{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:FA4T2E7MFMS7L2A5NI5POVLIBN","short_pith_number":"pith:FA4T2E7M","canonical_record":{"source":{"id":"2203.03439","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2022-03-07T14:46:02Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"49f880712ac10e39b896cae72ced551a46aa0a51b4845466bb5a524324baab91","abstract_canon_sha256":"e43f88ee5f31697b76298b30f860263cd706673b79c7d2c8d37b4f474860d585"},"schema_version":"1.0"},"canonical_sha256":"28393d13ec2b25f5e81d6a3af755680b5b3e58aa519dd2eebdc95fd76ae3b49d","source":{"kind":"arxiv","id":"2203.03439","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2203.03439","created_at":"2026-07-05T04:02:34Z"},{"alias_kind":"arxiv_version","alias_value":"2203.03439v1","created_at":"2026-07-05T04:02:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2203.03439","created_at":"2026-07-05T04:02:34Z"},{"alias_kind":"pith_short_12","alias_value":"FA4T2E7MFMS7","created_at":"2026-07-05T04:02:34Z"},{"alias_kind":"pith_short_16","alias_value":"FA4T2E7MFMS7L2A5","created_at":"2026-07-05T04:02:34Z"},{"alias_kind":"pith_short_8","alias_value":"FA4T2E7M","created_at":"2026-07-05T04:02:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:FA4T2E7MFMS7L2A5NI5POVLIBN","target":"record","payload":{"canonical_record":{"source":{"id":"2203.03439","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2022-03-07T14:46:02Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"49f880712ac10e39b896cae72ced551a46aa0a51b4845466bb5a524324baab91","abstract_canon_sha256":"e43f88ee5f31697b76298b30f860263cd706673b79c7d2c8d37b4f474860d585"},"schema_version":"1.0"},"canonical_sha256":"28393d13ec2b25f5e81d6a3af755680b5b3e58aa519dd2eebdc95fd76ae3b49d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:02:34.494464Z","signature_b64":"/RrI8DtOGFWk5ij3KuE3ycXaEuET6Nk6Om4UUFUw71tOEBMJWnZSOra8su66QjGoD3h776RmMfqCGYgHI240Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"28393d13ec2b25f5e81d6a3af755680b5b3e58aa519dd2eebdc95fd76ae3b49d","last_reissued_at":"2026-07-05T04:02:34.494042Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:02:34.494042Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2203.03439","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":"2026-07-05T04:02:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VLIWoazQGJByGSM3a9mMA1TVnRUHa3KvOHb3oITklQaP81A/H1O43RlgSzGc2M0bU7Z+CDAKp8soeC1L7lymDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T06:14:42.362499Z"},"content_sha256":"14dc792568a3edeb0ca414368ed92a84747c1c552f7deb5abaf5f70bfce97a29","schema_version":"1.0","event_id":"sha256:14dc792568a3edeb0ca414368ed92a84747c1c552f7deb5abaf5f70bfce97a29"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:FA4T2E7MFMS7L2A5NI5POVLIBN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Regularity of fully non-linear elliptic equations on Hermitian manifolds","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.AP","authors_text":"Rirong Yuan","submitted_at":"2022-03-07T14:46:02Z","abstract_excerpt":"In this paper we propose new insights and ideas to set up quantitative boundary estimates for solutions to Dirichlet problem of a class of fully non-linear elliptic equations on compact Hermitian manifolds with real analytic Levi flat boundary. With the quantitative boundary estimates at hand, we can establish the gradient estimate and give a unified approach to investigate the existence and regularity of solutions of Dirichlet problem with sufficiently smooth boundary data, which include the geodesic equation in the space of K\\\"ahler metrics as a special case. Our method can also be applied t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2203.03439","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2203.03439/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T04:02:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2AO/ayEznGDkM0tMXlVJBVzGjBZrd2krC9L6dCkn9BLriaPO8Q+VzHRQ8MpZ7zeh/f0HLu6DVv7onQeA3e9sAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T06:14:42.362994Z"},"content_sha256":"bb64e2d98d43e071293bcf52f84a87db3a2ba8b065b135143480b9b68211fe33","schema_version":"1.0","event_id":"sha256:bb64e2d98d43e071293bcf52f84a87db3a2ba8b065b135143480b9b68211fe33"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FA4T2E7MFMS7L2A5NI5POVLIBN/bundle.json","state_url":"https://pith.science/pith/FA4T2E7MFMS7L2A5NI5POVLIBN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FA4T2E7MFMS7L2A5NI5POVLIBN/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":"2026-08-08T06:14:42Z","links":{"resolver":"https://pith.science/pith/FA4T2E7MFMS7L2A5NI5POVLIBN","bundle":"https://pith.science/pith/FA4T2E7MFMS7L2A5NI5POVLIBN/bundle.json","state":"https://pith.science/pith/FA4T2E7MFMS7L2A5NI5POVLIBN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FA4T2E7MFMS7L2A5NI5POVLIBN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:FA4T2E7MFMS7L2A5NI5POVLIBN","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":"e43f88ee5f31697b76298b30f860263cd706673b79c7d2c8d37b4f474860d585","cross_cats_sorted":["math.DG"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2022-03-07T14:46:02Z","title_canon_sha256":"49f880712ac10e39b896cae72ced551a46aa0a51b4845466bb5a524324baab91"},"schema_version":"1.0","source":{"id":"2203.03439","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2203.03439","created_at":"2026-07-05T04:02:34Z"},{"alias_kind":"arxiv_version","alias_value":"2203.03439v1","created_at":"2026-07-05T04:02:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2203.03439","created_at":"2026-07-05T04:02:34Z"},{"alias_kind":"pith_short_12","alias_value":"FA4T2E7MFMS7","created_at":"2026-07-05T04:02:34Z"},{"alias_kind":"pith_short_16","alias_value":"FA4T2E7MFMS7L2A5","created_at":"2026-07-05T04:02:34Z"},{"alias_kind":"pith_short_8","alias_value":"FA4T2E7M","created_at":"2026-07-05T04:02:34Z"}],"graph_snapshots":[{"event_id":"sha256:bb64e2d98d43e071293bcf52f84a87db3a2ba8b065b135143480b9b68211fe33","target":"graph","created_at":"2026-07-05T04:02:34Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2203.03439/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper we propose new insights and ideas to set up quantitative boundary estimates for solutions to Dirichlet problem of a class of fully non-linear elliptic equations on compact Hermitian manifolds with real analytic Levi flat boundary. With the quantitative boundary estimates at hand, we can establish the gradient estimate and give a unified approach to investigate the existence and regularity of solutions of Dirichlet problem with sufficiently smooth boundary data, which include the geodesic equation in the space of K\\\"ahler metrics as a special case. Our method can also be applied t","authors_text":"Rirong Yuan","cross_cats":["math.DG"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2022-03-07T14:46:02Z","title":"Regularity of fully non-linear elliptic equations on Hermitian manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2203.03439","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":"sha256:14dc792568a3edeb0ca414368ed92a84747c1c552f7deb5abaf5f70bfce97a29","target":"record","created_at":"2026-07-05T04:02:34Z","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":"e43f88ee5f31697b76298b30f860263cd706673b79c7d2c8d37b4f474860d585","cross_cats_sorted":["math.DG"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2022-03-07T14:46:02Z","title_canon_sha256":"49f880712ac10e39b896cae72ced551a46aa0a51b4845466bb5a524324baab91"},"schema_version":"1.0","source":{"id":"2203.03439","kind":"arxiv","version":1}},"canonical_sha256":"28393d13ec2b25f5e81d6a3af755680b5b3e58aa519dd2eebdc95fd76ae3b49d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"28393d13ec2b25f5e81d6a3af755680b5b3e58aa519dd2eebdc95fd76ae3b49d","first_computed_at":"2026-07-05T04:02:34.494042Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:02:34.494042Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/RrI8DtOGFWk5ij3KuE3ycXaEuET6Nk6Om4UUFUw71tOEBMJWnZSOra8su66QjGoD3h776RmMfqCGYgHI240Aw==","signature_status":"signed_v1","signed_at":"2026-07-05T04:02:34.494464Z","signed_message":"canonical_sha256_bytes"},"source_id":"2203.03439","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:14dc792568a3edeb0ca414368ed92a84747c1c552f7deb5abaf5f70bfce97a29","sha256:bb64e2d98d43e071293bcf52f84a87db3a2ba8b065b135143480b9b68211fe33"],"state_sha256":"4ee9dbe6c1f5623136686789dd33b7f56f3bf3f7e490313c4c85dbd9c41200b9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xH00Ez8p7HG67SDsDphY8iu2tjvw0JFha1+C4L9woqGu8ZOLpf9T8RmLYrg1xdnj96MSjWcPnRmPiFussbQpAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-08T06:14:42.366167Z","bundle_sha256":"4676415fe672b6379340230bd190f8406ab83867262951af4adba393869c78e8"}}