{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:MEKFXZ5H46UUBZCE5TUL35IEZP","short_pith_number":"pith:MEKFXZ5H","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"},"canonical_sha256":"61145be7a7e7a940e444ece8bdf504cbffac57c8102c43fef1f795a6decaec52","source":{"kind":"arxiv","id":"1501.01256","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.01256","created_at":"2026-05-18T01:03:24Z"},{"alias_kind":"arxiv_version","alias_value":"1501.01256v3","created_at":"2026-05-18T01:03:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.01256","created_at":"2026-05-18T01:03:24Z"},{"alias_kind":"pith_short_12","alias_value":"MEKFXZ5H46UU","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_16","alias_value":"MEKFXZ5H46UUBZCE","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_8","alias_value":"MEKFXZ5H","created_at":"2026-05-18T12:29:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:MEKFXZ5H46UUBZCE5TUL35IEZP","target":"record","payload":{"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"},"canonical_sha256":"61145be7a7e7a940e444ece8bdf504cbffac57c8102c43fef1f795a6decaec52","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"},"source_kind":"arxiv","source_id":"1501.01256","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:03:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qr4FXz/196Iv0+oblOPzmWch9MAqzNsMKV58nfggSPUrl5UG65ZymfkAlearPqTNLzqgCyX/VRXqDoTE/ZXMCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T22:27:55.006591Z"},"content_sha256":"eec465a996820c20db4a83636353211d99639a07b6c21ee9e900c153b8dbadd6","schema_version":"1.0","event_id":"sha256:eec465a996820c20db4a83636353211d99639a07b6c21ee9e900c153b8dbadd6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:MEKFXZ5H46UUBZCE5TUL35IEZP","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:03:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RgE1z2haZgehwHRN8G4zE0NrvOEgoPhuVCKO0OEMA3C+yBy2Q79OaHPPgypHN81Lr6i+o/An78JqGyIw4ykmBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T22:27:55.006935Z"},"content_sha256":"153cfe7fc8d8567affe395cf9517a534d930a34b1ec21d5a6176e901dd2a48e1","schema_version":"1.0","event_id":"sha256:153cfe7fc8d8567affe395cf9517a534d930a34b1ec21d5a6176e901dd2a48e1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MEKFXZ5H46UUBZCE5TUL35IEZP/bundle.json","state_url":"https://pith.science/pith/MEKFXZ5H46UUBZCE5TUL35IEZP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MEKFXZ5H46UUBZCE5TUL35IEZP/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-30T22:27:55Z","links":{"resolver":"https://pith.science/pith/MEKFXZ5H46UUBZCE5TUL35IEZP","bundle":"https://pith.science/pith/MEKFXZ5H46UUBZCE5TUL35IEZP/bundle.json","state":"https://pith.science/pith/MEKFXZ5H46UUBZCE5TUL35IEZP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MEKFXZ5H46UUBZCE5TUL35IEZP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:MEKFXZ5H46UUBZCE5TUL35IEZP","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":"dfa5841903bc3ac5061bfcd7d7559ba84953c8d3590cf5b67b8f35766f6c6b38","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-01-06T18:06:49Z","title_canon_sha256":"1b1709645531fe1a4f060199212573e9ad9f04f4f42d5ca3bae4f8406db0e976"},"schema_version":"1.0","source":{"id":"1501.01256","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.01256","created_at":"2026-05-18T01:03:24Z"},{"alias_kind":"arxiv_version","alias_value":"1501.01256v3","created_at":"2026-05-18T01:03:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.01256","created_at":"2026-05-18T01:03:24Z"},{"alias_kind":"pith_short_12","alias_value":"MEKFXZ5H46UU","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_16","alias_value":"MEKFXZ5H46UUBZCE","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_8","alias_value":"MEKFXZ5H","created_at":"2026-05-18T12:29:32Z"}],"graph_snapshots":[{"event_id":"sha256:153cfe7fc8d8567affe395cf9517a534d930a34b1ec21d5a6176e901dd2a48e1","target":"graph","created_at":"2026-05-18T01:03:24Z","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"},"paper":{"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","authors_text":"Getachew K. Befekadu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-01-06T18:06:49Z","title":"On the controlled eigenvalue problem for stochastically perturbed multi-channel systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.01256","kind":"arxiv","version":3},"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:eec465a996820c20db4a83636353211d99639a07b6c21ee9e900c153b8dbadd6","target":"record","created_at":"2026-05-18T01:03:24Z","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":"dfa5841903bc3ac5061bfcd7d7559ba84953c8d3590cf5b67b8f35766f6c6b38","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-01-06T18:06:49Z","title_canon_sha256":"1b1709645531fe1a4f060199212573e9ad9f04f4f42d5ca3bae4f8406db0e976"},"schema_version":"1.0","source":{"id":"1501.01256","kind":"arxiv","version":3}},"canonical_sha256":"61145be7a7e7a940e444ece8bdf504cbffac57c8102c43fef1f795a6decaec52","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"61145be7a7e7a940e444ece8bdf504cbffac57c8102c43fef1f795a6decaec52","first_computed_at":"2026-05-18T01:03:24.056036Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:03:24.056036Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"EB8HtVKkloCJwO3f6QeiPrJHdJTX5yfvshNtV195Z6wzo8OkQm2TAn29CFB95eeu7twn96sfd0dubVDygBQPDw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:03:24.056529Z","signed_message":"canonical_sha256_bytes"},"source_id":"1501.01256","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:eec465a996820c20db4a83636353211d99639a07b6c21ee9e900c153b8dbadd6","sha256:153cfe7fc8d8567affe395cf9517a534d930a34b1ec21d5a6176e901dd2a48e1"],"state_sha256":"7a3e73dc9593b06c43b7cbc1af7a5f6bdc1460871268f713fda781bcfc2e769d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"m4+VldCpSrLYMwXVICjOfiLzl303S9b7AeUouLCp4MED8cTree9aRipuXH2reSeGpIMtxtp291OE38cZ310RBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T22:27:55.009054Z","bundle_sha256":"d8bc737b4c54949949149eed6855b0061a90963c725600ac014c9512a2fdf114"}}