{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:OHZRBQTUQRDKCGEHY7JKILXVCI","short_pith_number":"pith:OHZRBQTU","canonical_record":{"source":{"id":"1804.00407","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2018-04-02T06:13:07Z","cross_cats_sorted":[],"title_canon_sha256":"b2d91c90cbfbd6e71630cad9bf9a531859a33711626bcf819e27011e05d3f9f3","abstract_canon_sha256":"7573da04bbd6b6860b1d0364840e4229eb3b45a48820ab07eb201b9730ae3064"},"schema_version":"1.0"},"canonical_sha256":"71f310c2748446a11887c7d2a42ef51201df88bc55cc344779653b0f90266066","source":{"kind":"arxiv","id":"1804.00407","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.00407","created_at":"2026-05-18T00:02:18Z"},{"alias_kind":"arxiv_version","alias_value":"1804.00407v2","created_at":"2026-05-18T00:02:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.00407","created_at":"2026-05-18T00:02:18Z"},{"alias_kind":"pith_short_12","alias_value":"OHZRBQTUQRDK","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_16","alias_value":"OHZRBQTUQRDKCGEH","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_8","alias_value":"OHZRBQTU","created_at":"2026-05-18T12:32:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:OHZRBQTUQRDKCGEHY7JKILXVCI","target":"record","payload":{"canonical_record":{"source":{"id":"1804.00407","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2018-04-02T06:13:07Z","cross_cats_sorted":[],"title_canon_sha256":"b2d91c90cbfbd6e71630cad9bf9a531859a33711626bcf819e27011e05d3f9f3","abstract_canon_sha256":"7573da04bbd6b6860b1d0364840e4229eb3b45a48820ab07eb201b9730ae3064"},"schema_version":"1.0"},"canonical_sha256":"71f310c2748446a11887c7d2a42ef51201df88bc55cc344779653b0f90266066","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:02:18.083460Z","signature_b64":"pxb8i9pXZqhgGLd0GG9NrFTgS59CwJd2WHeVLiWH6zeZ9KzlrrZEVsdhLiFUW8kAV1VE73BDjpUUzRuWESCVCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"71f310c2748446a11887c7d2a42ef51201df88bc55cc344779653b0f90266066","last_reissued_at":"2026-05-18T00:02:18.082861Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:02:18.082861Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1804.00407","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":"2026-05-18T00:02:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ptDA3qNrowSroj7orzICGQBGFtuhJPPIY6lUy5HyeQvZFBU6ca23bAuAy4SvhqnU/HhQ56mDeA5W8w4JcT++Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T18:32:34.238335Z"},"content_sha256":"182e2791a55115f0ebb7a613b19c9018d2b963d261b0100c6ba2188292a561bd","schema_version":"1.0","event_id":"sha256:182e2791a55115f0ebb7a613b19c9018d2b963d261b0100c6ba2188292a561bd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:OHZRBQTUQRDKCGEHY7JKILXVCI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Convergence of energy functionals and stability of lower bounds of Ricci curvature via metric measure foliation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"Daisuke Kazukawa","submitted_at":"2018-04-02T06:13:07Z","abstract_excerpt":"The notion of the metric measure foliation is introduced by Galaz-Garc\\'ia, Kell, Mondino, and Sosa. They studied the relation between a metric measure space with a metric measure foliation and its quotient space. They showed that the curvature-dimension condition and the Cheeger energy functional preserve from a such space to its quotient space. Via the metric measure foliation, we investigate the convergence theory for a sequence of metric measure spaces whose dimensions are unbounded."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.00407","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":"2026-05-18T00:02:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"s1JzRZ5A6AOBAUOz8trZj83IJmjf1c2Zhyqk+auAjWrAxIpnpxlKJC5bhGeKTMOULCX7ro+dfYtu7fYErq2uDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T18:32:34.238685Z"},"content_sha256":"3f68d75f9acb9eb66c812b1077830c9fbd4319efe6e68856b4811756e256c2d0","schema_version":"1.0","event_id":"sha256:3f68d75f9acb9eb66c812b1077830c9fbd4319efe6e68856b4811756e256c2d0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OHZRBQTUQRDKCGEHY7JKILXVCI/bundle.json","state_url":"https://pith.science