{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:NBATKHMRBO3EY7F6XIDRLOVCCX","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":"192ea936960a0110cf8b5bb8893995d0bbbee0e6723c2735fcd8a3948300000f","cross_cats_sorted":["math.CA","math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-11-19T18:25:39Z","title_canon_sha256":"d22d098aa8fd97881df75cfd6a43f673ad7fd2f0e9c595620d8a65c8c3159549"},"schema_version":"1.0","source":{"id":"1411.5303","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.5303","created_at":"2026-05-18T02:34:39Z"},{"alias_kind":"arxiv_version","alias_value":"1411.5303v1","created_at":"2026-05-18T02:34:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.5303","created_at":"2026-05-18T02:34:39Z"},{"alias_kind":"pith_short_12","alias_value":"NBATKHMRBO3E","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_16","alias_value":"NBATKHMRBO3EY7F6","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_8","alias_value":"NBATKHMR","created_at":"2026-05-18T12:28:41Z"}],"graph_snapshots":[{"event_id":"sha256:6d027d9fce1f7ed50e929134af105bb804b77215baa4bf3b8aef9ffcc8288551","target":"graph","created_at":"2026-05-18T02:34:39Z","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 optimal continuity results for the action of the Hessian determinant on spaces of Besov type into the space of distributions on $\\mathbb{R}^N$. In particular, inspired by recent work of Brezis and Nguyen on the distributional Jacobian determinant, we show that the action is continuous on the Besov space of fractional order $B(2-\\frac{2}{N},N)$, and that all continuity results in this scale of Besov spaces are consequences of this result.\n  A key ingredient in the argument is the characterization of $B(2-\\frac{2}{N},N)$ as the space of traces of functions in the Sobolev space $W^{2","authors_text":"David Jerison, Eric Baer","cross_cats":["math.CA","math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-11-19T18:25:39Z","title":"Optimal function spaces for continuity of the Hessian determinant as a distribution"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.5303","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":"sha256:6f3e7b7b31e35b69bdf9a411e0ebc8482c59cf89e8e36aa80b3559a05a0424bc","target":"record","created_at":"2026-05-18T02:34:39Z","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":"192ea936960a0110cf8b5bb8893995d0bbbee0e6723c2735fcd8a3948300000f","cross_cats_sorted":["math.CA","math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-11-19T18:25:39Z","title_canon_sha256":"d22d098aa8fd97881df75cfd6a43f673ad7fd2f0e9c595620d8a65c8c3159549"},"schema_version":"1.0","source":{"id":"1411.5303","kind":"arxiv","version":1}},"canonical_sha256":"6841351d910bb64c7cbeba0715baa215cd51a2e5c2e2a78b16dfa535b98fb25d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6841351d910bb64c7cbeba0715baa215cd51a2e5c2e2a78b16dfa535b98fb25d","first_computed_at":"2026-05-18T02:34:39.288087Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:34:39.288087Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CQ4K7S4nm7JDUnpZdXARmtSqWtTkPb727Y3qsZxx0+8/jERvTI3JHl6oW2WR97raQRjTQvz2g7g5hLtQF/eTCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:34:39.288485Z","signed_message":"canonical_sha256_bytes"},"source_id":"1411.5303","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6f3e7b7b31e35b69bdf9a411e0ebc8482c59cf89e8e36aa80b3559a05a0424bc","sha256:6d027d9fce1f7ed50e929134af105bb804b77215baa4bf3b8aef9ffcc8288551"],"state_sha256":"8e388495a2f9ee4a5efa4b47ec011d50519b16bf34004dd3d8c62c370dbec67f"}