{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:GGQMYLC7DVN2SDN32PI5J4CVCQ","short_pith_number":"pith:GGQMYLC7","canonical_record":{"source":{"id":"1610.09644","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-10-30T13:22:49Z","cross_cats_sorted":[],"title_canon_sha256":"14360d3408829a511b72b5f4ce6e07b719418347c2631c1efc8805053bc1e01e","abstract_canon_sha256":"152256155eaf6b918865a02b8c8bc489171f4df591ffeece30c0247f60428e1a"},"schema_version":"1.0"},"canonical_sha256":"31a0cc2c5f1d5ba90dbbd3d1d4f05514286f1ade3228349604de669c58017289","source":{"kind":"arxiv","id":"1610.09644","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.09644","created_at":"2026-05-18T01:00:51Z"},{"alias_kind":"arxiv_version","alias_value":"1610.09644v1","created_at":"2026-05-18T01:00:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.09644","created_at":"2026-05-18T01:00:51Z"},{"alias_kind":"pith_short_12","alias_value":"GGQMYLC7DVN2","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_16","alias_value":"GGQMYLC7DVN2SDN3","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_8","alias_value":"GGQMYLC7","created_at":"2026-05-18T12:30:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:GGQMYLC7DVN2SDN32PI5J4CVCQ","target":"record","payload":{"canonical_record":{"source":{"id":"1610.09644","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-10-30T13:22:49Z","cross_cats_sorted":[],"title_canon_sha256":"14360d3408829a511b72b5f4ce6e07b719418347c2631c1efc8805053bc1e01e","abstract_canon_sha256":"152256155eaf6b918865a02b8c8bc489171f4df591ffeece30c0247f60428e1a"},"schema_version":"1.0"},"canonical_sha256":"31a0cc2c5f1d5ba90dbbd3d1d4f05514286f1ade3228349604de669c58017289","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:00:51.405971Z","signature_b64":"9tD2bWqB+HLyjtvRVWuiPTyeyxHwDt1PPz9EXhPlzP/KBH1i8cyNes/8ndSbTwnJV2EJo2ZoSSEGRetRvfnPDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"31a0cc2c5f1d5ba90dbbd3d1d4f05514286f1ade3228349604de669c58017289","last_reissued_at":"2026-05-18T01:00:51.405504Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:00:51.405504Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1610.09644","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":"2026-05-18T01:00:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6T421I57GgwjbYQddq6EgpnCUOUEtZt450Ju/k7bUsRI/6djR/BSoXeGQkbJve4+nDublh2ct2/rBctsnE7JDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T06:20:11.054920Z"},"content_sha256":"9049853c640c98e5d0f546b9471eb2cb8e53c327e15477b554465286d635aa5a","schema_version":"1.0","event_id":"sha256:9049853c640c98e5d0f546b9471eb2cb8e53c327e15477b554465286d635aa5a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:GGQMYLC7DVN2SDN32PI5J4CVCQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Monge-Amp\\`ere type equations with Neumann boundary conditions on Riemannian manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Jing Mao, Ni Xiang, Xi Guo","submitted_at":"2016-10-30T13:22:49Z","abstract_excerpt":"In this paper, we consider the global regularity for Monge-Amp\\`ere type equations with the Neumann boundary conditions on Riemannian manifolds. It is known that the classical solvability of the Neumann boundary value problem is obtained under some necessary assumptions. Our main result extends the main theorem from the case of Euclidean space $R^n$ in [11] to Riemannian manifolds."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.09644","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":"2026-05-18T01:00:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AAYK9L/Ubn1bP+cmkfVsXQZw/yPXlzrksRDhDs6VZFM9NMWXZWx9Yeo7OZszIIi5ltGvZyzlJYWK0ZnYTmrcBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T06:20:11.055263Z"},"content_sha256":"034ac0d75a04e7e803d4ed18b2006d78f5bafbead7dbb75e487433b677c8ed1a","schema_version":"1.0","event_id":"sha256:034ac0d75a04e7e803d4ed18b2006d78f5bafbead7dbb75e487433b677c8ed1a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GGQMYLC7DVN2SDN32PI5J4CVCQ/bundle.json","state_url":"https://pith.science