{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:TR6RIIJ62C46H7XRLEQPWUALI3","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":"982ee40e2e06963f7fe4ac1b3168d8ab5cb8314128a5b138eb2ce40c4f0d210a","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-04-01T17:09:18Z","title_canon_sha256":"2c636a9fb97697609e22edd9ad6ba4d972f8cd744d2604936b701bb805bee028"},"schema_version":"1.0","source":{"id":"1604.00995","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.00995","created_at":"2026-05-18T01:17:47Z"},{"alias_kind":"arxiv_version","alias_value":"1604.00995v1","created_at":"2026-05-18T01:17:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.00995","created_at":"2026-05-18T01:17:47Z"},{"alias_kind":"pith_short_12","alias_value":"TR6RIIJ62C46","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_16","alias_value":"TR6RIIJ62C46H7XR","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_8","alias_value":"TR6RIIJ6","created_at":"2026-05-18T12:30:46Z"}],"graph_snapshots":[{"event_id":"sha256:656fc26fd784399a0b57a3358b261304c2a13afe453afc6fc5c20cccfef035d5","target":"graph","created_at":"2026-05-18T01:17:47Z","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 study various regularity properties of minimizers of the $\\Phi$--perimeter, where $\\Phi$ is a norm. Under suitable assumptions on $\\Phi$ and on the dimension of the ambient space, we prove that the boundary of a cartesian minimizer is locally a Lipschitz graph out of a closed singular set of small Hausdorff dimension. Moreover, we show the following anisotropic Bernstein-type result: any entire cartesian minimizer is the subgraph of a monotone function depending only on one variable.","authors_text":"G. Bellettini, M. Novaga, Sh. Yu. Kholmatov","cross_cats":["math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-04-01T17:09:18Z","title":"Minimizers of anisotropic perimeters with cylindrical norms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.00995","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":"sha256:2900a9c7ba753502c6bf5270b74aefb6ab4ebe0dc9abed0884a76c4969c389e8","target":"record","created_at":"2026-05-18T01:17:47Z","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":"982ee40e2e06963f7fe4ac1b3168d8ab5cb8314128a5b138eb2ce40c4f0d210a","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-04-01T17:09:18Z","title_canon_sha256":"2c636a9fb97697609e22edd9ad6ba4d972f8cd744d2604936b701bb805bee028"},"schema_version":"1.0","source":{"id":"1604.00995","kind":"arxiv","version":1}},"canonical_sha256":"9c7d14213ed0b9e3fef15920fb500b46d87891265a7c1e7ca0a73b37bcdbbb65","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9c7d14213ed0b9e3fef15920fb500b46d87891265a7c1e7ca0a73b37bcdbbb65","first_computed_at":"2026-05-18T01:17:47.525511Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:17:47.525511Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cSVXfgU4lD0BmFLI7a7DA0epdu3fj5z0YpEcJ491OVEgR0eB3MP/dZuSKSjxMaRdvOFT+L/7SsSuu/uMhYK4Cw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:17:47.526186Z","signed_message":"canonical_sha256_bytes"},"source_id":"1604.00995","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2900a9c7ba753502c6bf5270b74aefb6ab4ebe0dc9abed0884a76c4969c389e8","sha256:656fc26fd784399a0b57a3358b261304c2a13afe453afc6fc5c20cccfef035d5"],"state_sha256":"de8a6d7eb118633f2ff41d8a387dfdd6e8c2981782638f8dbbd6c9bf17f7fa61"}