{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:4NW6YYPCGN4ZT6BBRPMHNOMRKC","short_pith_number":"pith:4NW6YYPC","canonical_record":{"source":{"id":"1811.12448","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-11-29T19:39:36Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"b30c769abb9e7db7fada7a3107c7518b36408cfa60cc5f069106a1a53fe47314","abstract_canon_sha256":"022979370a21376fe7fdac6dcac239ed2feba8c555185356a0383d37dec0857a"},"schema_version":"1.0"},"canonical_sha256":"e36dec61e2337999f8218bd876b99150884c978fbd0b76806e94913d422d424e","source":{"kind":"arxiv","id":"1811.12448","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.12448","created_at":"2026-05-17T23:59:31Z"},{"alias_kind":"arxiv_version","alias_value":"1811.12448v1","created_at":"2026-05-17T23:59:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.12448","created_at":"2026-05-17T23:59:31Z"},{"alias_kind":"pith_short_12","alias_value":"4NW6YYPCGN4Z","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_16","alias_value":"4NW6YYPCGN4ZT6BB","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_8","alias_value":"4NW6YYPC","created_at":"2026-05-18T12:32:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:4NW6YYPCGN4ZT6BBRPMHNOMRKC","target":"record","payload":{"canonical_record":{"source":{"id":"1811.12448","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-11-29T19:39:36Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"b30c769abb9e7db7fada7a3107c7518b36408cfa60cc5f069106a1a53fe47314","abstract_canon_sha256":"022979370a21376fe7fdac6dcac239ed2feba8c555185356a0383d37dec0857a"},"schema_version":"1.0"},"canonical_sha256":"e36dec61e2337999f8218bd876b99150884c978fbd0b76806e94913d422d424e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:59:31.647338Z","signature_b64":"qzhMocsVWEdZonz/cj8HHKRyH0wFSPrgw94p0AGJdyASyMve8B7cgSGxrgE3/JY4wbeI50fiddS2qLCGRAMTBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e36dec61e2337999f8218bd876b99150884c978fbd0b76806e94913d422d424e","last_reissued_at":"2026-05-17T23:59:31.646734Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:59:31.646734Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1811.12448","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":"2026-05-17T23:59:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"txTIq8OyfBSLUrTjx5uVQfZ2FfC2K+na4DaOCrLawQ632H//16nL8609DK5wHwhakUCP6XEVGtDslHZP8kgqBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T10:51:21.510622Z"},"content_sha256":"1543d4e95d0664e39fae1993c6589eeade026211eac5c7801b3d681ae17e07f2","schema_version":"1.0","event_id":"sha256:1543d4e95d0664e39fae1993c6589eeade026211eac5c7801b3d681ae17e07f2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:4NW6YYPCGN4ZT6BBRPMHNOMRKC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On estimates for fully nonlinear elliptic equations with Neumann boundary conditions on Riemannian Manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.AP","authors_text":"Bo Guan, Ni Xiang","submitted_at":"2018-11-29T19:39:36Z","abstract_excerpt":"We derive gradient and second order {\\em a priori} estimates for solutions of the Neumann problem for a general class of fully nonlinear elliptic equations on compact Riemannian manifolds with boundary. These estimates yield regularity and existence results."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.12448","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":"2026-05-17T23:59:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ok7Y7wSjYlJZgbmlvgLjuOS4Vpm21pZFZ6BJvG72ZEaSPEydO2IFRuOIA/TMJySMMAVSQS2NBLe/ntPkFPz9DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T10:51:21.510952Z"},"content_sha256":"cf28e5a9c461ff747ce52d813e70a46a6b61dbca6a7036e323345328eb88bc47","schema_version":"1.0","event_id":"sha256:cf28e5a9c461ff747ce52d813e70a46a6b61dbca6a7036e323345328eb88bc47"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4NW6YYPCGN4ZT6BBRPMHNOMRKC/bundle.json","state_url":"https://pith.