{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:Y252ZKGNPS4RII332HNOSPF2DV","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":"6657f8d5d2e09f70d1f4f768131e0d9a85ffa7f9a3ced0c392bcdd152c230222","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-04-24T14:22:00Z","title_canon_sha256":"ea54343f228d79a4b4e30b73e442c029c22f8444c343ae325c8ebef7ebd7c18a"},"schema_version":"1.0","source":{"id":"1704.07253","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.07253","created_at":"2026-05-18T00:22:16Z"},{"alias_kind":"arxiv_version","alias_value":"1704.07253v3","created_at":"2026-05-18T00:22:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.07253","created_at":"2026-05-18T00:22:16Z"},{"alias_kind":"pith_short_12","alias_value":"Y252ZKGNPS4R","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_16","alias_value":"Y252ZKGNPS4RII33","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_8","alias_value":"Y252ZKGN","created_at":"2026-05-18T12:31:56Z"}],"graph_snapshots":[{"event_id":"sha256:307abcf4652de8c50dc9e6324f985a228543e4b9e87c0be40083b7cfb3be824c","target":"graph","created_at":"2026-05-18T00:22:16Z","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 show that the maximal Cheeger set of a Jordan domain $\\Omega$ without necks is the union of all balls of radius $r = h(\\Omega)^{-1}$ contained in $\\Omega$. Here, $h(\\Omega)$ denotes the Cheeger constant of $\\Omega$, that is, the infimum of the ratio of perimeter over area among subsets of $\\Omega$, and a Cheeger set is a set attaining the infimum. The radius $r$ is shown to be the unique number such that the area of the inner parallel set $\\Omega^r$ is equal to $\\pi r^2$. The proof of the main theorem requires the combination of several intermediate facts, some of which are of interest in t","authors_text":"Gian Paolo Leonardi, Giorgio Saracco, Robin Neumayer","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-04-24T14:22:00Z","title":"The Cheeger constant of a Jordan domain without necks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.07253","kind":"arxiv","version":3},"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:bdb606ddfcc5127b8effc6564b8716bfb92c03fa9e241a4116f69db311046c03","target":"record","created_at":"2026-05-18T00:22:16Z","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":"6657f8d5d2e09f70d1f4f768131e0d9a85ffa7f9a3ced0c392bcdd152c230222","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-04-24T14:22:00Z","title_canon_sha256":"ea54343f228d79a4b4e30b73e442c029c22f8444c343ae325c8ebef7ebd7c18a"},"schema_version":"1.0","source":{"id":"1704.07253","kind":"arxiv","version":3}},"canonical_sha256":"c6bbaca8cd7cb914237bd1dae93cba1d60049899cb35a5dfe1b3611d1a7c607e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c6bbaca8cd7cb914237bd1dae93cba1d60049899cb35a5dfe1b3611d1a7c607e","first_computed_at":"2026-05-18T00:22:16.263844Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:22:16.263844Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YwOsmkZQWy44M7/KyDSdoVd/t1QRSGeeHi1EItq2xBRuXiTlNF8UixwhZh3VoOcDhiNuh+qvY+KRxiPu3dhGAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:22:16.264592Z","signed_message":"canonical_sha256_bytes"},"source_id":"1704.07253","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bdb606ddfcc5127b8effc6564b8716bfb92c03fa9e241a4116f69db311046c03","sha256:307abcf4652de8c50dc9e6324f985a228543e4b9e87c0be40083b7cfb3be824c"],"state_sha256":"d853943d388d8602bbdcf5b662d8a69cdb8810301277589880adae2d008d4932"}