{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:DXJGLK73QEXMUOIOTRGEEZNFCM","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":"f77cf244f0d4dec0c7ccfb0ebd07e2538a035cfbc302d16b902fbd8b53957e9a","cross_cats_sorted":["math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-06-21T09:23:41Z","title_canon_sha256":"78e9bc6dba0f90aaf9c0937f7b9b4035b848d8dc8c0d0d0a166b171c76b99639"},"schema_version":"1.0","source":{"id":"1706.07282","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.07282","created_at":"2026-05-18T00:01:10Z"},{"alias_kind":"arxiv_version","alias_value":"1706.07282v1","created_at":"2026-05-18T00:01:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.07282","created_at":"2026-05-18T00:01:10Z"},{"alias_kind":"pith_short_12","alias_value":"DXJGLK73QEXM","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_16","alias_value":"DXJGLK73QEXMUOIO","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_8","alias_value":"DXJGLK73","created_at":"2026-05-18T12:31:12Z"}],"graph_snapshots":[{"event_id":"sha256:01b358ee23931dd867bf296a1b38d000e9231d676350e00d2c9af314c1187f71","target":"graph","created_at":"2026-05-18T00:01:10Z","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":"We develop the notion of higher Cheeger constants for a measurable set $\\Omega \\subset \\mathbb{R}^N$. By the $k$-th Cheeger constant we mean the value \\[h_k(\\Omega) = \\inf \\max \\{h_1(E_1), \\dots, h_1(E_k)\\},\\] where the infimum is taken over all $k$-tuples of mutually disjoint subsets of $\\Omega$, and $h_1(E_i)$ is the classical Cheeger constant of $E_i$. We prove the existence of minimizers satisfying additional \"adjustment\" conditions and study their properties. A relation between $h_k(\\Omega)$ and spectral minimal $k$-partitions of $\\Omega$ associated with the first eigenvalues of the $p$-L","authors_text":"Enea Parini, Vladimir Bobkov","cross_cats":["math.OC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-06-21T09:23:41Z","title":"On the higher Cheeger problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.07282","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":"sha256:1bcc657188f6b5adc59ccd9b5b746de41a38b66e69f3b0f3880f89f26e006034","target":"record","created_at":"2026-05-18T00:01:10Z","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":"f77cf244f0d4dec0c7ccfb0ebd07e2538a035cfbc302d16b902fbd8b53957e9a","cross_cats_sorted":["math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-06-21T09:23:41Z","title_canon_sha256":"78e9bc6dba0f90aaf9c0937f7b9b4035b848d8dc8c0d0d0a166b171c76b99639"},"schema_version":"1.0","source":{"id":"1706.07282","kind":"arxiv","version":1}},"canonical_sha256":"1dd265abfb812eca390e9c4c4265a5132a498c9b3aeebc782d1d67693ca38f63","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1dd265abfb812eca390e9c4c4265a5132a498c9b3aeebc782d1d67693ca38f63","first_computed_at":"2026-05-18T00:01:10.410735Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:01:10.410735Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BDCJtkJH9jjPGqOEMyKq5n4eM4KBLlfi3cbAcOfKcJqXAfrn82unQwFzTmCS/opC/CjXDXVhN50Zq7xgYy2EBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:01:10.411429Z","signed_message":"canonical_sha256_bytes"},"source_id":"1706.07282","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1bcc657188f6b5adc59ccd9b5b746de41a38b66e69f3b0f3880f89f26e006034","sha256:01b358ee23931dd867bf296a1b38d000e9231d676350e00d2c9af314c1187f71"],"state_sha256":"e2597cae55f075c3fc97daffa87f2cfa5acbd4fabdfc8180da062f71d7d75dd1"}