/pith/OHZRBQTUQRDKCGEHY7JKILXVCI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OHZRBQTUQRDKCGEHY7JKILXVCI/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":"2026-06-25T18:32:34Z","links":{"resolver":"https://pith.science/pith/OHZRBQTUQRDKCGEHY7JKILXVCI","bundle":"https://pith.science/pith/OHZRBQTUQRDKCGEHY7JKILXVCI/bundle.json","state":"https://pith.science/pith/OHZRBQTUQRDKCGEHY7JKILXVCI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OHZRBQTUQRDKCGEHY7JKILXVCI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:OHZRBQTUQRDKCGEHY7JKILXVCI","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":"7573da04bbd6b6860b1d0364840e4229eb3b45a48820ab07eb201b9730ae3064","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2018-04-02T06:13:07Z","title_canon_sha256":"b2d91c90cbfbd6e71630cad9bf9a531859a33711626bcf819e27011e05d3f9f3"},"schema_version":"1.0","source":{"id":"1804.00407","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.00407","created_at":"2026-05-18T00:02:18Z"},{"alias_kind":"arxiv_version","alias_value":"1804.00407v2","created_at":"2026-05-18T00:02:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.00407","created_at":"2026-05-18T00:02:18Z"},{"alias_kind":"pith_short_12","alias_value":"OHZRBQTUQRDK","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_16","alias_value":"OHZRBQTUQRDKCGEH","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_8","alias_value":"OHZRBQTU","created_at":"2026-05-18T12:32:43Z"}],"graph_snapshots":[{"event_id":"sha256:3f68d75f9acb9eb66c812b1077830c9fbd4319efe6e68856b4811756e256c2d0","target":"graph","created_at":"2026-05-18T00:02:18Z","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 notion of the metric measure foliation is introduced by Galaz-Garc\\'ia, Kell, Mondino, and Sosa. They studied the relation between a metric measure space with a metric measure foliation and its quotient space. They showed that the curvature-dimension condition and the Cheeger energy functional preserve from a such space to its quotient space. Via the metric measure foliation, we investigate the convergence theory for a sequence of metric measure spaces whose dimensions are unbounded.","authors_text":"Daisuke Kazukawa","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2018-04-02T06:13:07Z","title":"Convergence of energy functionals and stability of lower bounds of Ricci curvature via metric measure foliation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.00407","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":"sha256:182e2791a55115f0ebb7a613b19c9018d2b963d261b0100c6ba2188292a561bd","target":"record","created_at":"2026-05-18T00:02:18Z","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":"7573da04bbd6b6860b1d0364840e4229eb3b45a48820ab07eb201b9730ae3064","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2018-04-02T06:13:07Z","title_canon_sha256":"b2d91c90cbfbd6e71630cad9bf9a531859a33711626bcf819e27011e05d3f9f3"},"schema_version":"1.0","source":{"id":"1804.00407","kind":"arxiv","version":2}},"canonical_sha256":"71f310c2748446a11887c7d2a42ef51201df88bc55cc344779653b0f90266066","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"71f310c2748446a11887c7d2a42ef51201df88bc55cc344779653b0f90266066","first_computed_at":"2026-05-18T00:02:18.082861Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:02:18.082861Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pxb8i9pXZqhgGLd0GG9NrFTgS59CwJd2WHeVLiWH6zeZ9KzlrrZEVsdhLiFUW8kAV1VE73BDjpUUzRuWESCVCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:02:18.083460Z","signed_message":"canonical_sha256_bytes"},"source_id":"1804.00407","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:182e2791a55115f0ebb7a613b19c9018d2b963d261b0100c6ba2188292a561bd","sha256:3f68d75f9acb9eb66c812b1077830c9fbd4319efe6e68856b4811756e256c2d0"],"state_sha256":"384b8dd5f455a54eef9ad3917bfd46166f8da7f6b2c29e0860c9f9386ef7a64d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nB92JV3lngKigDjpc8PC42aBCluGg4C4UUtkAdI49SW8u2xCSGI4qVK4PcB4toWajD0L1wm9EtTjB2KS2p7hAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T18:32:34.240665Z","bundle_sha256":"01d063fa89e0d88bd09c9114c82f0355b61c5e2628420a47e59ceb47989e59c8"}}