{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:TMBURF43JTOS7ROQN7ZDCRRFSF","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":"288e016c36efc0495c4d91f7209f2eb2d5638b714d9a4448d45846822bf6493b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-06-10T17:54:24Z","title_canon_sha256":"4279370d6ceadbc0f8b92c2b83be2d37eae236ecf9366f47269ea0dca740becc"},"schema_version":"1.0","source":{"id":"1506.03409","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.03409","created_at":"2026-05-18T01:35:22Z"},{"alias_kind":"arxiv_version","alias_value":"1506.03409v2","created_at":"2026-05-18T01:35:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.03409","created_at":"2026-05-18T01:35:22Z"},{"alias_kind":"pith_short_12","alias_value":"TMBURF43JTOS","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_16","alias_value":"TMBURF43JTOS7ROQ","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_8","alias_value":"TMBURF43","created_at":"2026-05-18T12:29:42Z"}],"graph_snapshots":[{"event_id":"sha256:7c4b2a2022391cf4c2003ad59c1c13d874138bec11f2115c771f8d61bb00419d","target":"graph","created_at":"2026-05-18T01:35:22Z","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":"The goal of this note is to have a systematic approach to generating isoperimetric inequalities from two concrete type of PDEs. We call these PDEs Bellman type because a totally analogous equations happen to rule many sharp estimates for singular integrals in harmonic analysis, and such estimates were obtained with the use of Hamilton--Jacobi--Bellman PDE. We show how classical inequalities of Brascamp--Lieb, Prekopa--Leindler, Ehrhard are particular case of this scheme, which allows us to augment the stock of such inequalities. We approach the isoperimetric inequalities as a maximum (minimum)","authors_text":"Alexander Volberg, Paata Ivanisvili","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-06-10T17:54:24Z","title":"Bellman partial differential equation and the hill property for classical isoperimetric problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.03409","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:b1f1ea1b00aa08fae9360669ba1fd1377dc4876d9638ce4e29783484e23e06bf","target":"record","created_at":"2026-05-18T01:35:22Z","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":"288e016c36efc0495c4d91f7209f2eb2d5638b714d9a4448d45846822bf6493b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-06-10T17:54:24Z","title_canon_sha256":"4279370d6ceadbc0f8b92c2b83be2d37eae236ecf9366f47269ea0dca740becc"},"schema_version":"1.0","source":{"id":"1506.03409","kind":"arxiv","version":2}},"canonical_sha256":"9b0348979b4cdd2fc5d06ff231462591651166441aba0015dc0481bd8b60d52d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9b0348979b4cdd2fc5d06ff231462591651166441aba0015dc0481bd8b60d52d","first_computed_at":"2026-05-18T01:35:22.181337Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:35:22.181337Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qNEJj17Wk5Q/T5QJw4e9yMVITCuo0+kdzD5DFA/tEjT8x0iRpRJGm8e1zZT2twkP2iNbIdIjuZQL+hz0YFSLCA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:35:22.182136Z","signed_message":"canonical_sha256_bytes"},"source_id":"1506.03409","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b1f1ea1b00aa08fae9360669ba1fd1377dc4876d9638ce4e29783484e23e06bf","sha256:7c4b2a2022391cf4c2003ad59c1c13d874138bec11f2115c771f8d61bb00419d"],"state_sha256":"cf4f8b400b3f2d2ad55f6fc6b62881217a2945bcc012bfbfdaa9b9edb7fe052c"}