{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:UTC4MAN7CVOZPP7DPH5KFG45ER","short_pith_number":"pith:UTC4MAN7","canonical_record":{"source":{"id":"1703.08243","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SY","submitted_at":"2017-03-23T22:18:36Z","cross_cats_sorted":["cs.RO","math.OC"],"title_canon_sha256":"f7f070669ad1b5da1cac88e799f06fd51e8c0f10c2c14eccf7d1e599c53967a2","abstract_canon_sha256":"1f11c3cd6dbc910c2bd98959b713e7c119c278870c39793d09d96be12818384b"},"schema_version":"1.0"},"canonical_sha256":"a4c5c601bf155d97bfe379faa29b9d247170ca1da55f985488d3b39e45087588","source":{"kind":"arxiv","id":"1703.08243","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.08243","created_at":"2026-05-18T00:47:45Z"},{"alias_kind":"arxiv_version","alias_value":"1703.08243v3","created_at":"2026-05-18T00:47:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.08243","created_at":"2026-05-18T00:47:45Z"},{"alias_kind":"pith_short_12","alias_value":"UTC4MAN7CVOZ","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_16","alias_value":"UTC4MAN7CVOZPP7D","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_8","alias_value":"UTC4MAN7","created_at":"2026-05-18T12:31:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:UTC4MAN7CVOZPP7DPH5KFG45ER","target":"record","payload":{"canonical_record":{"source":{"id":"1703.08243","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SY","submitted_at":"2017-03-23T22:18:36Z","cross_cats_sorted":["cs.RO","math.OC"],"title_canon_sha256":"f7f070669ad1b5da1cac88e799f06fd51e8c0f10c2c14eccf7d1e599c53967a2","abstract_canon_sha256":"1f11c3cd6dbc910c2bd98959b713e7c119c278870c39793d09d96be12818384b"},"schema_version":"1.0"},"canonical_sha256":"a4c5c601bf155d97bfe379faa29b9d247170ca1da55f985488d3b39e45087588","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:47:45.267673Z","signature_b64":"KMSmi7UOwvTv8zHj3kvIc/83BDObTrWvmeRFIMwwoPNp7+Wudpd4m6RfJ7qn9XMvETyu5v7AlFdWl0yjs4QrCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a4c5c601bf155d97bfe379faa29b9d247170ca1da55f985488d3b39e45087588","last_reissued_at":"2026-05-18T00:47:45.267006Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:47:45.267006Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1703.08243","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":"2026-05-18T00:47:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+j7sb6E1nDBfFTVDS2U5Yraq2Zs0o7LxgncTqa9vyzOdj7cFaqyOtiFlB7aL3AasIWmDHgz8oYYXepn2lhidDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T05:17:21.592270Z"},"content_sha256":"02acab1e64ef30235b81f5365513098dff1bcb39b1fe8b3af093fd0e32c09de4","schema_version":"1.0","event_id":"sha256:02acab1e64ef30235b81f5365513098dff1bcb39b1fe8b3af093fd0e32c09de4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:UTC4MAN7CVOZPP7DPH5KFG45ER","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Mean-Field Controllability and Decentralized Stabilization of Markov Chains, Part I: Global Controllability and Rational Feedbacks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.RO","math.OC"],"primary_cat":"cs.SY","authors_text":"Karthik Elamvazhuthi, Matthias kawski, Spring Berman, Vaibhav Deshmukh","submitted_at":"2017-03-23T22:18:36Z","abstract_excerpt":"In this paper, we study the controllability and stabilizability properties of the Kolmogorov forward equation of a continuous time Markov chain (CTMC) evolving on a finite state space, using the transition rates as the control parameters. Firstly, we prove small-time local and global controllability from and to strictly positive equilibrium configurations when the underlying graph is strongly connected. Secondly, we show that there always exists a locally exponentially stabilizing decentralized linear (density-)feedback law that takes zero valu at equilibrium and respects the graph structure, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.08243","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":"2026-05-18T00:47:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hkDUUORU99dDxMMIz3LHLBGOyTTIqQZyA4+tXbJYQntcIUeY8OWKPIu6t1FJZ76bTSIHgVgvI7VNXB8svGXDDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T05:17:21.592639Z"},"content_sha256":"373b3b8a12cd0f7f06682e89d27dbd6853e5a30bef976e1e93e2c74980dcfeac","schema_version":"1.0","event_id":"sha256:373b3b8a12cd0f7f06682e89d27dbd6853e5a30bef976e1e93e2c74980dcfeac"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UTC4MAN7CVOZPP7DPH5KFG45ER/bundle.json","state_url":"https://pith.science/pith/UTC