{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:LZJTPVXLUUL6566EOY3Y6ZCFAF","short_pith_number":"pith:LZJTPVXL","canonical_record":{"source":{"id":"1209.4192","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-09-19T09:29:11Z","cross_cats_sorted":[],"title_canon_sha256":"56ae64889c1ada89064d94312b2818003a49a0a538a6e3149dbed8f26661a2e2","abstract_canon_sha256":"e20381ca8b99086c0f68f4f384798982c35189a24b68e3f3a4b2a36d083fbb12"},"schema_version":"1.0"},"canonical_sha256":"5e5337d6eba517eefbc476378f644501612cb40922047ff400b405e801b9108d","source":{"kind":"arxiv","id":"1209.4192","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.4192","created_at":"2026-05-18T03:32:05Z"},{"alias_kind":"arxiv_version","alias_value":"1209.4192v2","created_at":"2026-05-18T03:32:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.4192","created_at":"2026-05-18T03:32:05Z"},{"alias_kind":"pith_short_12","alias_value":"LZJTPVXLUUL6","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_16","alias_value":"LZJTPVXLUUL6566E","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_8","alias_value":"LZJTPVXL","created_at":"2026-05-18T12:27:14Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:LZJTPVXLUUL6566EOY3Y6ZCFAF","target":"record","payload":{"canonical_record":{"source":{"id":"1209.4192","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-09-19T09:29:11Z","cross_cats_sorted":[],"title_canon_sha256":"56ae64889c1ada89064d94312b2818003a49a0a538a6e3149dbed8f26661a2e2","abstract_canon_sha256":"e20381ca8b99086c0f68f4f384798982c35189a24b68e3f3a4b2a36d083fbb12"},"schema_version":"1.0"},"canonical_sha256":"5e5337d6eba517eefbc476378f644501612cb40922047ff400b405e801b9108d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:32:05.313760Z","signature_b64":"kaY5psowE/NF5smXY+DfMz3XvMw7fOeUrdmJ6mHR8CS61dFM9vPTyESKWIeqBWyGt1cuBwl3DEeLqSiBU3TvCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5e5337d6eba517eefbc476378f644501612cb40922047ff400b405e801b9108d","last_reissued_at":"2026-05-18T03:32:05.313235Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:32:05.313235Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1209.4192","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":"2026-05-18T03:32:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Y7GuGvg8tO5X9vFOwUnebTigdgMx8VsZrnG17TNPf5eFpyJ97dgv3osiFHeHDm7fo4phfYTYrs4se+ZNukI9BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T14:42:20.966961Z"},"content_sha256":"35bb9552ca3852fa302ff43cc31bec707a8cb4b244649470e30cfc85cfe25ebb","schema_version":"1.0","event_id":"sha256:35bb9552ca3852fa302ff43cc31bec707a8cb4b244649470e30cfc85cfe25ebb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:LZJTPVXLUUL6566EOY3Y6ZCFAF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On an inequality of Andrews, De Lellis and Topping","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Kwok-Kun Kwong","submitted_at":"2012-09-19T09:29:11Z","abstract_excerpt":"Using the method of De Lellis-Topping, we prove some almost Schur type results. For example, one of our results gives a quantitative measure of how close the higher mean curvature of a submanifold is to its average value. We also derive another sharp Andrews-De Lellis-Topping type inequality involving the Riemannian curvature tensor and discuss its equality case."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.4192","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":"2026-05-18T03:32:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tUv7LUgafCo7Gci5mZCOlNl3zxKgi8UuGC86rR1Ow4sqcR8aF4sFAG7R2JyYD5NF8HPjSPwSuZsDQmxpJvrSBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T14:42:20.967643Z"},"content_sha256":"cb8b3f8b1d78da86a1c6c5d47b264ae5d92a5b780cd16e9ce5a01ab45c3a6008","schema_version":"1.0","event_id":"sha256:cb8b3f8b1d78da86a1c6c5d47b264ae5d92a5b780cd16e9ce5a01ab45c3a6008"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LZJTPVXLUUL6566EOY3Y6ZCFAF/bundle.json","state_url":"https://pith.science/