{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:V4Y75LRSDJ7ZTMQCGMXQ2VQVWV","short_pith_number":"pith:V4Y75LRS","canonical_record":{"source":{"id":"1312.1758","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-12-06T02:44:42Z","cross_cats_sorted":[],"title_canon_sha256":"7af85f9965d61c20f51ab05f5c459b32fa0dcfc194146169eec12b0e5b3ad795","abstract_canon_sha256":"93899274c892b8c3a0f0c54d12ae75533485c358cfa7f9248dd4afdedb50c6dd"},"schema_version":"1.0"},"canonical_sha256":"af31feae321a7f99b202332f0d5615b57e5c3671f42b8e2d8cff998d4597c42c","source":{"kind":"arxiv","id":"1312.1758","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.1758","created_at":"2026-05-18T02:28:13Z"},{"alias_kind":"arxiv_version","alias_value":"1312.1758v2","created_at":"2026-05-18T02:28:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.1758","created_at":"2026-05-18T02:28:13Z"},{"alias_kind":"pith_short_12","alias_value":"V4Y75LRSDJ7Z","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_16","alias_value":"V4Y75LRSDJ7ZTMQC","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_8","alias_value":"V4Y75LRS","created_at":"2026-05-18T12:28:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:V4Y75LRSDJ7ZTMQCGMXQ2VQVWV","target":"record","payload":{"canonical_record":{"source":{"id":"1312.1758","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-12-06T02:44:42Z","cross_cats_sorted":[],"title_canon_sha256":"7af85f9965d61c20f51ab05f5c459b32fa0dcfc194146169eec12b0e5b3ad795","abstract_canon_sha256":"93899274c892b8c3a0f0c54d12ae75533485c358cfa7f9248dd4afdedb50c6dd"},"schema_version":"1.0"},"canonical_sha256":"af31feae321a7f99b202332f0d5615b57e5c3671f42b8e2d8cff998d4597c42c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:28:13.462177Z","signature_b64":"aYFWx+AGQxmy/DuvON5L8wa+Ol2CK569dyoHbRyF5jHkirEnH9b5c1DGN9HLBfCs3LMkbETkPFLmCR08xEhzAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"af31feae321a7f99b202332f0d5615b57e5c3671f42b8e2d8cff998d4597c42c","last_reissued_at":"2026-05-18T02:28:13.461614Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:28:13.461614Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1312.1758","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:28:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"H01w+boY4fVjJN7sFWV4mK6aOtCR5dLnaFWkmT2tYx9bGGmVcA2R8DQpGWSGXYg5OTk8VovVNliOHPvWf1uPDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T08:35:37.557481Z"},"content_sha256":"8efff894d7993f3c8f7e465574717293e4d8b389327dcdc832ee5714ade69a83","schema_version":"1.0","event_id":"sha256:8efff894d7993f3c8f7e465574717293e4d8b389327dcdc832ee5714ade69a83"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:V4Y75LRSDJ7ZTMQCGMXQ2VQVWV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A multi-dimensional SRBM: Geometric views of its product form stationary distribution","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":"2013-12-06T02:44:42Z","abstract_excerpt":"We present a geometric interpretation of a product form stationary distribution for a $d$-dimensional semimartingale reflecting Brownian motion (SRBM) that lives in the nonnegative orthant. The $d$-dimensional SRBM data can be equivalently specified by $d+1$ geometric objects: an ellipse and $d$ rays. Using these geometric objects, we establish necessary and sufficient conditions for characterizing product form stationary distribution. The key idea in the characterization is that we decompose the $d$-dimensional problem to $\\frac{1}{2}d(d-1)$ two-dimensional SRBMs, each of which is determined "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.1758","kind":"arxiv","version":2},"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":"2026-05-18T02:28:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sMXXOlP8GJokOujZPk9cxN1QSntiTmdO53EWHB3FGLifOwOZ+1w9NGJwILlFWYZqRHKHDd6LGcEDvsLQDT1WBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T08:35:37.557824Z"},"content_sha256":"4ab3de22c3e62afbf4fe7e89466044eaeace3009c220777dbd88ac599dd177fb","schema_version":"1.0","event_id":"sha256:4ab3de22c3e62afbf4fe7e89466044eaeace3009c220777dbd88ac599dd177fb"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/V4Y75LRSDJ7ZTMQCGMXQ2VQVWV/bundle.json","state_url":"https://pith.science/pith