4MAN7CVOZPP7DPH5KFG45ER/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UTC4MAN7CVOZPP7DPH5KFG45ER/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":"2026-06-01T05:17:21Z","links":{"resolver":"https://pith.science/pith/UTC4MAN7CVOZPP7DPH5KFG45ER","bundle":"https://pith.science/pith/UTC4MAN7CVOZPP7DPH5KFG45ER/bundle.json","state":"https://pith.science/pith/UTC4MAN7CVOZPP7DPH5KFG45ER/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UTC4MAN7CVOZPP7DPH5KFG45ER/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:UTC4MAN7CVOZPP7DPH5KFG45ER","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":"1f11c3cd6dbc910c2bd98959b713e7c119c278870c39793d09d96be12818384b","cross_cats_sorted":["cs.RO","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SY","submitted_at":"2017-03-23T22:18:36Z","title_canon_sha256":"f7f070669ad1b5da1cac88e799f06fd51e8c0f10c2c14eccf7d1e599c53967a2"},"schema_version":"1.0","source":{"id":"1703.08243","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.08243","created_at":"2026-05-18T00:47:45Z"},{"alias_kind":"arxiv_version","alias_value":"1703.08243v3","created_at":"2026-05-18T00:47:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.08243","created_at":"2026-05-18T00:47:45Z"},{"alias_kind":"pith_short_12","alias_value":"UTC4MAN7CVOZ","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_16","alias_value":"UTC4MAN7CVOZPP7D","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_8","alias_value":"UTC4MAN7","created_at":"2026-05-18T12:31:49Z"}],"graph_snapshots":[{"event_id":"sha256:373b3b8a12cd0f7f06682e89d27dbd6853e5a30bef976e1e93e2c74980dcfeac","target":"graph","created_at":"2026-05-18T00:47:45Z","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 paper, we study the controllability and stabilizability properties of the Kolmogorov forward equation of a continuous time Markov chain (CTMC) evolving on a finite state space, using the transition rates as the control parameters. Firstly, we prove small-time local and global controllability from and to strictly positive equilibrium configurations when the underlying graph is strongly connected. Secondly, we show that there always exists a locally exponentially stabilizing decentralized linear (density-)feedback law that takes zero valu at equilibrium and respects the graph structure, ","authors_text":"Karthik Elamvazhuthi, Matthias kawski, Spring Berman, Vaibhav Deshmukh","cross_cats":["cs.RO","math.OC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SY","submitted_at":"2017-03-23T22:18:36Z","title":"Mean-Field Controllability and Decentralized Stabilization of Markov Chains, Part I: Global Controllability and Rational Feedbacks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.08243","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":"sha256:02acab1e64ef30235b81f5365513098dff1bcb39b1fe8b3af093fd0e32c09de4","target":"record","created_at":"2026-05-18T00:47:45Z","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":"1f11c3cd6dbc910c2bd98959b713e7c119c278870c39793d09d96be12818384b","cross_cats_sorted":["cs.RO","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SY","submitted_at":"2017-03-23T22:18:36Z","title_canon_sha256":"f7f070669ad1b5da1cac88e799f06fd51e8c0f10c2c14eccf7d1e599c53967a2"},"schema_version":"1.0","source":{"id":"1703.08243","kind":"arxiv","version":3}},"canonical_sha256":"a4c5c601bf155d97bfe379faa29b9d247170ca1da55f985488d3b39e45087588","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a4c5c601bf155d97bfe379faa29b9d247170ca1da55f985488d3b39e45087588","first_computed_at":"2026-05-18T00:47:45.267006Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:47:45.267006Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KMSmi7UOwvTv8zHj3kvIc/83BDObTrWvmeRFIMwwoPNp7+Wudpd4m6RfJ7qn9XMvETyu5v7AlFdWl0yjs4QrCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:47:45.267673Z","signed_message":"canonical_sha256_bytes"},"source_id":"1703.08243","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:02acab1e64ef30235b81f5365513098dff1bcb39b1fe8b3af093fd0e32c09de4","sha256:373b3b8a12cd0f7f06682e89d27dbd6853e5a30bef976e1e93e2c74980dcfeac"],"state_sha256":"be37b2648f0c99387ee4d3331c7b3e6527ee550b3b4fc17fe4de834decd80dcd"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GXyHBeciKJFX9tvwBl0gmxhDpP9H8JrmhC+5bnvK/MtpOSYNJr3f5qk0nlklH4Drm0Fl8zQm98qAyGBtpmVCBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T05:17:21.594739Z","bundle_sha256":"3f65e490c2f4a8af2a516de7e9e4f97685f09af29676062c6e669ca790b18dd0"}}