{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:MEKFXZ5H46UUBZCE5TUL35IEZP","short_pith_number":"pith:MEKFXZ5H","schema_version":"1.0","canonical_sha256":"61145be7a7e7a940e444ece8bdf504cbffac57c8102c43fef1f795a6decaec52","source":{"kind":"arxiv","id":"1501.01256","version":3},"attestation_state":"computed","paper":{"title":"On the controlled eigenvalue problem for stochastically perturbed multi-channel systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Getachew K. Befekadu","submitted_at":"2015-01-06T18:06:49Z","abstract_excerpt":"In this brief paper, we consider the problem of minimizing the asymptotic exit rate of diffusion processes from an open connected bounded set pertaining to a multi-channel system with small random perturbations. Specifically, we establish a connection between: (i) the existence of an invariant set for the unperturbed multi-channel system w.r.t. certain class of state-feedback controllers; and (ii) the asymptotic behavior of the principal eigenvalues and the solutions of the Hamilton-Jacobi-Bellman (HJB) equations corresponding to a family of singularly perturbed elliptic operators. Finally, we"},"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":"1501.01256","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-01-06T18:06:49Z","cross_cats_sorted":[],"title_canon_sha256":"1b1709645531fe1a4f060199212573e9ad9f04f4f42d5ca3bae4f8406db0e976","abstract_canon_sha256":"dfa5841903bc3ac5061bfcd7d7559ba84953c8d3590cf5b67b8f35766f6c6b38"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:03:24.056529Z","signature_b64":"EB8HtVKkloCJwO3f6QeiPrJHdJTX5yfvshNtV195Z6wzo8OkQm2TAn29CFB95eeu7twn96sfd0dubVDygBQPDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"61145be7a7e7a940e444ece8bdf504cbffac57c8102c43fef1f795a6decaec52","last_reissued_at":"2026-05-18T01:03:24.056036Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:03:24.056036Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the controlled eigenvalue problem for stochastically perturbed multi-channel systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Getachew K. Befekadu","submitted_at":"2015-01-06T18:06:49Z","abstract_excerpt":"In this brief paper, we consider the problem of minimizing the asymptotic exit rate of diffusion processes from an open connected bounded set pertaining to a multi-channel system with small random perturbations. Specifically, we establish a connection between: (i) the existence of an invariant set for the unperturbed multi-channel system w.r.t. certain class of state-feedback controllers; and (ii) the asymptotic behavior of the principal eigenvalues and the solutions of the Hamilton-Jacobi-Bellman (HJB) equations corresponding to a family of singularly perturbed elliptic operators. Finally, we"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.01256","kind":"arxiv","version":3},"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":"1501.01256","created_at":"2026-05-18T01:03:24.056117+00:00"},{"alias_kind":"arxiv_version","alias_value":"1501.01256v3","created_at":"2026-05-18T01:03:24.056117+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.01256","created_at":"2026-05-18T01:03:24.056117+00:00"},{"alias_kind":"pith_short_12","alias_value":"MEKFXZ5H46UU","created_at":"2026-05-18T12:29:32.376354+00:00"},{"alias_kind":"pith_short_16","alias_value":"MEKFXZ5H46UUBZCE","created_at":"2026-05-18T12:29:32.376354+00:00"},{"alias_kind":"pith_short_8","alias_value":"MEKFXZ5H","created_at":"2026-05-18T12:29:32.376354+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/MEKFXZ5H46UUBZCE5TUL35IEZP","json":"https://pith.science/pith/MEKFXZ5H46UUBZCE5TUL35IEZP.json","graph_json":"https://pith.science/api/pith-number/MEKFXZ5H46UUBZCE5TUL35IEZP/graph.json","events_json":"https://pith.science/api/pith-number/MEKFXZ5H46UUBZCE5TUL35IEZP/events.json","paper":"https://pith.science/paper/MEKFXZ5H"},"agent_actions":{"view_html":"https://pith.science/pith/MEKFXZ5H46UUBZCE5TUL35IEZP","download_json":"https://pith.science/pith/MEKFXZ5H46UUBZCE5TUL35IEZP.json","view_paper":"https://pith.science/paper/MEKFXZ5H","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1501.01256&json=true","fetch_graph":"https://pith.science/api/pith-number/MEKFXZ5H46UUBZCE5TUL35IEZP/graph.json","fetch_events":"https://pith.science/api/pith-number/MEKFXZ5H46UUBZCE5TUL35IEZP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MEKFXZ5H46UUBZCE5TUL35IEZP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MEKFXZ5H46UUBZCE5TUL35IEZP/action/storage_attestation","attest_author":"https://pith.science/pith/MEKFXZ5H46UUBZCE5TUL35IEZP/action/author_attestation","sign_citation":"https://pith.science/pith/MEKFXZ5H46UUBZCE5TUL35IEZP/action/citation_signature","submit_replication":"https://pith.science/pith/MEKFXZ5H46UUBZCE5TUL35IEZP/action/replication_record"}},"created_at":"2026-05-18T01:03:24.056117+00:00","updated_at":"2026-05-18T01:03:24.056117+00:00"}