{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:FNS2YFFFVGBRNJNMVLHSMWENBF","short_pith_number":"pith:FNS2YFFF","canonical_record":{"source":{"id":"1806.03065","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-06-08T10:13:18Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"e1fe2537726f3bae830738147a73a82a4bac560859c142841aeeb62c873de294","abstract_canon_sha256":"15b6db56cb274617d418f24840b3cdd5af99e5bf906453fecc32d311810b34dd"},"schema_version":"1.0"},"canonical_sha256":"2b65ac14a5a98316a5acaacf26588d09599debc125e79fb5e63b03ba3bed3e9f","source":{"kind":"arxiv","id":"1806.03065","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.03065","created_at":"2026-05-18T00:11:56Z"},{"alias_kind":"arxiv_version","alias_value":"1806.03065v2","created_at":"2026-05-18T00:11:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.03065","created_at":"2026-05-18T00:11:56Z"},{"alias_kind":"pith_short_12","alias_value":"FNS2YFFFVGBR","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_16","alias_value":"FNS2YFFFVGBRNJNM","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_8","alias_value":"FNS2YFFF","created_at":"2026-05-18T12:32:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:FNS2YFFFVGBRNJNMVLHSMWENBF","target":"record","payload":{"canonical_record":{"source":{"id":"1806.03065","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-06-08T10:13:18Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"e1fe2537726f3bae830738147a73a82a4bac560859c142841aeeb62c873de294","abstract_canon_sha256":"15b6db56cb274617d418f24840b3cdd5af99e5bf906453fecc32d311810b34dd"},"schema_version":"1.0"},"canonical_sha256":"2b65ac14a5a98316a5acaacf26588d09599debc125e79fb5e63b03ba3bed3e9f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:11:56.665495Z","signature_b64":"ntJQ59nqo2emSejx09EYFbfIw3r6tTQA3tW1e39PwEeztIwS9hapBqk32pe189NH3sp6HHh3vOWEK1+DWVXPBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2b65ac14a5a98316a5acaacf26588d09599debc125e79fb5e63b03ba3bed3e9f","last_reissued_at":"2026-05-18T00:11:56.664842Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:11:56.664842Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1806.03065","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":"2026-05-18T00:11:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CY9Z+zzaFvFJH9g2Ag5TBmq2rQAzaCHLN9TRKxovJo/SVYhvZZt/WonF8IlYtADsHY9nu6WWoezY0BUnSe9DBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T07:20:39.641452Z"},"content_sha256":"0fd81fcc7f9b55c7dc81b8d1b1734bdbc4374308aa28ecfb79c67f728f483ae5","schema_version":"1.0","event_id":"sha256:0fd81fcc7f9b55c7dc81b8d1b1734bdbc4374308aa28ecfb79c67f728f483ae5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:FNS2YFFFVGBRNJNMVLHSMWENBF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"$C^{1,1}$ regularity of geodesics in the space of volume forms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Jianchun Chu","submitted_at":"2018-06-08T10:13:18Z","abstract_excerpt":"We prove a $C^{1,1}$ estimate for solutions of a class of fully nonlinear equations introduced by Chen-He. As an application, we prove the $C^{1,1}$ regularity of geodesics in the space of volume forms."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.03065","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":"2026-05-18T00:11:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KagIlmPzl7iHwPh46Lhq65z9ARUUnJKQf+P4eatplQV4n8boRGwVmiW301ACYcfHv7PwBVHALCxkTayAvX0FAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T07:20:39.641915Z"},"content_sha256":"63c169a70b88951c89d28f92908e339efb00faf1b7f9ab38ba82445f49dce1f0","schema_version":"1.0","event_id":"sha256:63c169a70b88951c89d28f92908e339efb00faf1b7f9ab38ba82445f49dce1f0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FNS2YFFFVGBRNJNMVLHSMWENBF/bundle.json","state_url":"https://pith.science/pith/FNS2YFFFVGBRNJNMVLHSMWENBF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FNS2YFFFVGBRNJNMVLHSMWENBF/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":"2026-05-30T07:20:39Z","links":{"resolver":"https://pith.science/pith/FNS2YFFFVGBRNJNMVLHSMWENBF","bundle":"https://pith.science/pith/FNS2YFFFVGBRNJNMVLHSMWENBF/bundle.json","state":"https://pith.science/pith/FNS2YFFFVGBRNJNMVLHSMWENBF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FNS2YFFFVGBRNJNMVLHSMWENBF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:FNS2YFFFVGBRNJNMVLHSMWENBF","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":"15b6db56cb274617d418f24840b3cdd5af99e5bf906453fecc32d311810b34dd","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-06-08T10:13:18Z","title_canon_sha256":"e1fe2537726f3bae830738147a73a82a4bac560859c142841aeeb62c873de294"},"schema_version":"1.0","source":{"id":"1806.03065","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.03065","created_at":"2026-05-18T00:11:56Z"},{"alias_kind":"arxiv_version","alias_value":"1806.03065v2","created_at":"2026-05-18T00:11:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.03065","created_at":"2026-05-18T00:11:56Z"},{"alias_kind":"pith_short_12","alias_value":"FNS2YFFFVGBR","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_16","alias_value":"FNS2YFFFVGBRNJNM","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_8","alias_value":"FNS2YFFF","created_at":"2026-05-18T12:32:25Z"}],"graph_snapshots":[{"event_id":"sha256:63c169a70b88951c89d28f92908e339efb00faf1b7f9ab38ba82445f49dce1f0","target":"graph","created_at":"2026-05-18T00:11:56Z","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 a $C^{1,1}$ estimate for solutions of a class of fully nonlinear equations introduced by Chen-He. As an application, we prove the $C^{1,1}$ regularity of geodesics in the space of volume forms.","authors_text":"Jianchun Chu","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-06-08T10:13:18Z","title":"$C^{1,1}$ regularity of geodesics in the space of volume forms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.03065","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":"sha256:0fd81fcc7f9b55c7dc81b8d1b1734bdbc4374308aa28ecfb79c67f728f483ae5","target":"record","created_at":"2026-05-18T00:11:56Z","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":"15b6db56cb274617d418f24840b3cdd5af99e5bf906453fecc32d311810b34dd","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-06-08T10:13:18Z","title_canon_sha256":"e1fe2537726f3bae830738147a73a82a4bac560859c142841aeeb62c873de294"},"schema_version":"1.0","source":{"id":"1806.03065","kind":"arxiv","version":2}},"canonical_sha256":"2b65ac14a5a98316a5acaacf26588d09599debc125e79fb5e63b03ba3bed3e9f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2b65ac14a5a98316a5acaacf26588d09599debc125e79fb5e63b03ba3bed3e9f","first_computed_at":"2026-05-18T00:11:56.664842Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:11:56.664842Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ntJQ59nqo2emSejx09EYFbfIw3r6tTQA3tW1e39PwEeztIwS9hapBqk32pe189NH3sp6HHh3vOWEK1+DWVXPBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:11:56.665495Z","signed_message":"canonical_sha256_bytes"},"source_id":"1806.03065","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0fd81fcc7f9b55c7dc81b8d1b1734bdbc4374308aa28ecfb79c67f728f483ae5","sha256:63c169a70b88951c89d28f92908e339efb00faf1b7f9ab38ba82445f49dce1f0"],"state_sha256":"eebb5216faac4f525a2979c9093053e30b940a8f41393808d88cbb69ef8416e5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"h4V8qNIRjKsbF+kaOpBH2wXVxW2ljxmROFhOSjelk/mOUSywQbCMofR+zIq4a1tlpiAp3FQN5rzwlrHNKvyXAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T07:20:39.645077Z","bundle_sha256":"5091dda71f64773f223923678726aa3681b4af6196c180ca03ad6009073102cc"}}