/pith/GGQMYLC7DVN2SDN32PI5J4CVCQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GGQMYLC7DVN2SDN32PI5J4CVCQ/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":"2026-06-25T06:20:11Z","links":{"resolver":"https://pith.science/pith/GGQMYLC7DVN2SDN32PI5J4CVCQ","bundle":"https://pith.science/pith/GGQMYLC7DVN2SDN32PI5J4CVCQ/bundle.json","state":"https://pith.science/pith/GGQMYLC7DVN2SDN32PI5J4CVCQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GGQMYLC7DVN2SDN32PI5J4CVCQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:GGQMYLC7DVN2SDN32PI5J4CVCQ","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":"152256155eaf6b918865a02b8c8bc489171f4df591ffeece30c0247f60428e1a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-10-30T13:22:49Z","title_canon_sha256":"14360d3408829a511b72b5f4ce6e07b719418347c2631c1efc8805053bc1e01e"},"schema_version":"1.0","source":{"id":"1610.09644","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.09644","created_at":"2026-05-18T01:00:51Z"},{"alias_kind":"arxiv_version","alias_value":"1610.09644v1","created_at":"2026-05-18T01:00:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.09644","created_at":"2026-05-18T01:00:51Z"},{"alias_kind":"pith_short_12","alias_value":"GGQMYLC7DVN2","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_16","alias_value":"GGQMYLC7DVN2SDN3","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_8","alias_value":"GGQMYLC7","created_at":"2026-05-18T12:30:19Z"}],"graph_snapshots":[{"event_id":"sha256:034ac0d75a04e7e803d4ed18b2006d78f5bafbead7dbb75e487433b677c8ed1a","target":"graph","created_at":"2026-05-18T01:00:51Z","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":"In this paper, we consider the global regularity for Monge-Amp\\`ere type equations with the Neumann boundary conditions on Riemannian manifolds. It is known that the classical solvability of the Neumann boundary value problem is obtained under some necessary assumptions. Our main result extends the main theorem from the case of Euclidean space $R^n$ in [11] to Riemannian manifolds.","authors_text":"Jing Mao, Ni Xiang, Xi Guo","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-10-30T13:22:49Z","title":"Monge-Amp\\`ere type equations with Neumann boundary conditions on Riemannian manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.09644","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":"sha256:9049853c640c98e5d0f546b9471eb2cb8e53c327e15477b554465286d635aa5a","target":"record","created_at":"2026-05-18T01:00:51Z","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":"152256155eaf6b918865a02b8c8bc489171f4df591ffeece30c0247f60428e1a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-10-30T13:22:49Z","title_canon_sha256":"14360d3408829a511b72b5f4ce6e07b719418347c2631c1efc8805053bc1e01e"},"schema_version":"1.0","source":{"id":"1610.09644","kind":"arxiv","version":1}},"canonical_sha256":"31a0cc2c5f1d5ba90dbbd3d1d4f05514286f1ade3228349604de669c58017289","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"31a0cc2c5f1d5ba90dbbd3d1d4f05514286f1ade3228349604de669c58017289","first_computed_at":"2026-05-18T01:00:51.405504Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:00:51.405504Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9tD2bWqB+HLyjtvRVWuiPTyeyxHwDt1PPz9EXhPlzP/KBH1i8cyNes/8ndSbTwnJV2EJo2ZoSSEGRetRvfnPDw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:00:51.405971Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.09644","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9049853c640c98e5d0f546b9471eb2cb8e53c327e15477b554465286d635aa5a","sha256:034ac0d75a04e7e803d4ed18b2006d78f5bafbead7dbb75e487433b677c8ed1a"],"state_sha256":"ba2bcc3ef2a898e45d39d66fc3343f9fb5eb0d21d644c334030f0dac2f007a57"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Sb41v+PUUvYjUHXYzYrky+w/qhMmq/rC0+XGEuDgvVlMYJz/jW79zicArdMcqdj22OsFuaWo9SE8SismESKQBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T06:20:11.057201Z","bundle_sha256":"7b93eafbd9809a48cf77e2623c4d3c1041a4b6d7c017abae720d073e0efb4134"}}