{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:QOJN4NNFCKWDNZRL2LXWS6VJUJ","short_pith_number":"pith:QOJN4NNF","schema_version":"1.0","canonical_sha256":"8392de35a512ac36e62bd2ef697aa9a2490df6e92b76d3be076c372f3fdae769","source":{"kind":"arxiv","id":"1607.02087","version":1},"attestation_state":"computed","paper":{"title":"Minimising Dirichlet eigenvalues on cuboids of unit measure","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"Katie Gittins, Michiel van den Berg","submitted_at":"2016-07-07T17:20:41Z","abstract_excerpt":"We consider the minimisation of Dirichlet eigenvalues $\\lambda_k$, $k \\in \\N$, of the Laplacian on cuboids of unit measure in $\\R^3$. We prove that any sequence of optimal cuboids in $\\R^3$ converges to a cube of unit measure in the sense of Hausdorff as $k \\rightarrow \\infty$."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1607.02087","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2016-07-07T17:20:41Z","cross_cats_sorted":[],"title_canon_sha256":"9989a8711bd223d587f433d183bacbb92192a16735c95f943bdf8a92996fc9f5","abstract_canon_sha256":"ac770ce653198ed73d26e55273a92d743511f3f7c35192af13a35904fb94a89c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:48:17.503492Z","signature_b64":"Q7/LXrUKVJa/DObzIUMzVIEMU0i/QrZcnQiJBiH5zaGBNoVD9ICl198v5+EwFCdxRCKgHvwGYGiamX/LjshUBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8392de35a512ac36e62bd2ef697aa9a2490df6e92b76d3be076c372f3fdae769","last_reissued_at":"2026-05-18T00:48:17.502882Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:48:17.502882Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Minimising Dirichlet eigenvalues on cuboids of unit measure","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"Katie Gittins, Michiel van den Berg","submitted_at":"2016-07-07T17:20:41Z","abstract_excerpt":"We consider the minimisation of Dirichlet eigenvalues $\\lambda_k$, $k \\in \\N$, of the Laplacian on cuboids of unit measure in $\\R^3$. We prove that any sequence of optimal cuboids in $\\R^3$ converges to a cube of unit measure in the sense of Hausdorff as $k \\rightarrow \\infty$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.02087","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1607.02087","created_at":"2026-05-18T00:48:17.502975+00:00"},{"alias_kind":"arxiv_version","alias_value":"1607.02087v1","created_at":"2026-05-18T00:48:17.502975+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.02087","created_at":"2026-05-18T00:48:17.502975+00:00"},{"alias_kind":"pith_short_12","alias_value":"QOJN4NNFCKWD","created_at":"2026-05-18T12:30:39.010887+00:00"},{"alias_kind":"pith_short_16","alias_value":"QOJN4NNFCKWDNZRL","created_at":"2026-05-18T12:30:39.010887+00:00"},{"alias_kind":"pith_short_8","alias_value":"QOJN4NNF","created_at":"2026-05-18T12:30:39.010887+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/QOJN4NNFCKWDNZRL2LXWS6VJUJ","json":"https://pith.science/pith/QOJN4NNFCKWDNZRL2LXWS6VJUJ.json","graph_json":"https://pith.science/api/pith-number/QOJN4NNFCKWDNZRL2LXWS6VJUJ/graph.json","events_json":"https://pith.science/api/pith-number/QOJN4NNFCKWDNZRL2LXWS6VJUJ/events.json","paper":"https://pith.science/paper/QOJN4NNF"},"agent_actions":{"view_html":"https://pith.science/pith/QOJN4NNFCKWDNZRL2LXWS6VJUJ","download_json":"https://pith.science/pith/QOJN4NNFCKWDNZRL2LXWS6VJUJ.json","view_paper":"https://pith.science/paper/QOJN4NNF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1607.02087&json=true","fetch_graph":"https://pith.science/api/pith-number/QOJN4NNFCKWDNZRL2LXWS6VJUJ/graph.json","fetch_events":"https://pith.science/api/pith-number/QOJN4NNFCKWDNZRL2LXWS6VJUJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QOJN4NNFCKWDNZRL2LXWS6VJUJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QOJN4NNFCKWDNZRL2LXWS6VJUJ/action/storage_attestation","attest_author":"https://pith.science/pith/QOJN4NNFCKWDNZRL2LXWS6VJUJ/action/author_attestation","sign_citation":"https://pith.science/pith/QOJN4NNFCKWDNZRL2LXWS6VJUJ/action/citation_signature","submit_replication":"https://pith.science/pith/QOJN4NNFCKWDNZRL2LXWS6VJUJ/action/replication_record"}},"created_at":"2026-05-18T00:48:17.502975+00:00","updated_at":"2026-05-18T00:48:17.502975+00:00"}