pith/LZJTPVXLUUL6566EOY3Y6ZCFAF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LZJTPVXLUUL6566EOY3Y6ZCFAF/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":"2026-05-30T14:42:20Z","links":{"resolver":"https://pith.science/pith/LZJTPVXLUUL6566EOY3Y6ZCFAF","bundle":"https://pith.science/pith/LZJTPVXLUUL6566EOY3Y6ZCFAF/bundle.json","state":"https://pith.science/pith/LZJTPVXLUUL6566EOY3Y6ZCFAF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LZJTPVXLUUL6566EOY3Y6ZCFAF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:LZJTPVXLUUL6566EOY3Y6ZCFAF","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":"e20381ca8b99086c0f68f4f384798982c35189a24b68e3f3a4b2a36d083fbb12","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-09-19T09:29:11Z","title_canon_sha256":"56ae64889c1ada89064d94312b2818003a49a0a538a6e3149dbed8f26661a2e2"},"schema_version":"1.0","source":{"id":"1209.4192","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.4192","created_at":"2026-05-18T03:32:05Z"},{"alias_kind":"arxiv_version","alias_value":"1209.4192v2","created_at":"2026-05-18T03:32:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.4192","created_at":"2026-05-18T03:32:05Z"},{"alias_kind":"pith_short_12","alias_value":"LZJTPVXLUUL6","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_16","alias_value":"LZJTPVXLUUL6566E","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_8","alias_value":"LZJTPVXL","created_at":"2026-05-18T12:27:14Z"}],"graph_snapshots":[{"event_id":"sha256:cb8b3f8b1d78da86a1c6c5d47b264ae5d92a5b780cd16e9ce5a01ab45c3a6008","target":"graph","created_at":"2026-05-18T03:32:05Z","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":"Using the method of De Lellis-Topping, we prove some almost Schur type results. For example, one of our results gives a quantitative measure of how close the higher mean curvature of a submanifold is to its average value. We also derive another sharp Andrews-De Lellis-Topping type inequality involving the Riemannian curvature tensor and discuss its equality case.","authors_text":"Kwok-Kun Kwong","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-09-19T09:29:11Z","title":"On an inequality of Andrews, De Lellis and Topping"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.4192","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":"sha256:35bb9552ca3852fa302ff43cc31bec707a8cb4b244649470e30cfc85cfe25ebb","target":"record","created_at":"2026-05-18T03:32:05Z","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":"e20381ca8b99086c0f68f4f384798982c35189a24b68e3f3a4b2a36d083fbb12","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-09-19T09:29:11Z","title_canon_sha256":"56ae64889c1ada89064d94312b2818003a49a0a538a6e3149dbed8f26661a2e2"},"schema_version":"1.0","source":{"id":"1209.4192","kind":"arxiv","version":2}},"canonical_sha256":"5e5337d6eba517eefbc476378f644501612cb40922047ff400b405e801b9108d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5e5337d6eba517eefbc476378f644501612cb40922047ff400b405e801b9108d","first_computed_at":"2026-05-18T03:32:05.313235Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:32:05.313235Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kaY5psowE/NF5smXY+DfMz3XvMw7fOeUrdmJ6mHR8CS61dFM9vPTyESKWIeqBWyGt1cuBwl3DEeLqSiBU3TvCw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:32:05.313760Z","signed_message":"canonical_sha256_bytes"},"source_id":"1209.4192","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:35bb9552ca3852fa302ff43cc31bec707a8cb4b244649470e30cfc85cfe25ebb","sha256:cb8b3f8b1d78da86a1c6c5d47b264ae5d92a5b780cd16e9ce5a01ab45c3a6008"],"state_sha256":"efe1a06bac2d95d22601cd1edd43fa43905958f8c207a8a0ddb83ce360af38b2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MBe/mK2yGqRyqRSWDR101lo1aywIh+20PvPVwSHAwRfxN0y9EiYlCeV7JLaIaQnMF3xc6CXRtUkaEyr8Tdp6DQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T14:42:20.971054Z","bundle_sha256":"c26fe3320b8d7bb0f724c4cfdcbdf0502cbe864fa4e02ad00652dccd00f013c6"}}