{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:C74F7W2BPHLYAA4CDIRRLNR7BO","short_pith_number":"pith:C74F7W2B","canonical_record":{"source":{"id":"1504.00963","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-04-04T01:02:51Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"b89b1b4157d4310aa11ba0af24e703c2d72b06f0e95be6e3fe5bc5dcbad42272","abstract_canon_sha256":"63dc41a5d6fefe3e4adcdc54fafaac8b6cae358cd516bc61545491133b5894d3"},"schema_version":"1.0"},"canonical_sha256":"17f85fdb4179d78003821a2315b63f0b82c44a97ef5cd4b5d9bc75a31ab7a412","source":{"kind":"arxiv","id":"1504.00963","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.00963","created_at":"2026-05-18T02:19:35Z"},{"alias_kind":"arxiv_version","alias_value":"1504.00963v1","created_at":"2026-05-18T02:19:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.00963","created_at":"2026-05-18T02:19:35Z"},{"alias_kind":"pith_short_12","alias_value":"C74F7W2BPHLY","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_16","alias_value":"C74F7W2BPHLYAA4C","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_8","alias_value":"C74F7W2B","created_at":"2026-05-18T12:29:14Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:C74F7W2BPHLYAA4CDIRRLNR7BO","target":"record","payload":{"canonical_record":{"source":{"id":"1504.00963","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-04-04T01:02:51Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"b89b1b4157d4310aa11ba0af24e703c2d72b06f0e95be6e3fe5bc5dcbad42272","abstract_canon_sha256":"63dc41a5d6fefe3e4adcdc54fafaac8b6cae358cd516bc61545491133b5894d3"},"schema_version":"1.0"},"canonical_sha256":"17f85fdb4179d78003821a2315b63f0b82c44a97ef5cd4b5d9bc75a31ab7a412","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:19:35.460243Z","signature_b64":"Vwnc/gLq2NwsBMcA/5KLHpawg62kL8TgBB9C8dAKQ+d9secK+aOU7uOl/1eVjhDeZOGB5Xbidy58Fv47WWRPDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"17f85fdb4179d78003821a2315b63f0b82c44a97ef5cd4b5d9bc75a31ab7a412","last_reissued_at":"2026-05-18T02:19:35.459751Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:19:35.459751Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1504.00963","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":"2026-05-18T02:19:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"x6t/E+YGvcI2c1rgSjy07/W4V9u9qhewMHRWPzFrhc1QYDq+Xx7oRMhkBLBmLA0dB8TDLpF+No1vddNYxklMAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T05:39:04.483173Z"},"content_sha256":"6f861a86d63b731768ee5cc012ee9499ca50fcba45833376adfbb07fefac50c4","schema_version":"1.0","event_id":"sha256:6f861a86d63b731768ee5cc012ee9499ca50fcba45833376adfbb07fefac50c4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:C74F7W2BPHLYAA4CDIRRLNR7BO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"$C^{2,\\alpha}$ estimates and existence results for certain nonconcave PDE","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.AP","authors_text":"Vamsi P. Pingali","submitted_at":"2015-04-04T01:02:51Z","abstract_excerpt":"We establish $C^{2,\\alpha}$ estimates for PDE of the form convex $+$ a sum of weakly concave functions of the Hessian, thus generalising a recent result of Collins which is in turn inspired by a theorem of Caffarelli and Yuan. Independently, we also prove an existence result for a certain generalised Monge-Amp\\`ere PDE."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.00963","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":"2026-05-18T02:19:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FWIdEDwSnpxYXl6b69ZGhwLElp9VhdTrNb0GGUT/HZH0F1wTTWCZVypPTTivbZ3ldKLEXjHtdWBMyj4HQsLgBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T05:39:04.483535Z"},"content_sha256":"61b8bdb4b433dfbf17ed6e6f1e4383c48487af2a61093d2760da1d83fcf16469","schema_version":"1.0","event_id":"sha256:61b8bdb4b433dfbf17ed6e6f1e4383c48487af2a61093d2760da1d83fcf16469"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/C74F7W2BPHLYAA4CDIRRLNR7BO/bundle.json","state_url":"https://pith