{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:PQIESDYCRU4U4YM5U3Q2COXTGO","short_pith_number":"pith:PQIESDYC","canonical_record":{"source":{"id":"1707.05475","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-07-18T05:32:22Z","cross_cats_sorted":[],"title_canon_sha256":"54a5837e561e71dc846b079c786fc9af86784ff71aa9446dc09f5eacae75ee9d","abstract_canon_sha256":"a0f37d27e250a5818907bf8ff07e6e33f83ea24c5db0aca4af4941ef8e0f6a3a"},"schema_version":"1.0"},"canonical_sha256":"7c10490f028d394e619da6e1a13af333926b8cd5290ba6a2a67bba4dca8114f1","source":{"kind":"arxiv","id":"1707.05475","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.05475","created_at":"2026-05-18T00:40:02Z"},{"alias_kind":"arxiv_version","alias_value":"1707.05475v1","created_at":"2026-05-18T00:40:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.05475","created_at":"2026-05-18T00:40:02Z"},{"alias_kind":"pith_short_12","alias_value":"PQIESDYCRU4U","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_16","alias_value":"PQIESDYCRU4U4YM5","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_8","alias_value":"PQIESDYC","created_at":"2026-05-18T12:31:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:PQIESDYCRU4U4YM5U3Q2COXTGO","target":"record","payload":{"canonical_record":{"source":{"id":"1707.05475","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-07-18T05:32:22Z","cross_cats_sorted":[],"title_canon_sha256":"54a5837e561e71dc846b079c786fc9af86784ff71aa9446dc09f5eacae75ee9d","abstract_canon_sha256":"a0f37d27e250a5818907bf8ff07e6e33f83ea24c5db0aca4af4941ef8e0f6a3a"},"schema_version":"1.0"},"canonical_sha256":"7c10490f028d394e619da6e1a13af333926b8cd5290ba6a2a67bba4dca8114f1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:40:02.236270Z","signature_b64":"dpJpD/Ia60khl3KclRVzZw/UDG4GvyFg+DlXJhiJDYzk//Ajckzq6LZIESwlNaaedtr2fNp306OZAg78n7mnBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7c10490f028d394e619da6e1a13af333926b8cd5290ba6a2a67bba4dca8114f1","last_reissued_at":"2026-05-18T00:40:02.235820Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:40:02.235820Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1707.05475","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:40:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kl66tjU1vwvPdu8X96DocC+x7Nmf9qj7Dd4J/IXuhgjbwTOt/dlg7hmz8BzZzoBZQ/HUM2ircXecag3YwFUbAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T21:38:46.879954Z"},"content_sha256":"1920a7e6478b918c690f170d46fe5dce795d2db6e039a1d9f6cbd5aa56a645b5","schema_version":"1.0","event_id":"sha256:1920a7e6478b918c690f170d46fe5dce795d2db6e039a1d9f6cbd5aa56a645b5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:PQIESDYCRU4U4YM5U3Q2COXTGO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Exact asymptotic formulae of the stationary distribution of a discrete-time two-dimensional QBD process","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Masahiro Kobayashi, Toshihisa Ozawa","submitted_at":"2017-07-18T05:32:22Z","abstract_excerpt":"We consider a discrete-time two-dimensional process $\\{(L_{1,n},L_{2,n})\\}$ on $\\mathbb{Z}_+^2$ with a supplemental process $\\{J_n\\}$ on a finite set, where individual processes $\\{L_{1,n}\\}$ and $\\{L_{2,n}\\}$ are both skip free. We assume that the joint process $\\{Y_n\\}=\\{(L_{1,n},L_{2,n},J_n)\\}$ is Markovian and that the transition probabilities of the two-dimensional process $\\{(L_{1,n},L_{2,n})\\}$ are modulated depending on the state of the background process $\\{J_n\\}$. This modulation is space homogeneous except for the boundaries of $\\mathbb{Z}_+^2$. We call this process a discrete-time "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.05475","kind":"arxiv","version":1},"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":"2026-05-18T00:40:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DK2J3/RAblKBgbcR9PUmwdNuoLvKGaAVU19P1vnE1pbkBU0H1PVXBYTqs7T4fQzIe6RNBLaeurV3HgVHzEyQDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T21:38:46.880295Z"},"content_sha256":"aa7d6aedc4418b4453e717624f1394dc04b8fbf50887ef883516e4bdbc1f3e24","schema_version":"1.0","event_id":"sha256:aa7d6aedc4418b4453e717624f1394dc04b8fbf50887ef883516e4bdbc1f3e24"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PQIESDYCRU4U4YM5U3Q2COXTGO/bundle.json","state_url":"https://