science/pith/4NW6YYPCGN4ZT6BBRPMHNOMRKC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4NW6YYPCGN4ZT6BBRPMHNOMRKC/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":"2026-06-25T10:51:21Z","links":{"resolver":"https://pith.science/pith/4NW6YYPCGN4ZT6BBRPMHNOMRKC","bundle":"https://pith.science/pith/4NW6YYPCGN4ZT6BBRPMHNOMRKC/bundle.json","state":"https://pith.science/pith/4NW6YYPCGN4ZT6BBRPMHNOMRKC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4NW6YYPCGN4ZT6BBRPMHNOMRKC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:4NW6YYPCGN4ZT6BBRPMHNOMRKC","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":"022979370a21376fe7fdac6dcac239ed2feba8c555185356a0383d37dec0857a","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-11-29T19:39:36Z","title_canon_sha256":"b30c769abb9e7db7fada7a3107c7518b36408cfa60cc5f069106a1a53fe47314"},"schema_version":"1.0","source":{"id":"1811.12448","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.12448","created_at":"2026-05-17T23:59:31Z"},{"alias_kind":"arxiv_version","alias_value":"1811.12448v1","created_at":"2026-05-17T23:59:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.12448","created_at":"2026-05-17T23:59:31Z"},{"alias_kind":"pith_short_12","alias_value":"4NW6YYPCGN4Z","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_16","alias_value":"4NW6YYPCGN4ZT6BB","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_8","alias_value":"4NW6YYPC","created_at":"2026-05-18T12:32:05Z"}],"graph_snapshots":[{"event_id":"sha256:cf28e5a9c461ff747ce52d813e70a46a6b61dbca6a7036e323345328eb88bc47","target":"graph","created_at":"2026-05-17T23:59:31Z","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 derive gradient and second order {\\em a priori} estimates for solutions of the Neumann problem for a general class of fully nonlinear elliptic equations on compact Riemannian manifolds with boundary. These estimates yield regularity and existence results.","authors_text":"Bo Guan, Ni Xiang","cross_cats":["math.DG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-11-29T19:39:36Z","title":"On estimates for fully nonlinear elliptic equations with Neumann boundary conditions on Riemannian Manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.12448","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":"sha256:1543d4e95d0664e39fae1993c6589eeade026211eac5c7801b3d681ae17e07f2","target":"record","created_at":"2026-05-17T23:59:31Z","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":"022979370a21376fe7fdac6dcac239ed2feba8c555185356a0383d37dec0857a","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-11-29T19:39:36Z","title_canon_sha256":"b30c769abb9e7db7fada7a3107c7518b36408cfa60cc5f069106a1a53fe47314"},"schema_version":"1.0","source":{"id":"1811.12448","kind":"arxiv","version":1}},"canonical_sha256":"e36dec61e2337999f8218bd876b99150884c978fbd0b76806e94913d422d424e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e36dec61e2337999f8218bd876b99150884c978fbd0b76806e94913d422d424e","first_computed_at":"2026-05-17T23:59:31.646734Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:59:31.646734Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qzhMocsVWEdZonz/cj8HHKRyH0wFSPrgw94p0AGJdyASyMve8B7cgSGxrgE3/JY4wbeI50fiddS2qLCGRAMTBw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:59:31.647338Z","signed_message":"canonical_sha256_bytes"},"source_id":"1811.12448","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1543d4e95d0664e39fae1993c6589eeade026211eac5c7801b3d681ae17e07f2","sha256:cf28e5a9c461ff747ce52d813e70a46a6b61dbca6a7036e323345328eb88bc47"],"state_sha256":"9339435db8bbe962e4c676ea0f8e41f8c1ba665c5c1689e699466883d5c43343"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xVkq5+BWK2c4AZkubbV/jAJsjI3R+swVTXwyrUEcU3omXv9aSScGe+Ow5BSuB7IVZxb5/zVfvRndPOdSg4R/AQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T10:51:21.513016Z","bundle_sha256":"a6a65808b5f751d729327f145c907c73cfc3729d543a4f0d96abea00d32a148c"}}