{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:RY5O56UEPG6HIAWSRMN7VRLZTK","short_pith_number":"pith:RY5O56UE","canonical_record":{"source":{"id":"1312.1387","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-12-04T23:50:37Z","cross_cats_sorted":[],"title_canon_sha256":"c93e826cf8be7df4cf47e21991806cfbfee4c04194364ae6080c6bde5f8f99b0","abstract_canon_sha256":"a89c7c6ae87fe1f178190faa5e760aeee0ca27b60dc1fce4a4f3a8086691e881"},"schema_version":"1.0"},"canonical_sha256":"8e3aeefa8479bc7402d28b1bfac5799ab9f815ebbee8683dcba0e57f6a0d9d35","source":{"kind":"arxiv","id":"1312.1387","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.1387","created_at":"2026-05-18T02:32:31Z"},{"alias_kind":"arxiv_version","alias_value":"1312.1387v4","created_at":"2026-05-18T02:32:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.1387","created_at":"2026-05-18T02:32:31Z"},{"alias_kind":"pith_short_12","alias_value":"RY5O56UEPG6H","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_16","alias_value":"RY5O56UEPG6HIAWS","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_8","alias_value":"RY5O56UE","created_at":"2026-05-18T12:27:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:RY5O56UEPG6HIAWSRMN7VRLZTK","target":"record","payload":{"canonical_record":{"source":{"id":"1312.1387","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-12-04T23:50:37Z","cross_cats_sorted":[],"title_canon_sha256":"c93e826cf8be7df4cf47e21991806cfbfee4c04194364ae6080c6bde5f8f99b0","abstract_canon_sha256":"a89c7c6ae87fe1f178190faa5e760aeee0ca27b60dc1fce4a4f3a8086691e881"},"schema_version":"1.0"},"canonical_sha256":"8e3aeefa8479bc7402d28b1bfac5799ab9f815ebbee8683dcba0e57f6a0d9d35","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:32:31.662090Z","signature_b64":"7JXe5zC+moORghrNaLP+buf9AG6CpAUi/LKYpRHIV8Qgklh8EnnqtAzqZ1HHNmE/TeqBhpa1uQG23a4qybRhBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8e3aeefa8479bc7402d28b1bfac5799ab9f815ebbee8683dcba0e57f6a0d9d35","last_reissued_at":"2026-05-18T02:32:31.661483Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:32:31.661483Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1312.1387","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:32:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Zd4EzeP3ND8DUAgiNCZK4vsO33Ip3T3eVT2MDlh0URUTCR/QIZMlFfuaD3vfrB4vrHVGMkX0Gxkt3b2LV2BCBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T18:38:37.954182Z"},"content_sha256":"1629ab148b9a30da6e6e1454d4403633d93f8c3a5b71c0847ac3b5dc643b82ed","schema_version":"1.0","event_id":"sha256:1629ab148b9a30da6e6e1454d4403633d93f8c3a5b71c0847ac3b5dc643b82ed"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:RY5O56UEPG6HIAWSRMN7VRLZTK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Decomposable stationary distribution of a multidimensional SRBM","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"J. G. Dai, Jian Wu, Masakiyo Miyazawa","submitted_at":"2013-12-04T23:50:37Z","abstract_excerpt":"We call a multidimensional distribution to be decomposable with respect to a partition of two sets of coordinates if the original distribution is the product of the marginal distributions associated with these two sets. We focus on the stationary distribution of a multidimensional semimartingale reflecting Brownian motion (SRBM) on a nonnegative orthant. An SRBM is uniquely determined (in distribution) by its data that consists of a covariance matrix, a drift vector, and a reflection matrix. Assume that the stationary distribution of an SRBM exists. We first characterize two marginal distribut"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.1387","kind":"arxiv","version":4},"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":"2026-05-18T02:32:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2ZS70qLRKwuWudiaKKFjwcjs9dHcMIbrNeHiG1SJ3zfLFX0bwION/x5OqakOZ246irp/HC67wsxJIRS2tGhFAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T18:38:37.954925Z"},"content_sha256":"58d355b7cb5e504de35b6b00f6de6840b1622bdcd00c08a37b42c84d7c6cd370","schema_version":"1.0","event_id":"sha256:58d355b7cb5e504de35b6b00f6de6840b1622bdcd00c08a37b42c84d7c6cd370"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RY5O56UEPG6HIAWSRMN7VRLZTK/bundle.json","state_url":"https://pith.science/pith/RY5O56UEPG6HIAWSRMN7VRLZTK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RY5O56UEPG6HIAWSRMN7VRLZTK/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":"2026-06-08T18:38:37Z","links":{"resolver":"https://pith.science/pith/RY5O56UEPG6HIAWSRMN7VRLZTK","bundle":"https://pith.science/pith/RY5O56UEPG6HIAWSRMN7VRLZTK/bundle.json","state":"https://pith.science/pith/RY5O56UEPG6HIAWSRMN7VRLZTK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RY5O56UEPG6HIAWSRMN7VRLZTK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:RY5O56UEPG6HIAWSRMN7VRLZTK","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":"a89c7c6ae87fe1f178190faa5e760aeee0ca27b60dc1fce4a4f3a8086691e881","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-12-04T23:50:37Z","title_canon_sha256":"c93e826cf8be7df4cf47e21991806cfbfee4c04194364ae6080c6bde5f8f99b0"},"schema_version":"1.0","source":{"id":"1312.1387","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.1387","created_at":"2026-05-18T02:32:31Z"},{"alias_kind":"arxiv_version","alias_value":"1312.1387v4","created_at":"2026-05-18T02:32:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.1387","created_at":"2026-05-18T02:32:31Z"},{"alias_kind":"pith_short_12","alias_value":"RY5O56UEPG6H","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_16","alias_value":"RY5O56UEPG6HIAWS","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_8","alias_value":"RY5O56UE","created_at":"2026-05-18T12:27:59Z"}],"graph_snapshots":[{"event_id":"sha256:58d355b7cb5e504de35b6b00f6de6840b1622bdcd00c08a37b42c84d7c6cd370","target":"graph","created_at":"2026-05-18T02:32:31Z","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":"We call a multidimensional distribution to be decomposable with respect to a partition of two sets of coordinates if the original distribution is the product of the marginal distributions associated with these two sets. We focus on the stationary distribution of a multidimensional semimartingale reflecting Brownian motion (SRBM) on a nonnegative orthant. An SRBM is uniquely determined (in distribution) by its data that consists of a covariance matrix, a drift vector, and a reflection matrix. Assume that the stationary distribution of an SRBM exists. We first characterize two marginal distribut","authors_text":"J. G. Dai, Jian Wu, Masakiyo Miyazawa","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-12-04T23:50:37Z","title":"Decomposable stationary distribution of a multidimensional SRBM"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.1387","kind":"arxiv","version":4},"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":"sha256:1629ab148b9a30da6e6e1454d4403633d93f8c3a5b71c0847ac3b5dc643b82ed","target":"record","created_at":"2026-05-18T02:32:31Z","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":"a89c7c6ae87fe1f178190faa5e760aeee0ca27b60dc1fce4a4f3a8086691e881","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-12-04T23:50:37Z","title_canon_sha256":"c93e826cf8be7df4cf47e21991806cfbfee4c04194364ae6080c6bde5f8f99b0"},"schema_version":"1.0","source":{"id":"1312.1387","kind":"arxiv","version":4}},"canonical_sha256":"8e3aeefa8479bc7402d28b1bfac5799ab9f815ebbee8683dcba0e57f6a0d9d35","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8e3aeefa8479bc7402d28b1bfac5799ab9f815ebbee8683dcba0e57f6a0d9d35","first_computed_at":"2026-05-18T02:32:31.661483Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:32:31.661483Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7JXe5zC+moORghrNaLP+buf9AG6CpAUi/LKYpRHIV8Qgklh8EnnqtAzqZ1HHNmE/TeqBhpa1uQG23a4qybRhBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:32:31.662090Z","signed_message":"canonical_sha256_bytes"},"source_id":"1312.1387","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1629ab148b9a30da6e6e1454d4403633d93f8c3a5b71c0847ac3b5dc643b82ed","sha256:58d355b7cb5e504de35b6b00f6de6840b1622bdcd00c08a37b42c84d7c6cd370"],"state_sha256":"d383cfcdc60d34bf0425f2d2a95cca123d5aa2f5807c866a23ecd588ad9f503b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hZZSi5fmoHWuDjdm10zmMOj92BeKa6ryoS5Ig8k+FDgVjYALFlw/o/Sm93ashp7rislCctcLoKMn7QABb04UDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T18:38:37.958901Z","bundle_sha256":"45a9b45e0887a65c986fe18194bdbf6bb667ad635aaf80c3fba0bb081a382c1b"}}