"canonical_sha256":"8c5e80c9708142be361b0d68502d795f81bee3b6cbfb345e7275b51c52dbd6c4","source":{"kind":"arxiv","id":"1812.05022","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.05022","created_at":"2026-05-17T23:54:38Z"},{"alias_kind":"arxiv_version","alias_value":"1812.05022v2","created_at":"2026-05-17T23:54:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.05022","created_at":"2026-05-17T23:54:38Z"},{"alias_kind":"pith_short_12","alias_value":"RRPIBSLQQFBL","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_16","alias_value":"RRPIBSLQQFBL4NQ3","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_8","alias_value":"RRPIBSLQ","created_at":"2026-05-18T12:32:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:RRPIBSLQQFBL4NQ3BVUFALLZL6","target":"record","payload":{"canonical_record":{"source":{"id":"1812.05022","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-12-12T16:48:01Z","cross_cats_sorted":["math.AP","math.MG"],"title_canon_sha256":"1bfdead373e445ad3ce0310ba1d9006d76b9408bb308adb29e96c9d1060acec4","abstract_canon_sha256":"28a201f7edd82b88d4897b57e6feeb25890692d54af08b05425230cc73771ff7"},"schema_version":"1.0"},"canonical_sha256":"8c5e80c9708142be361b0d68502d795f81bee3b6cbfb345e7275b51c52dbd6c4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:54:38.951828Z","signature_b64":"0LzvQ9bdXGKFSN1PireDp2tYb7UQEKqHY+gqElBXi8RKxONj3wqVdFYIIqOfNLSOfNzZ/qcQ755wCYzFNqaqAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8c5e80c9708142be361b0d68502d795f81bee3b6cbfb345e7275b51c52dbd6c4","last_reissued_at":"2026-05-17T23:54:38.950998Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:54:38.950998Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1812.05022","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":"2026-05-17T23:54:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"86agq/ydwCAvl6Xdl+rvPZIcDbEMD5SltwYlVTggC2D60Vxwr/CjzQi3C1UCV1Uwtx91R6xnkPhZsLSHWa9kCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T05:40:28.400882Z"},"content_sha256":"280428fd1056edef9cdfc70a7f79b669db3e8d1add3dceddff8a20a5f738d961","schema_version":"1.0","event_id":"sha256:280428fd1056edef9cdfc70a7f79b669db3e8d1add3dceddff8a20a5f738d961"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:RRPIBSLQQFBL4NQ3BVUFALLZL6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Sharp geometric inequalities for closed hypersurfaces in manifolds with nonnegative Ricci curvature","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.MG"],"primary_cat":"math.DG","authors_text":"Lorenzo Mazzieri, Mattia Fogagnolo, Virginia Agostiniani","submitted_at":"2018-12-12T16:48:01Z","abstract_excerpt":"In this paper we consider complete noncompact Riemannian manifolds $(M, g)$ with nonnegative Ricci curvature and Euclidean volume growth, of dimension $n \\geq 3$. We prove a sharp Willmore-type inequality for closed hypersurfaces $\\partial \\Omega$ in $M$, with equality holding true if and only if $(M{\\setminus}\\Omega, g)$ is isometric to a truncated cone over $\\partial\\Omega$. An optimal version of Huisken's Isoperimetric Inequality for $3$-manifolds is obtained using this result. Finally, exploiting a natural extension of our techniques to the case of parabolic manifolds, we also deduce an en"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.05022","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":"2026-05-17T23:54:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"n4IGSp6gvlq870qwMPv47YRd62+5LLz0M4Ju1W813uhYnqgEATo45x+sGdigc6KmgfS045hGYGbPjlabqc/9CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T05:40:28.401234Z"},"content_sha256":"d4cf68f1fcd77602afe26cb3c4d8744fa97ed6b061ce32462abb8bcd02b12246","schema_version":"1.0","event_id":"sha256:d4cf68f1fcd77602afe26cb3c4d8744fa97ed6b061ce32462abb8bcd02b12246"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RRPIBSLQQFBL4NQ3BVUFALLZL6/bundle.json","state_url":"https://pith.science/pith/RRPIBSLQQFBL4NQ3BVUFALLZL6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RRPIBSLQQFBL4NQ3BVUFALLZL6/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":"2026-07-02T05:40:28Z","links":{"resolver":"https://pith.science/pith/RRPIBSLQQFBL4NQ3BVUFALLZL6","bundle":"https://pith.science/pith/RRPIBSLQQFBL4NQ3BVUFALLZL6/bundle.json","state":"https://pith.science/pith/RRPIBSLQQFBL4NQ3BVUFALLZL6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RRPIBSLQQFBL4NQ3BVUFALLZL6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:RRPIBSLQQFBL4NQ3BVUFALLZL6","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":"28a201f7edd82b88d4897b57e6feeb25890692d54af08b05425230cc73771ff7","cross_cats_sorted":["math.AP","math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-12-12T16:48:01Z","title_canon_sha256":"1bfdead373e445ad3ce0310ba1d9006d76b9408bb308adb29e96c9d1060acec4"},"schema_version":"1.0","source":{"id":"1812.05022","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.05022","created_at":"2026-05-17T23:54:38Z"},{"alias_kind":"arxiv_version","alias_value":"1812.05022v2","created_at":"2026-05-17T23:54:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.05022","created_at":"2026-05-17T23:54:38Z"},{"alias_kind":"pith_short_12","alias_value":"RRPIBSLQQFBL","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_16","alias_value":"RRPIBSLQQFBL4NQ3","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_8","alias_value":"RRPIBSLQ","created_at":"2026-05-18T12:32:50Z"}],"graph_snapshots":[{"event_id":"sha256:d4cf68f1fcd77602afe26cb3c4d8744fa97ed6b061ce32462abb8bcd02b12246","target":"graph","created_at":"2026-05-17T23:54:38Z","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 consider complete noncompact Riemannian manifolds $(M, g)$ with nonnegative Ricci curvature and Euclidean volume growth, of dimension $n \\geq 3$. We prove a sharp Willmore-type inequality for closed hypersurfaces $\\partial \\Omega$ in $M$, with equality holding true if and only if $(M{\\setminus}\\Omega, g)$ is isometric to a truncated cone over $\\partial\\Omega$. An optimal version of Huisken's Isoperimetric Inequality for $3$-manifolds is obtained using this result. Finally, exploiting a natural extension of our techniques to the case of parabolic manifolds, we also deduce an en","authors_text":"Lorenzo Mazzieri, Mattia Fogagnolo, Virginia Agostiniani","cross_cats":["math.AP","math.MG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-12-12T16:48:01Z","title":"Sharp geometric inequalities for closed hypersurfaces in manifolds with nonnegative Ricci curvature"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.05022","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":"sha256:280428fd1056edef9cdfc70a7f79b669db3e8d1add3dceddff8a20a5f738d961","target":"record","created_at":"2026-05-17T23:54:38Z","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":"28a201f7edd82b88d4897b57e6feeb25890692d54af08b05425230cc73771ff7","cross_cats_sorted":["math.AP","math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-12-12T16:48:01Z","title_canon_sha256":"1bfdead373e445ad3ce0310ba1d9006d76b9408bb308adb29e96c9d1060acec4"},"schema_version":"1.0","source":{"id":"1812.05022","kind":"arxiv","version":2}},"canonical_sha256":"8c5e80c9708142be361b0d68502d795f81bee3b6cbfb345e7275b51c52dbd6c4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8c5e80c9708142be361b0d68502d795f81bee3b6cbfb345e7275b51c52dbd6c4","first_computed_at":"2026-05-17T23:54:38.950998Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:54:38.950998Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0LzvQ9bdXGKFSN1PireDp2tYb7UQEKqHY+gqElBXi8RKxONj3wqVdFYIIqOfNLSOfNzZ/qcQ755wCYzFNqaqAg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:54:38.951828Z","signed_message":"canonical_sha256_bytes"},"source_id":"1812.05022","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:280428fd1056edef9cdfc70a7f79b669db3e8d1add3dceddff8a20a5f738d961","sha256:d4cf68f1fcd77602afe26cb3c4d8744fa97ed6b061ce32462abb8bcd02b12246"],"state_sha256":"15adf51b4e9bee840a4c00e0378d043e01d2f954c160fd8ef8add7d80af57420"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CYRKJs0R5ILGval5YNBz4Osc43VXudiEs+bdCW2EkAvL9fEeHFcgdZ6Vbdt0FykGTFU/sUt5HHSQLMtjEEgsBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-02T05:40:28.403232Z","bundle_sha256":"500297786ad50a11cd03302fe3ef421cf2bfa18e68ca6b861a8ba4b2eb500ae4"}}