{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:DX76JAVV525ORGXWI5LLAP5FEE","short_pith_number":"pith:DX76JAVV","canonical_record":{"source":{"id":"1408.6322","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-08-27T06:14:35Z","cross_cats_sorted":["math.MG"],"title_canon_sha256":"8fa33f855889a33479ce3eaaeb9351108de8711db408b52df8929f46806be8c9","abstract_canon_sha256":"642bae9fde00144ae0b3260eae26ac539a0a1c2fa836544c3873a1654412e6d1"},"schema_version":"1.0"},"canonical_sha256":"1dffe482b5eebae89af64756b03fa52116f80af9cf4ab389bf4d0d025517dae4","source":{"kind":"arxiv","id":"1408.6322","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1408.6322","created_at":"2026-05-18T02:44:07Z"},{"alias_kind":"arxiv_version","alias_value":"1408.6322v1","created_at":"2026-05-18T02:44:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.6322","created_at":"2026-05-18T02:44:07Z"},{"alias_kind":"pith_short_12","alias_value":"DX76JAVV525O","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_16","alias_value":"DX76JAVV525ORGXW","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_8","alias_value":"DX76JAVV","created_at":"2026-05-18T12:28:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:DX76JAVV525ORGXWI5LLAP5FEE","target":"record","payload":{"canonical_record":{"source":{"id":"1408.6322","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-08-27T06:14:35Z","cross_cats_sorted":["math.MG"],"title_canon_sha256":"8fa33f855889a33479ce3eaaeb9351108de8711db408b52df8929f46806be8c9","abstract_canon_sha256":"642bae9fde00144ae0b3260eae26ac539a0a1c2fa836544c3873a1654412e6d1"},"schema_version":"1.0"},"canonical_sha256":"1dffe482b5eebae89af64756b03fa52116f80af9cf4ab389bf4d0d025517dae4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:44:07.754346Z","signature_b64":"XkwfeyzMXxQNirPtPAVjdb8cAI1awxG39dOc2WL/yG+wGUefb8VvEAQSvYTit/1x2Tp2lS7Nbci0NEM8sg/2DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1dffe482b5eebae89af64756b03fa52116f80af9cf4ab389bf4d0d025517dae4","last_reissued_at":"2026-05-18T02:44:07.753795Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:44:07.753795Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1408.6322","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":"2026-05-18T02:44:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0YVGaKCo+mKcQpYPpoeWLwQH+NEz0ZKIsRs33OAXSG5M3VjOCjM64YPOKpcnQFGQot2tdb4dd7ZgsCz0ADyVDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T04:24:26.393582Z"},"content_sha256":"131090f7b804b2264164749cc26334eb99804ce8980ca32a44a6faf07925cfd5","schema_version":"1.0","event_id":"sha256:131090f7b804b2264164749cc26334eb99804ce8980ca32a44a6faf07925cfd5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:DX76JAVV525ORGXWI5LLAP5FEE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Needle decompositions in Riemannian geometry","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.DG","authors_text":"Bo'az Klartag","submitted_at":"2014-08-27T06:14:35Z","abstract_excerpt":"The localization technique from convex geometry is generalized to the setting of Riemannian manifolds whose Ricci curvature is bounded from below. In a nutshell, our method is based on the following observation: When the Ricci curvature is non-negative, log-concave measures are obtained when conditioning the Riemannian volume measure with respect to an integrable geodesic foliation. The Monge mass transfer problem plays an important role in our analysis."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.6322","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":"2026-05-18T02:44:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Uly0U3LT0GCRH1CgCUE7sxe8lk6CRQqA/ogPKz/LbgpBp8I7D0wx1j1Z42kO1KT0pyFFaArL/dM93IB7OOSmBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T04:24:26.393927Z"},"content_sha256":"cb4e71a4f84f61c78100353ee373a2809e0b5ac2e3a4307d79bbddaf77e9f3fb","schema_version":"1.0","event_id":"sha256:cb4e71a4f84f61c78100353ee373a2809e0b5ac2e3a4307d79bbddaf77e9f3fb"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DX76JAVV525ORGXWI5LLAP5FEE/bundle.json","state_url":"https://pith.science/pith/DX76JAVV525