pith.science/pith/PQIESDYCRU4U4YM5U3Q2COXTGO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PQIESDYCRU4U4YM5U3Q2COXTGO/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":"2026-06-24T21:38:46Z","links":{"resolver":"https://pith.science/pith/PQIESDYCRU4U4YM5U3Q2COXTGO","bundle":"https://pith.science/pith/PQIESDYCRU4U4YM5U3Q2COXTGO/bundle.json","state":"https://pith.science/pith/PQIESDYCRU4U4YM5U3Q2COXTGO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PQIESDYCRU4U4YM5U3Q2COXTGO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:PQIESDYCRU4U4YM5U3Q2COXTGO","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":"a0f37d27e250a5818907bf8ff07e6e33f83ea24c5db0aca4af4941ef8e0f6a3a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-07-18T05:32:22Z","title_canon_sha256":"54a5837e561e71dc846b079c786fc9af86784ff71aa9446dc09f5eacae75ee9d"},"schema_version":"1.0","source":{"id":"1707.05475","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.05475","created_at":"2026-05-18T00:40:02Z"},{"alias_kind":"arxiv_version","alias_value":"1707.05475v1","created_at":"2026-05-18T00:40:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.05475","created_at":"2026-05-18T00:40:02Z"},{"alias_kind":"pith_short_12","alias_value":"PQIESDYCRU4U","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_16","alias_value":"PQIESDYCRU4U4YM5","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_8","alias_value":"PQIESDYC","created_at":"2026-05-18T12:31:37Z"}],"graph_snapshots":[{"event_id":"sha256:aa7d6aedc4418b4453e717624f1394dc04b8fbf50887ef883516e4bdbc1f3e24","target":"graph","created_at":"2026-05-18T00:40:02Z","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 consider a discrete-time two-dimensional process $\\{(L_{1,n},L_{2,n})\\}$ on $\\mathbb{Z}_+^2$ with a supplemental process $\\{J_n\\}$ on a finite set, where individual processes $\\{L_{1,n}\\}$ and $\\{L_{2,n}\\}$ are both skip free. We assume that the joint process $\\{Y_n\\}=\\{(L_{1,n},L_{2,n},J_n)\\}$ is Markovian and that the transition probabilities of the two-dimensional process $\\{(L_{1,n},L_{2,n})\\}$ are modulated depending on the state of the background process $\\{J_n\\}$. This modulation is space homogeneous except for the boundaries of $\\mathbb{Z}_+^2$. We call this process a discrete-time ","authors_text":"Masahiro Kobayashi, Toshihisa Ozawa","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-07-18T05:32:22Z","title":"Exact asymptotic formulae of the stationary distribution of a discrete-time two-dimensional QBD process"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.05475","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":"sha256:1920a7e6478b918c690f170d46fe5dce795d2db6e039a1d9f6cbd5aa56a645b5","target":"record","created_at":"2026-05-18T00:40:02Z","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":"a0f37d27e250a5818907bf8ff07e6e33f83ea24c5db0aca4af4941ef8e0f6a3a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-07-18T05:32:22Z","title_canon_sha256":"54a5837e561e71dc846b079c786fc9af86784ff71aa9446dc09f5eacae75ee9d"},"schema_version":"1.0","source":{"id":"1707.05475","kind":"arxiv","version":1}},"canonical_sha256":"7c10490f028d394e619da6e1a13af333926b8cd5290ba6a2a67bba4dca8114f1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7c10490f028d394e619da6e1a13af333926b8cd5290ba6a2a67bba4dca8114f1","first_computed_at":"2026-05-18T00:40:02.235820Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:40:02.235820Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dpJpD/Ia60khl3KclRVzZw/UDG4GvyFg+DlXJhiJDYzk//Ajckzq6LZIESwlNaaedtr2fNp306OZAg78n7mnBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:40:02.236270Z","signed_message":"canonical_sha256_bytes"},"source_id":"1707.05475","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1920a7e6478b918c690f170d46fe5dce795d2db6e039a1d9f6cbd5aa56a645b5","sha256:aa7d6aedc4418b4453e717624f1394dc04b8fbf50887ef883516e4bdbc1f3e24"],"state_sha256":"583c57abb246e0bc3562d3bae09a387a1537a660b07bf08df04c6b3004ca1f52"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sWon5CeyUL7MJWecRczEsdhHQwZybau+xSsE5UjkCsply+kL17lr/bbGi0PwLmwy210WcKawV3c8AU/NP/ThDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T21:38:46.882163Z","bundle_sha256":"7051390e5058c97cefd933c6e0345cab49ef231751b5d0b3f6df6580114f2ccb"}}