{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:YEXOB42G2P5OHRAZMY7PXPJQNV","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":"e88ab3926f920d47a0c588c0c43666ad2200f120b136375191685b3985f82389","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-05-29T04:15:47Z","title_canon_sha256":"1f44b80a08a185cbe6c5dc3d4331abb5c161beaadab3f8f3eb9e34c3b20989f7"},"schema_version":"1.0","source":{"id":"2605.30823","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.30823","created_at":"2026-06-01T01:03:19Z"},{"alias_kind":"arxiv_version","alias_value":"2605.30823v1","created_at":"2026-06-01T01:03:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.30823","created_at":"2026-06-01T01:03:19Z"},{"alias_kind":"pith_short_12","alias_value":"YEXOB42G2P5O","created_at":"2026-06-01T01:03:19Z"},{"alias_kind":"pith_short_16","alias_value":"YEXOB42G2P5OHRAZ","created_at":"2026-06-01T01:03:19Z"},{"alias_kind":"pith_short_8","alias_value":"YEXOB42G","created_at":"2026-06-01T01:03:19Z"}],"graph_snapshots":[{"event_id":"sha256:da3447421b7f50d8721bb038b243285198697e8f080bea4e3c98905f0be069b2","target":"graph","created_at":"2026-06-01T01:03:19Z","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/2605.30823/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove interior $C^{2}$ regularity result for convex viscosity solutions of the quadratic Hessian equation $\\sigma_2(D^2u) = f(x)$, under the assumption that $f\\in C^{0,1}$ with $\\inf f>0$. The result is almost sharp: if $f$ are merely continuous, there exist convex viscosity solutions that fail to be $C^{1,1}$. When $f\\in C^{\\alpha}$ for some $\\alpha\\in (0,1)$, the corresponding interior regularity remains open.","authors_text":"Chen Ruosi, Jian Huaiyu, Tu Xushan, Zhou Xingchen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-05-29T04:15:47Z","title":"Regularity for convex viscosity solutions of $\\sigma_2$ Equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.30823","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":"sha256:1cb531cf2065e997c7111ccef348979b681fc86620e702bb9bffc29708d28f1a","target":"record","created_at":"2026-06-01T01:03:19Z","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":"e88ab3926f920d47a0c588c0c43666ad2200f120b136375191685b3985f82389","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-05-29T04:15:47Z","title_canon_sha256":"1f44b80a08a185cbe6c5dc3d4331abb5c161beaadab3f8f3eb9e34c3b20989f7"},"schema_version":"1.0","source":{"id":"2605.30823","kind":"arxiv","version":1}},"canonical_sha256":"c12ee0f346d3fae3c419663efbbd306d6b9a29dfb95e072909f40d6d7bf6cbaf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c12ee0f346d3fae3c419663efbbd306d6b9a29dfb95e072909f40d6d7bf6cbaf","first_computed_at":"2026-06-01T01:03:19.090349Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-01T01:03:19.090349Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PdF8qUJQOdoyScwYXffOVGaqfuuDRF3IFTbF1BD36iV09lx0RbPWZ4aIvcO5LgRYXbddKwAxb8Nr7SZDLERJAg==","signature_status":"signed_v1","signed_at":"2026-06-01T01:03:19.091466Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.30823","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1cb531cf2065e997c7111ccef348979b681fc86620e702bb9bffc29708d28f1a","sha256:da3447421b7f50d8721bb038b243285198697e8f080bea4e3c98905f0be069b2"],"state_sha256":"91f87fd5821b77812f4d4fed478869dc8678144d496f3cdceb0d0046d2bce6b0"}