{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:JVRQU62UMLP2NRWGU3SLW527XY","short_pith_number":"pith:JVRQU62U","schema_version":"1.0","canonical_sha256":"4d630a7b5462dfa6c6c6a6e4bb775fbe230688e976e0aa1e638c87f53f43bac0","source":{"kind":"arxiv","id":"1407.5555","version":1},"attestation_state":"computed","paper":{"title":"Global behavior of N competing species with strong diffusion: diffusion leads to exclusion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.AP","authors_text":"CARE), Fran\\c{c}ois Castella (IRMAR, Inria - Irmar), Sten Madec (LMPT), Yvan Lagadeuc (ECOBIO","submitted_at":"2014-07-21T16:36:29Z","abstract_excerpt":"It is known that the competitive exclusion principle holds for a large kind of models involving several species competing for a single resource in an homogeneous environment. Various works indicate that the coexistence is possible in an heterogeneous environment. We propose a spatially heterogeneous system modeling the competition of several species for a single resource. If spatial movements are fast enough, we show that our system can be well approximated by a spatially homogeneous system, called aggregated model, which can be explicitly computed. Moreover, we show that if the competitive ex"},"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":"1407.5555","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-07-21T16:36:29Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"ce725708c53997e594dfeb14d1ff7c51ef51d5203a13f74d6dc9a4d41a5dbdc4","abstract_canon_sha256":"642e800ffdc038fb5095335b89479a9e2cc20e65b74241622b5334fdc1ab9759"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:47:13.768449Z","signature_b64":"ZY8N6J/XUOrQniJjX9PvRh/4LDDZREBhFcLup70NfQVVRm58W/o+L3NzUymBZJBMydfeUzk0GPb70YRhRucuBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4d630a7b5462dfa6c6c6a6e4bb775fbe230688e976e0aa1e638c87f53f43bac0","last_reissued_at":"2026-05-18T02:47:13.767796Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:47:13.767796Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Global behavior of N competing species with strong diffusion: diffusion leads to exclusion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.AP","authors_text":"CARE), Fran\\c{c}ois Castella (IRMAR, Inria - Irmar), Sten Madec (LMPT), Yvan Lagadeuc (ECOBIO","submitted_at":"2014-07-21T16:36:29Z","abstract_excerpt":"It is known that the competitive exclusion principle holds for a large kind of models involving several species competing for a single resource in an homogeneous environment. Various works indicate that the coexistence is possible in an heterogeneous environment. We propose a spatially heterogeneous system modeling the competition of several species for a single resource. If spatial movements are fast enough, we show that our system can be well approximated by a spatially homogeneous system, called aggregated model, which can be explicitly computed. Moreover, we show that if the competitive ex"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.5555","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":"1407.5555","created_at":"2026-05-18T02:47:13.767877+00:00"},{"alias_kind":"arxiv_version","alias_value":"1407.5555v1","created_at":"2026-05-18T02:47:13.767877+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.5555","created_at":"2026-05-18T02:47:13.767877+00:00"},{"alias_kind":"pith_short_12","alias_value":"JVRQU62UMLP2","created_at":"2026-05-18T12:28:35.611951+00:00"},{"alias_kind":"pith_short_16","alias_value":"JVRQU62UMLP2NRWG","created_at":"2026-05-18T12:28:35.611951+00:00"},{"alias_kind":"pith_short_8","alias_value":"JVRQU62U","created_at":"2026-05-18T12:28:35.611951+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/JVRQU62UMLP2NRWGU3SLW527XY","json":"https://pith.science/pith/JVRQU62UMLP2NRWGU3SLW527XY.json","graph_json":"https://pith.science/api/pith-number/JVRQU62UMLP2NRWGU3SLW527XY/graph.json","events_json":"https://pith.science/api/pith-number/JVRQU62UMLP2NRWGU3SLW527XY/events.json","paper":"https://pith.science/paper/JVRQU62U"},"agent_actions":{"view_html":"https://pith.science/pith/JVRQU62UMLP2NRWGU3SLW527XY","download_json":"https://pith.science/pith/JVRQU62UMLP2NRWGU3SLW527XY.json","view_paper":"https://pith.science/paper/JVRQU62U","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1407.5555&json=true","fetch_graph":"https://pith.science/api/pith-number/JVRQU62UMLP2NRWGU3SLW527XY/graph.json","fetch_events":"https://pith.science/api/pith-number/JVRQU62UMLP2NRWGU3SLW527XY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JVRQU62UMLP2NRWGU3SLW527XY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JVRQU62UMLP2NRWGU3SLW527XY/action/storage_attestation","attest_author":"https://pith.science/pith/JVRQU62UMLP2NRWGU3SLW527XY/action/author_attestation","sign_citation":"https://pith.science/pith/JVRQU62UMLP2NRWGU3SLW527XY/action/citation_signature","submit_replication":"https://pith.science/pith/JVRQU62UMLP2NRWGU3SLW527XY/action/replication_record"}},"created_at":"2026-05-18T02:47:13.767877+00:00","updated_at":"2026-05-18T02:47:13.767877+00:00"}