{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:DBCNCIGV73Q2Y75GTGRBY54K7H","short_pith_number":"pith:DBCNCIGV","schema_version":"1.0","canonical_sha256":"1844d120d5fee1ac7fa699a21c778af9ef1b64e8dfe758a8dc20ff3dc8fe67f2","source":{"kind":"arxiv","id":"1609.01442","version":1},"attestation_state":"computed","paper":{"title":"The Effect of the Schwarz Rearrangement on the Periodic Principal Eigenvalue of a Nonsymmetric Operator","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"math.AP","authors_text":"Gr\\'egoire Nadin (LJLL)","submitted_at":"2016-09-06T08:59:59Z","abstract_excerpt":"This paper is concerned with the periodic principal eigenvalue $k_\\lambda(\\mu)$ associated with the operator $- {d^2\\over dx^2} - 2\\lambda {d\\over dx} - \\mu(x) - \\lambda^2$ , (1) where $\\lambda\\in \\mathbb{R}$ and $\\mu$ is continuous and periodic in $x\\in\\mathbb{R}$. Our main result is that $k_\\lambda(\\mu^*) \\le k_\\lambda(\\mu)$, where $\\mu^*$ is the Schwarz rearrangement of the function $\\mu$. From a population dynamics point of view, using reaction-diffusion modeling, this result means that the fragmentation of the habitat of an invading population slows down the invasion. We prove that this p"},"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":"1609.01442","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-09-06T08:59:59Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"f1e9b3866e1c949a6f6ff26948709b5838d2191fee6fb5c009c321b222960297","abstract_canon_sha256":"411423780707ed6a8524d8b8513d223d165e26f830379e14b911eca8040e3d72"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:05:39.569594Z","signature_b64":"iEjZD5JqNQVIzHj1dZ8WWeRUrSuBmAQza3MXHl0FVopijfbEdcC30+bzvd6QOHT2VXZCDdZhC5/qHtWPK6WOCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1844d120d5fee1ac7fa699a21c778af9ef1b64e8dfe758a8dc20ff3dc8fe67f2","last_reissued_at":"2026-05-18T01:05:39.569203Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:05:39.569203Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Effect of the Schwarz Rearrangement on the Periodic Principal Eigenvalue of a Nonsymmetric Operator","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"math.AP","authors_text":"Gr\\'egoire Nadin (LJLL)","submitted_at":"2016-09-06T08:59:59Z","abstract_excerpt":"This paper is concerned with the periodic principal eigenvalue $k_\\lambda(\\mu)$ associated with the operator $- {d^2\\over dx^2} - 2\\lambda {d\\over dx} - \\mu(x) - \\lambda^2$ , (1) where $\\lambda\\in \\mathbb{R}$ and $\\mu$ is continuous and periodic in $x\\in\\mathbb{R}$. Our main result is that $k_\\lambda(\\mu^*) \\le k_\\lambda(\\mu)$, where $\\mu^*$ is the Schwarz rearrangement of the function $\\mu$. From a population dynamics point of view, using reaction-diffusion modeling, this result means that the fragmentation of the habitat of an invading population slows down the invasion. We prove that this p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.01442","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":"1609.01442","created_at":"2026-05-18T01:05:39.569261+00:00"},{"alias_kind":"arxiv_version","alias_value":"1609.01442v1","created_at":"2026-05-18T01:05:39.569261+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.01442","created_at":"2026-05-18T01:05:39.569261+00:00"},{"alias_kind":"pith_short_12","alias_value":"DBCNCIGV73Q2","created_at":"2026-05-18T12:30:09.641336+00:00"},{"alias_kind":"pith_short_16","alias_value":"DBCNCIGV73Q2Y75G","created_at":"2026-05-18T12:30:09.641336+00:00"},{"alias_kind":"pith_short_8","alias_value":"DBCNCIGV","created_at":"2026-05-18T12:30:09.641336+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/DBCNCIGV73Q2Y75GTGRBY54K7H","json":"https://pith.science/pith/DBCNCIGV73Q2Y75GTGRBY54K7H.json","graph_json":"https://pith.science/api/pith-number/DBCNCIGV73Q2Y75GTGRBY54K7H/graph.json","events_json":"https://pith.science/api/pith-number/DBCNCIGV73Q2Y75GTGRBY54K7H/events.json","paper":"https://pith.science/paper/DBCNCIGV"},"agent_actions":{"view_html":"https://pith.science/pith/DBCNCIGV73Q2Y75GTGRBY54K7H","download_json":"https://pith.science/pith/DBCNCIGV73Q2Y75GTGRBY54K7H.json","view_paper":"https://pith.science/paper/DBCNCIGV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1609.01442&json=true","fetch_graph":"https://pith.science/api/pith-number/DBCNCIGV73Q2Y75GTGRBY54K7H/graph.json","fetch_events":"https://pith.science/api/pith-number/DBCNCIGV73Q2Y75GTGRBY54K7H/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DBCNCIGV73Q2Y75GTGRBY54K7H/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DBCNCIGV73Q2Y75GTGRBY54K7H/action/storage_attestation","attest_author":"https://pith.science/pith/DBCNCIGV73Q2Y75GTGRBY54K7H/action/author_attestation","sign_citation":"https://pith.science/pith/DBCNCIGV73Q2Y75GTGRBY54K7H/action/citation_signature","submit_replication":"https://pith.science/pith/DBCNCIGV73Q2Y75GTGRBY54K7H/action/replication_record"}},"created_at":"2026-05-18T01:05:39.569261+00:00","updated_at":"2026-05-18T01:05:39.569261+00:00"}