ORGXWI5LLAP5FEE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DX76JAVV525ORGXWI5LLAP5FEE/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":"2026-06-03T04:24:26Z","links":{"resolver":"https://pith.science/pith/DX76JAVV525ORGXWI5LLAP5FEE","bundle":"https://pith.science/pith/DX76JAVV525ORGXWI5LLAP5FEE/bundle.json","state":"https://pith.science/pith/DX76JAVV525ORGXWI5LLAP5FEE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DX76JAVV525ORGXWI5LLAP5FEE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:DX76JAVV525ORGXWI5LLAP5FEE","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":"642bae9fde00144ae0b3260eae26ac539a0a1c2fa836544c3873a1654412e6d1","cross_cats_sorted":["math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-08-27T06:14:35Z","title_canon_sha256":"8fa33f855889a33479ce3eaaeb9351108de8711db408b52df8929f46806be8c9"},"schema_version":"1.0","source":{"id":"1408.6322","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1408.6322","created_at":"2026-05-18T02:44:07Z"},{"alias_kind":"arxiv_version","alias_value":"1408.6322v1","created_at":"2026-05-18T02:44:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.6322","created_at":"2026-05-18T02:44:07Z"},{"alias_kind":"pith_short_12","alias_value":"DX76JAVV525O","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_16","alias_value":"DX76JAVV525ORGXW","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_8","alias_value":"DX76JAVV","created_at":"2026-05-18T12:28:25Z"}],"graph_snapshots":[{"event_id":"sha256:cb4e71a4f84f61c78100353ee373a2809e0b5ac2e3a4307d79bbddaf77e9f3fb","target":"graph","created_at":"2026-05-18T02:44:07Z","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":"The localization technique from convex geometry is generalized to the setting of Riemannian manifolds whose Ricci curvature is bounded from below. In a nutshell, our method is based on the following observation: When the Ricci curvature is non-negative, log-concave measures are obtained when conditioning the Riemannian volume measure with respect to an integrable geodesic foliation. The Monge mass transfer problem plays an important role in our analysis.","authors_text":"Bo'az Klartag","cross_cats":["math.MG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-08-27T06:14:35Z","title":"Needle decompositions in Riemannian geometry"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.6322","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":"sha256:131090f7b804b2264164749cc26334eb99804ce8980ca32a44a6faf07925cfd5","target":"record","created_at":"2026-05-18T02:44:07Z","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":"642bae9fde00144ae0b3260eae26ac539a0a1c2fa836544c3873a1654412e6d1","cross_cats_sorted":["math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-08-27T06:14:35Z","title_canon_sha256":"8fa33f855889a33479ce3eaaeb9351108de8711db408b52df8929f46806be8c9"},"schema_version":"1.0","source":{"id":"1408.6322","kind":"arxiv","version":1}},"canonical_sha256":"1dffe482b5eebae89af64756b03fa52116f80af9cf4ab389bf4d0d025517dae4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1dffe482b5eebae89af64756b03fa52116f80af9cf4ab389bf4d0d025517dae4","first_computed_at":"2026-05-18T02:44:07.753795Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:44:07.753795Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XkwfeyzMXxQNirPtPAVjdb8cAI1awxG39dOc2WL/yG+wGUefb8VvEAQSvYTit/1x2Tp2lS7Nbci0NEM8sg/2DQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:44:07.754346Z","signed_message":"canonical_sha256_bytes"},"source_id":"1408.6322","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:131090f7b804b2264164749cc26334eb99804ce8980ca32a44a6faf07925cfd5","sha256:cb4e71a4f84f61c78100353ee373a2809e0b5ac2e3a4307d79bbddaf77e9f3fb"],"state_sha256":"b63cf9428705aacbc7cd39ceb819c944d1710a5f730ede2035f122eceac27d2b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4/W7fZWJgIDrmD55gnx4NzsB4w2zJskK5HZDUXwz6ypYkG+hC8vxXP4j5HKD2LpPGKSTQeGexm4tSume49YHAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T04:24:26.395868Z","bundle_sha256":"d2bb08db4bdaaa93e2385f716d7f1a3807d0b3fd17100b5826db458976153d42"}}