{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:PXHKGJT6RZZHSY2VJEYXZH6Z7P","short_pith_number":"pith:PXHKGJT6","canonical_record":{"source":{"id":"1512.01147","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-12-02T12:55:33Z","cross_cats_sorted":[],"title_canon_sha256":"d6a9d1361928e0d1e01d206916374c344cf11febf7d45a7f25c3c27026fe21ea","abstract_canon_sha256":"09e944a4f1c7f32937785b9913156bdc30c2ca53cff641e035f4d94863a28f6b"},"schema_version":"1.0"},"canonical_sha256":"7dcea3267e8e7279635549317c9fd9fbf3e52f6b0aebf2347f1204f126404439","source":{"kind":"arxiv","id":"1512.01147","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.01147","created_at":"2026-05-18T01:17:30Z"},{"alias_kind":"arxiv_version","alias_value":"1512.01147v2","created_at":"2026-05-18T01:17:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.01147","created_at":"2026-05-18T01:17:30Z"},{"alias_kind":"pith_short_12","alias_value":"PXHKGJT6RZZH","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_16","alias_value":"PXHKGJT6RZZHSY2V","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_8","alias_value":"PXHKGJT6","created_at":"2026-05-18T12:29:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:PXHKGJT6RZZHSY2VJEYXZH6Z7P","target":"record","payload":{"canonical_record":{"source":{"id":"1512.01147","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-12-02T12:55:33Z","cross_cats_sorted":[],"title_canon_sha256":"d6a9d1361928e0d1e01d206916374c344cf11febf7d45a7f25c3c27026fe21ea","abstract_canon_sha256":"09e944a4f1c7f32937785b9913156bdc30c2ca53cff641e035f4d94863a28f6b"},"schema_version":"1.0"},"canonical_sha256":"7dcea3267e8e7279635549317c9fd9fbf3e52f6b0aebf2347f1204f126404439","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:17:30.380118Z","signature_b64":"3K8cIZ0k9h6EpcNF6mTnAF8AiAYFU6PVnIRzxa71DH3X4riY2NF1y072+b4zvPXb8NxtRW4SQDraB0yU93UsDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7dcea3267e8e7279635549317c9fd9fbf3e52f6b0aebf2347f1204f126404439","last_reissued_at":"2026-05-18T01:17:30.379391Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:17:30.379391Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1512.01147","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":"2026-05-18T01:17:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ov33z9NWcQT05Di9TTPc3dxDU2k9lHyTv7asAVnryXcDQkP++SX79AFOsWKhM4Il+sSsg9I7n8hdPJz69TnRDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T00:54:23.157276Z"},"content_sha256":"d21d6bd061aa4607ce71482adacb84417d57ff0a9f984d0582ac7e0ac475fac0","schema_version":"1.0","event_id":"sha256:d21d6bd061aa4607ce71482adacb84417d57ff0a9f984d0582ac7e0ac475fac0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:PXHKGJT6RZZHSY2VJEYXZH6Z7P","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The interior $C^2$ estimate for prescribed Gauss curvature equation in dimension two","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Chuanqiang Chen, Fei Han, Qianzhong Ou","submitted_at":"2015-12-02T12:55:33Z","abstract_excerpt":"In this paper, we introduce a new auxiliary function, and establish the interior $C^2$ estimate for prescribed Gauss curvature equation in dimension two."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.01147","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":"2026-05-18T01:17:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dBeRIxJZ1yyfISn2C7kQnET2K1yCBUsYf/nfwP/cRMzc4hqThzQqCIHQuIZSDJa1UKKt/ggsjpGQZl2SB9ebCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T00:54:23.157660Z"},"content_sha256":"cce84879a2c6e4ce1c8b29fa4cc1acee4cb2affc2b59d7fdafb2acb657e8db20","schema_version":"1.0","event_id":"sha256:cce84879a2c6e4ce1c8b29fa4cc1acee4cb2affc2b59d7fdafb2acb657e8db20"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PXHKGJT6RZZHSY2VJEYXZH6Z7P/bundle.json","state_url":"https