.science/pith/C74F7W2BPHLYAA4CDIRRLNR7BO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/C74F7W2BPHLYAA4CDIRRLNR7BO/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":"2026-05-31T05:39:04Z","links":{"resolver":"https://pith.science/pith/C74F7W2BPHLYAA4CDIRRLNR7BO","bundle":"https://pith.science/pith/C74F7W2BPHLYAA4CDIRRLNR7BO/bundle.json","state":"https://pith.science/pith/C74F7W2BPHLYAA4CDIRRLNR7BO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/C74F7W2BPHLYAA4CDIRRLNR7BO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:C74F7W2BPHLYAA4CDIRRLNR7BO","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":"63dc41a5d6fefe3e4adcdc54fafaac8b6cae358cd516bc61545491133b5894d3","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-04-04T01:02:51Z","title_canon_sha256":"b89b1b4157d4310aa11ba0af24e703c2d72b06f0e95be6e3fe5bc5dcbad42272"},"schema_version":"1.0","source":{"id":"1504.00963","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.00963","created_at":"2026-05-18T02:19:35Z"},{"alias_kind":"arxiv_version","alias_value":"1504.00963v1","created_at":"2026-05-18T02:19:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.00963","created_at":"2026-05-18T02:19:35Z"},{"alias_kind":"pith_short_12","alias_value":"C74F7W2BPHLY","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_16","alias_value":"C74F7W2BPHLYAA4C","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_8","alias_value":"C74F7W2B","created_at":"2026-05-18T12:29:14Z"}],"graph_snapshots":[{"event_id":"sha256:61b8bdb4b433dfbf17ed6e6f1e4383c48487af2a61093d2760da1d83fcf16469","target":"graph","created_at":"2026-05-18T02:19:35Z","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 establish $C^{2,\\alpha}$ estimates for PDE of the form convex $+$ a sum of weakly concave functions of the Hessian, thus generalising a recent result of Collins which is in turn inspired by a theorem of Caffarelli and Yuan. Independently, we also prove an existence result for a certain generalised Monge-Amp\\`ere PDE.","authors_text":"Vamsi P. Pingali","cross_cats":["math.DG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-04-04T01:02:51Z","title":"$C^{2,\\alpha}$ estimates and existence results for certain nonconcave PDE"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.00963","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":"sha256:6f861a86d63b731768ee5cc012ee9499ca50fcba45833376adfbb07fefac50c4","target":"record","created_at":"2026-05-18T02:19:35Z","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":"63dc41a5d6fefe3e4adcdc54fafaac8b6cae358cd516bc61545491133b5894d3","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-04-04T01:02:51Z","title_canon_sha256":"b89b1b4157d4310aa11ba0af24e703c2d72b06f0e95be6e3fe5bc5dcbad42272"},"schema_version":"1.0","source":{"id":"1504.00963","kind":"arxiv","version":1}},"canonical_sha256":"17f85fdb4179d78003821a2315b63f0b82c44a97ef5cd4b5d9bc75a31ab7a412","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"17f85fdb4179d78003821a2315b63f0b82c44a97ef5cd4b5d9bc75a31ab7a412","first_computed_at":"2026-05-18T02:19:35.459751Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:19:35.459751Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Vwnc/gLq2NwsBMcA/5KLHpawg62kL8TgBB9C8dAKQ+d9secK+aOU7uOl/1eVjhDeZOGB5Xbidy58Fv47WWRPDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:19:35.460243Z","signed_message":"canonical_sha256_bytes"},"source_id":"1504.00963","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6f861a86d63b731768ee5cc012ee9499ca50fcba45833376adfbb07fefac50c4","sha256:61b8bdb4b433dfbf17ed6e6f1e4383c48487af2a61093d2760da1d83fcf16469"],"state_sha256":"d068d731382fe98977f44c130536ee029ad4a3282934369d6911a85447c99eb7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"adLDGIYO6YxCmp1Mlzx4CjAcICf7YRtAZl8CBPFKS81mhC5r3JHziL+xGPBE9tHP4NGdB/4J34MD3TMhvoD4Dg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T05:39:04.485494Z","bundle_sha256":"d50984e5e8ad032cd62854b01b407c2e9561c0726e88e3bc1eb4087f3aa348f8"}}