{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:TRUGLF43VVDPECWTRKDUHVIRKM","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":"3d99c854c1ff784b941a2a8d182f1442e4d32aad99ac79b6f41fffe0452e4b63","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2025-10-01T12:17:40Z","title_canon_sha256":"6f1faff19cbe8385175315438013e91171479991c7aa59cc6eb6918492596204"},"schema_version":"1.0","source":{"id":"2510.00811","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2510.00811","created_at":"2026-07-30T01:19:11Z"},{"alias_kind":"arxiv_version","alias_value":"2510.00811v2","created_at":"2026-07-30T01:19:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2510.00811","created_at":"2026-07-30T01:19:11Z"},{"alias_kind":"pith_short_12","alias_value":"TRUGLF43VVDP","created_at":"2026-07-30T01:19:11Z"},{"alias_kind":"pith_short_16","alias_value":"TRUGLF43VVDPECWT","created_at":"2026-07-30T01:19:11Z"},{"alias_kind":"pith_short_8","alias_value":"TRUGLF43","created_at":"2026-07-30T01:19:11Z"}],"graph_snapshots":[{"event_id":"sha256:c1b297a3103ea941fb6ec22a29c35d36f555297488b0000579092d41d5f72a3f","target":"graph","created_at":"2026-07-30T01:19:11Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2510.00811/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study the problem of constructing $k$-spectral minimal partitions of domains in $d$ dimensions, where the energy functional to be minimized is a $p$-norm ($1 \\le p \\le \\infty$) of the infimum of the spectrum of a suitable Schr\\\"odinger operator $-\\Delta +V$, with Dirichlet conditions on the boundary of the partition elements (cells). The main novelty of this paper is that the domains may be unbounded, including of infinite volume.\n  First, we prove a sharp upper bound for the infimal energy among all $k$-partitions by a threshold value which involves the infimum $\\Sigma$ of the essential sp","authors_text":"Hugo Tavares, James B. Kennedy, Matthias Hofmann","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2025-10-01T12:17:40Z","title":"Spectral minimal partitions of unbounded domains"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2510.00811","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":"sha256:25b6250bb8e9041dcdb015402f59623a6065c6b7a1eeb5bf3acd34907498fb32","target":"record","created_at":"2026-07-30T01:19:11Z","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":"3d99c854c1ff784b941a2a8d182f1442e4d32aad99ac79b6f41fffe0452e4b63","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2025-10-01T12:17:40Z","title_canon_sha256":"6f1faff19cbe8385175315438013e91171479991c7aa59cc6eb6918492596204"},"schema_version":"1.0","source":{"id":"2510.00811","kind":"arxiv","version":2}},"canonical_sha256":"9c6865979bad46f20ad38a8743d5115301b2d920b1deb1cde241942ed6e3b0b8","receipt":{"builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9c6865979bad46f20ad38a8743d5115301b2d920b1deb1cde241942ed6e3b0b8","first_computed_at":"2026-07-30T01:19:11.857114Z","kind":"pith_receipt","last_reissued_at":"2026-07-30T01:19:11.857114Z","receipt_version":"0.3","signature_status":"unsigned_v0"},"source_id":"2510.00811","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:25b6250bb8e9041dcdb015402f59623a6065c6b7a1eeb5bf3acd34907498fb32","sha256:c1b297a3103ea941fb6ec22a29c35d36f555297488b0000579092d41d5f72a3f"],"state_sha256":"950595ad306b207212d579b07ab36945f63b40f7b1a0842cadd872809f315791"}