{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:WTVIEWFNQP6236XZJYMSJG7CZY","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":"d624cf32381342d3c6f766047b32791e760a618c8ce731e567d2deb126b37965","cross_cats_sorted":["math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-01-15T11:00:54Z","title_canon_sha256":"59bcd032e9bcdb1e65bb207712432252d9dcbab6632adcdd68924acc1f2bd124"},"schema_version":"1.0","source":{"id":"1401.3542","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.3542","created_at":"2026-05-18T02:40:10Z"},{"alias_kind":"arxiv_version","alias_value":"1401.3542v2","created_at":"2026-05-18T02:40:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.3542","created_at":"2026-05-18T02:40:10Z"},{"alias_kind":"pith_short_12","alias_value":"WTVIEWFNQP62","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_16","alias_value":"WTVIEWFNQP6236XZ","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_8","alias_value":"WTVIEWFN","created_at":"2026-05-18T12:28:54Z"}],"graph_snapshots":[{"event_id":"sha256:d7b8ff688fddb4d56ac6d19b43db2e3416256f97b969076230959ce5bf43f2fc","target":"graph","created_at":"2026-05-18T02:40:10Z","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":"In this paper we consider the isoperimetric profile of convex cylinders $K\\times\\mathbb{R}^q$, where $K$ is an $m$-dimensional convex body, and of cylindrically bounded convex sets, i.e, those with a relatively compact orthogonal projection over some hyperplane of $\\mathbb{R}^{n+1}$, asymptotic to a right convex cylinder of the form $K\\times\\mathbb{R}$, with $K\\subset\\mathbb{R}^n$. Results concerning the concavity of the isoperimetric profile, existence of isoperimetric regions, and geometric descriptions of isoperimetric regions for small and large volumes are obtained.","authors_text":"Efstratios Vernadakis, Manuel Ritor\\'e","cross_cats":["math.MG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-01-15T11:00:54Z","title":"Isoperimetric inequalities in convex cylinders and cylindrically bounded convex bodies"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.3542","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:bd28548d2cd9d89aea0d1c6e80e79925d9993b58098be1d0670076313b7be28a","target":"record","created_at":"2026-05-18T02:40:10Z","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":"d624cf32381342d3c6f766047b32791e760a618c8ce731e567d2deb126b37965","cross_cats_sorted":["math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-01-15T11:00:54Z","title_canon_sha256":"59bcd032e9bcdb1e65bb207712432252d9dcbab6632adcdd68924acc1f2bd124"},"schema_version":"1.0","source":{"id":"1401.3542","kind":"arxiv","version":2}},"canonical_sha256":"b4ea8258ad83fdadfaf94e19249be2ce0e300a6c8108234c50b8fd5d485bd91e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b4ea8258ad83fdadfaf94e19249be2ce0e300a6c8108234c50b8fd5d485bd91e","first_computed_at":"2026-05-18T02:40:10.824672Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:40:10.824672Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"w57hiEhGctoDyvzejlyRbQVulN4niwGzIN7mMaDuJauXYtMdbzjm3CvuFxxgnio8GJLcJsnE+K/DBXIe/RjnBA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:40:10.825192Z","signed_message":"canonical_sha256_bytes"},"source_id":"1401.3542","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bd28548d2cd9d89aea0d1c6e80e79925d9993b58098be1d0670076313b7be28a","sha256:d7b8ff688fddb4d56ac6d19b43db2e3416256f97b969076230959ce5bf43f2fc"],"state_sha256":"c4e3faac08118450ef0957985d078fcc3b4b9b2ef6f908b1757220c343da8f3e"}