{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:GNNYHZUD4QQX6TW5NT5BJ3XWCC","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":"b4bbda849ea270e77516027a155dc34a72642eeed3863ba43a3363fd9286d359","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-05-05T03:29:07Z","title_canon_sha256":"82c90657a5a12557ffcf77046bf363dae9b3b419a80c37a5fc7352bb2cf3c175"},"schema_version":"1.0","source":{"id":"1605.01482","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.01482","created_at":"2026-05-18T01:15:33Z"},{"alias_kind":"arxiv_version","alias_value":"1605.01482v1","created_at":"2026-05-18T01:15:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.01482","created_at":"2026-05-18T01:15:33Z"},{"alias_kind":"pith_short_12","alias_value":"GNNYHZUD4QQX","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_16","alias_value":"GNNYHZUD4QQX6TW5","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_8","alias_value":"GNNYHZUD","created_at":"2026-05-18T12:30:19Z"}],"graph_snapshots":[{"event_id":"sha256:cb67b4d322ccf154bd731111c15332d830e20bada3830fa4d3f769d7308a825d","target":"graph","created_at":"2026-05-18T01:15:33Z","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":"Markov-modulated Brownian motion is a popular tool to model continuous-time phenomena in a stochastic context. The main quantity of interest is the invariant density, which satisfies a differential equation associated with the quadratic matrix polynomial $P(z) = Vz^2-Dz +Q$, where the matrices $V$ and $D$ are diagonal and $Q$ is the transition matrix of a discrete-time Markov chain. Its solution is typically constructed by computing an invariant pair of $P(z)$ associated with its eigenvalues in the left half-plane, or by solving the matrix equation $X^2V-XD+Q=0$. We show that these tasks can b","authors_text":"Federico Poloni, Giang T. Nguyen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-05-05T03:29:07Z","title":"Componentwise accurate Brownian motion computations using Cyclic Reduction"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.01482","kind":"arxiv","version":1},"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":"sha256:174aaf404a9fabcd4b90a18013529f06fcaa033784b6d94935afd8fd603d88e0","target":"record","created_at":"2026-05-18T01:15:33Z","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":"b4bbda849ea270e77516027a155dc34a72642eeed3863ba43a3363fd9286d359","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-05-05T03:29:07Z","title_canon_sha256":"82c90657a5a12557ffcf77046bf363dae9b3b419a80c37a5fc7352bb2cf3c175"},"schema_version":"1.0","source":{"id":"1605.01482","kind":"arxiv","version":1}},"canonical_sha256":"335b83e683e4217f4edd6cfa14eef61098901e6f0069999c410ce8cd506e958b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"335b83e683e4217f4edd6cfa14eef61098901e6f0069999c410ce8cd506e958b","first_computed_at":"2026-05-18T01:15:33.571667Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:15:33.571667Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SSDbv2QHoOqcZiJO4ayHvvfMOcFntHxcWEcSXXmAQLmCemQ4JJ2u5tQH0inHuoOlRRUgPwipB3jS4xT/axT2Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:15:33.572662Z","signed_message":"canonical_sha256_bytes"},"source_id":"1605.01482","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:174aaf404a9fabcd4b90a18013529f06fcaa033784b6d94935afd8fd603d88e0","sha256:cb67b4d322ccf154bd731111c15332d830e20bada3830fa4d3f769d7308a825d"],"state_sha256":"96b19d7e35c26f6a263547565e688f87b8a3eb7cb9a2129f8bd8b15ca683b4c7"}