{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:ERCJMYZX2POJBVBHSNTD3VFAJT","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":"ca401f0662582c9ce1b8caddb780842adf770019329e66e472095942e5e2981c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-09-27T20:48:33Z","title_canon_sha256":"f574cbd7ec0ecd39beff7bb32bd25dd84929e7af15c49d9d8f51e412cbdf0b27"},"schema_version":"1.0","source":{"id":"1809.10759","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.10759","created_at":"2026-05-17T23:54:58Z"},{"alias_kind":"arxiv_version","alias_value":"1809.10759v2","created_at":"2026-05-17T23:54:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.10759","created_at":"2026-05-17T23:54:58Z"},{"alias_kind":"pith_short_12","alias_value":"ERCJMYZX2POJ","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_16","alias_value":"ERCJMYZX2POJBVBH","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_8","alias_value":"ERCJMYZX","created_at":"2026-05-18T12:32:22Z"}],"graph_snapshots":[{"event_id":"sha256:85f23c40ad655a4d021c0ffb33f33a03ef6fad0517a11316e622758b7b306cb3","target":"graph","created_at":"2026-05-17T23:54:58Z","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 introduce a conjecture that we call the {\\it Two Hyperplane Conjecture}, saying that an isoperimetric surface that divides a convex body in half by volume is trapped between parallel hyperplanes. The conjecture is motivated by an approach we propose to the {\\it Hots Spots Conjecture} of J. Rauch using deformation and Lipschitz bounds for level sets of eigenfunctions. We will relate this approach to quantitative connectivity properties of level sets of solutions to elliptic variational problems, including isoperimetric inequalities, Poincar\\'e inequalities, Harnack inequalities, and NTA (non","authors_text":"David Jerison","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-09-27T20:48:33Z","title":"The Two Hyperplane Conjecture"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.10759","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":"sha256:82b7e7bebb0d7fd7a24372e526c2341eaf03f135ce981b144b1bd81dfd6d1d1e","target":"record","created_at":"2026-05-17T23:54:58Z","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":"ca401f0662582c9ce1b8caddb780842adf770019329e66e472095942e5e2981c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-09-27T20:48:33Z","title_canon_sha256":"f574cbd7ec0ecd39beff7bb32bd25dd84929e7af15c49d9d8f51e412cbdf0b27"},"schema_version":"1.0","source":{"id":"1809.10759","kind":"arxiv","version":2}},"canonical_sha256":"2444966337d3dc90d42793663dd4a04cc504cd15753e84c5afff7eda7a3d7cf1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2444966337d3dc90d42793663dd4a04cc504cd15753e84c5afff7eda7a3d7cf1","first_computed_at":"2026-05-17T23:54:58.937710Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:54:58.937710Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YwLxkh0wr+1pKQy3dWWlWUu7D3sdoV7W0iZJzEaY19FAYi/eNz5NncEX5PwlZYK2kMq7gwKcncxufOMvvm4uAg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:54:58.938331Z","signed_message":"canonical_sha256_bytes"},"source_id":"1809.10759","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:82b7e7bebb0d7fd7a24372e526c2341eaf03f135ce981b144b1bd81dfd6d1d1e","sha256:85f23c40ad655a4d021c0ffb33f33a03ef6fad0517a11316e622758b7b306cb3"],"state_sha256":"a531be89ebf78db45c13ef85ebdf35c78e9738afce962736109e8c419d795185"}