://pith.science/pith/PXHKGJT6RZZHSY2VJEYXZH6Z7P/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PXHKGJT6RZZHSY2VJEYXZH6Z7P/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":"2026-06-26T00:54:23Z","links":{"resolver":"https://pith.science/pith/PXHKGJT6RZZHSY2VJEYXZH6Z7P","bundle":"https://pith.science/pith/PXHKGJT6RZZHSY2VJEYXZH6Z7P/bundle.json","state":"https://pith.science/pith/PXHKGJT6RZZHSY2VJEYXZH6Z7P/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PXHKGJT6RZZHSY2VJEYXZH6Z7P/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:PXHKGJT6RZZHSY2VJEYXZH6Z7P","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":"09e944a4f1c7f32937785b9913156bdc30c2ca53cff641e035f4d94863a28f6b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-12-02T12:55:33Z","title_canon_sha256":"d6a9d1361928e0d1e01d206916374c344cf11febf7d45a7f25c3c27026fe21ea"},"schema_version":"1.0","source":{"id":"1512.01147","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.01147","created_at":"2026-05-18T01:17:30Z"},{"alias_kind":"arxiv_version","alias_value":"1512.01147v2","created_at":"2026-05-18T01:17:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.01147","created_at":"2026-05-18T01:17:30Z"},{"alias_kind":"pith_short_12","alias_value":"PXHKGJT6RZZH","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_16","alias_value":"PXHKGJT6RZZHSY2V","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_8","alias_value":"PXHKGJT6","created_at":"2026-05-18T12:29:37Z"}],"graph_snapshots":[{"event_id":"sha256:cce84879a2c6e4ce1c8b29fa4cc1acee4cb2affc2b59d7fdafb2acb657e8db20","target":"graph","created_at":"2026-05-18T01:17:30Z","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 introduce a new auxiliary function, and establish the interior $C^2$ estimate for prescribed Gauss curvature equation in dimension two.","authors_text":"Chuanqiang Chen, Fei Han, Qianzhong Ou","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-12-02T12:55:33Z","title":"The interior $C^2$ estimate for prescribed Gauss curvature equation in dimension two"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.01147","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:d21d6bd061aa4607ce71482adacb84417d57ff0a9f984d0582ac7e0ac475fac0","target":"record","created_at":"2026-05-18T01:17:30Z","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":"09e944a4f1c7f32937785b9913156bdc30c2ca53cff641e035f4d94863a28f6b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-12-02T12:55:33Z","title_canon_sha256":"d6a9d1361928e0d1e01d206916374c344cf11febf7d45a7f25c3c27026fe21ea"},"schema_version":"1.0","source":{"id":"1512.01147","kind":"arxiv","version":2}},"canonical_sha256":"7dcea3267e8e7279635549317c9fd9fbf3e52f6b0aebf2347f1204f126404439","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7dcea3267e8e7279635549317c9fd9fbf3e52f6b0aebf2347f1204f126404439","first_computed_at":"2026-05-18T01:17:30.379391Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:17:30.379391Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3K8cIZ0k9h6EpcNF6mTnAF8AiAYFU6PVnIRzxa71DH3X4riY2NF1y072+b4zvPXb8NxtRW4SQDraB0yU93UsDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:17:30.380118Z","signed_message":"canonical_sha256_bytes"},"source_id":"1512.01147","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d21d6bd061aa4607ce71482adacb84417d57ff0a9f984d0582ac7e0ac475fac0","sha256:cce84879a2c6e4ce1c8b29fa4cc1acee4cb2affc2b59d7fdafb2acb657e8db20"],"state_sha256":"46aa09931f149d6656351a5d72fc6ea8e44a322a6dfc3aa93356a48accb7cf64"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"l8mo0/w80/R8+M0RRSMq332GSnHy7EhaPq2JDQj1eZs82/MnYxVObmJPz2g7nEijKgOfs3+nQAQXX1HQnHbHDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T00:54:23.159505Z","bundle_sha256":"d788ed2325723dd90be7b21b72ec1195e76d60a26977a9c56a3cca4a12e78339"}}