/V4Y75LRSDJ7ZTMQCGMXQ2VQVWV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/V4Y75LRSDJ7ZTMQCGMXQ2VQVWV/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":"2026-06-23T08:35:37Z","links":{"resolver":"https://pith.science/pith/V4Y75LRSDJ7ZTMQCGMXQ2VQVWV","bundle":"https://pith.science/pith/V4Y75LRSDJ7ZTMQCGMXQ2VQVWV/bundle.json","state":"https://pith.science/pith/V4Y75LRSDJ7ZTMQCGMXQ2VQVWV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/V4Y75LRSDJ7ZTMQCGMXQ2VQVWV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:V4Y75LRSDJ7ZTMQCGMXQ2VQVWV","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":"93899274c892b8c3a0f0c54d12ae75533485c358cfa7f9248dd4afdedb50c6dd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-12-06T02:44:42Z","title_canon_sha256":"7af85f9965d61c20f51ab05f5c459b32fa0dcfc194146169eec12b0e5b3ad795"},"schema_version":"1.0","source":{"id":"1312.1758","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.1758","created_at":"2026-05-18T02:28:13Z"},{"alias_kind":"arxiv_version","alias_value":"1312.1758v2","created_at":"2026-05-18T02:28:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.1758","created_at":"2026-05-18T02:28:13Z"},{"alias_kind":"pith_short_12","alias_value":"V4Y75LRSDJ7Z","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_16","alias_value":"V4Y75LRSDJ7ZTMQC","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_8","alias_value":"V4Y75LRS","created_at":"2026-05-18T12:28:04Z"}],"graph_snapshots":[{"event_id":"sha256:4ab3de22c3e62afbf4fe7e89466044eaeace3009c220777dbd88ac599dd177fb","target":"graph","created_at":"2026-05-18T02:28:13Z","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 present a geometric interpretation of a product form stationary distribution for a $d$-dimensional semimartingale reflecting Brownian motion (SRBM) that lives in the nonnegative orthant. The $d$-dimensional SRBM data can be equivalently specified by $d+1$ geometric objects: an ellipse and $d$ rays. Using these geometric objects, we establish necessary and sufficient conditions for characterizing product form stationary distribution. The key idea in the characterization is that we decompose the $d$-dimensional problem to $\\frac{1}{2}d(d-1)$ two-dimensional SRBMs, each of which is determined ","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":"2013-12-06T02:44:42Z","title":"A multi-dimensional SRBM: Geometric views of its product form stationary distribution"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.1758","kind":"arxiv","version":2},"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":"sha256:8efff894d7993f3c8f7e465574717293e4d8b389327dcdc832ee5714ade69a83","target":"record","created_at":"2026-05-18T02:28:13Z","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":"93899274c892b8c3a0f0c54d12ae75533485c358cfa7f9248dd4afdedb50c6dd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-12-06T02:44:42Z","title_canon_sha256":"7af85f9965d61c20f51ab05f5c459b32fa0dcfc194146169eec12b0e5b3ad795"},"schema_version":"1.0","source":{"id":"1312.1758","kind":"arxiv","version":2}},"canonical_sha256":"af31feae321a7f99b202332f0d5615b57e5c3671f42b8e2d8cff998d4597c42c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"af31feae321a7f99b202332f0d5615b57e5c3671f42b8e2d8cff998d4597c42c","first_computed_at":"2026-05-18T02:28:13.461614Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:28:13.461614Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"aYFWx+AGQxmy/DuvON5L8wa+Ol2CK569dyoHbRyF5jHkirEnH9b5c1DGN9HLBfCs3LMkbETkPFLmCR08xEhzAw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:28:13.462177Z","signed_message":"canonical_sha256_bytes"},"source_id":"1312.1758","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8efff894d7993f3c8f7e465574717293e4d8b389327dcdc832ee5714ade69a83","sha256:4ab3de22c3e62afbf4fe7e89466044eaeace3009c220777dbd88ac599dd177fb"],"state_sha256":"2b9d2506d9b9ded4f41b513dd5db84c4737f184a6a6a8936b8f13e9230dedde4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"n9RFUQfArz/Y9m9RTS5ynEtl7/yv1j8IYQ5XQDUosblDevvtwoohvmYigCuT9cRt4k6iQtHyotRVpHuUYVuTAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T08:35:37.560020Z","bundle_sha256":"ddad15ca4b148ded64875f45b6555822e88f2f789fdb9373efda53499a11e7b8"}}