{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:GCLHJJ4REZ7MYLLZTZXA735BTX","short_pith_number":"pith:GCLHJJ4R","canonical_record":{"source":{"id":"1009.2152","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-09-11T10:28:12Z","cross_cats_sorted":[],"title_canon_sha256":"ba60b08c093cd8bca4472157ed8ff91f67211ef55c1e5fc55b217270a5d6c8fc","abstract_canon_sha256":"a4b9af173ad4ff1c4f323d8cd71b76d07cce6982ecd137fa21f908a56ea6f4d0"},"schema_version":"1.0"},"canonical_sha256":"309674a791267ecc2d799e6e0fefa19de1ff0ea4f502bc1aeb16bec081bcbab5","source":{"kind":"arxiv","id":"1009.2152","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1009.2152","created_at":"2026-05-18T04:41:04Z"},{"alias_kind":"arxiv_version","alias_value":"1009.2152v1","created_at":"2026-05-18T04:41:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.2152","created_at":"2026-05-18T04:41:04Z"},{"alias_kind":"pith_short_12","alias_value":"GCLHJJ4REZ7M","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_16","alias_value":"GCLHJJ4REZ7MYLLZ","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_8","alias_value":"GCLHJJ4R","created_at":"2026-05-18T12:26:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:GCLHJJ4REZ7MYLLZTZXA735BTX","target":"record","payload":{"canonical_record":{"source":{"id":"1009.2152","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-09-11T10:28:12Z","cross_cats_sorted":[],"title_canon_sha256":"ba60b08c093cd8bca4472157ed8ff91f67211ef55c1e5fc55b217270a5d6c8fc","abstract_canon_sha256":"a4b9af173ad4ff1c4f323d8cd71b76d07cce6982ecd137fa21f908a56ea6f4d0"},"schema_version":"1.0"},"canonical_sha256":"309674a791267ecc2d799e6e0fefa19de1ff0ea4f502bc1aeb16bec081bcbab5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:41:04.701359Z","signature_b64":"qb5lVA94AAqNQ792VmcrYdBcg1E+yEuRRfIz95OYnHFOQEFCSe9YBex+GKwRZfuJgJg7mh5PHzQ/Y67m37nQBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"309674a791267ecc2d799e6e0fefa19de1ff0ea4f502bc1aeb16bec081bcbab5","last_reissued_at":"2026-05-18T04:41:04.700880Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:41:04.700880Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1009.2152","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":"2026-05-18T04:41:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mniYZqbsT1XkVaHbaQOwwD1dfSquCSAA4SP1szQDGr96f5AWPNonSrzT53osXd0k7+TsVnj1oWOxKuSVWE1kDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-23T22:04:37.263056Z"},"content_sha256":"beee65b921e9e0bf87b3162a1ee21a1fa1190147b72c310030c70e31e2bee9d0","schema_version":"1.0","event_id":"sha256:beee65b921e9e0bf87b3162a1ee21a1fa1190147b72c310030c70e31e2bee9d0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:GCLHJJ4REZ7MYLLZTZXA735BTX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the Imbedding Problem for Three-state Time Homogeneous Markov Chains with Coinciding Negative Eigenvalues","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Jianmin Chen, Yong Chen","submitted_at":"2010-09-11T10:28:12Z","abstract_excerpt":"For an indecomposable $3\\times 3$ stochastic matrix (i.e., 1-step transition probability matrix) with coinciding negative eigenvalues, a new necessary and sufficient condition of the imbedding problem for time homogeneous Markov chains is shown by means of an alternate parameterization of the transition rate matrix (i.e., intensity matrix, infinitesimal generator), which avoids calculating matrix logarithm or matrix square root. In addition, an implicit description of the imbedding problem for the $3\\times 3$ stochastic matrix in Johansen [J. Lond. Math. Soc., 8, 345-351. (1974)] is pointed ou"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.2152","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":"2026-05-18T04:41:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kHd8qKn2ZGEA3UyQ25XMngKg0OEs5hWdQa1JOriwL+4ZcP8TgqySCm6GMk8W+5CTyZtPq5q5wacN2uMwYI5mCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-23T22:04:37.263800Z"},"content_sha256":"448bbc03ae3e05ad7252bc7cd5a8686c1d1e28013e40a4ea41a44176fcde7604","schema_version":"1.0","event_id":"sha256:448bbc03ae3e05ad7252bc7cd5a8686c1d1e28013e40a4ea41a44176fcde7604"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GCLHJJ4REZ7MYLLZTZXA735BTX/bundle.json","state_url":"https://pith.science/pith/GCLHJJ4REZ7MYLLZTZXA735BTX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GCLHJJ4REZ7MYLLZTZXA735BTX/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":"2026-05-23T22:04:37Z","links":{"resolver":"https://pith.science/pith/GCLHJJ4REZ7MYLLZTZXA735BTX","bundle":"https://pith.science/pith/GCLHJJ4REZ7MYLLZTZXA735BTX/bundle.json","state":"https://pith.science/pith/GCLHJJ4REZ7MYLLZTZXA735BTX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GCLHJJ4REZ7MYLLZTZXA735BTX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:GCLHJJ4REZ7MYLLZTZXA735BTX","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":"a4b9af173ad4ff1c4f323d8cd71b76d07cce6982ecd137fa21f908a56ea6f4d0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-09-11T10:28:12Z","title_canon_sha256":"ba60b08c093cd8bca4472157ed8ff91f67211ef55c1e5fc55b217270a5d6c8fc"},"schema_version":"1.0","source":{"id":"1009.2152","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1009.2152","created_at":"2026-05-18T04:41:04Z"},{"alias_kind":"arxiv_version","alias_value":"1009.2152v1","created_at":"2026-05-18T04:41:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.2152","created_at":"2026-05-18T04:41:04Z"},{"alias_kind":"pith_short_12","alias_value":"GCLHJJ4REZ7M","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_16","alias_value":"GCLHJJ4REZ7MYLLZ","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_8","alias_value":"GCLHJJ4R","created_at":"2026-05-18T12:26:07Z"}],"graph_snapshots":[{"event_id":"sha256:448bbc03ae3e05ad7252bc7cd5a8686c1d1e28013e40a4ea41a44176fcde7604","target":"graph","created_at":"2026-05-18T04:41:04Z","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":"For an indecomposable $3\\times 3$ stochastic matrix (i.e., 1-step transition probability matrix) with coinciding negative eigenvalues, a new necessary and sufficient condition of the imbedding problem for time homogeneous Markov chains is shown by means of an alternate parameterization of the transition rate matrix (i.e., intensity matrix, infinitesimal generator), which avoids calculating matrix logarithm or matrix square root. In addition, an implicit description of the imbedding problem for the $3\\times 3$ stochastic matrix in Johansen [J. Lond. Math. Soc., 8, 345-351. (1974)] is pointed ou","authors_text":"Jianmin Chen, Yong Chen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-09-11T10:28:12Z","title":"On the Imbedding Problem for Three-state Time Homogeneous Markov Chains with Coinciding Negative Eigenvalues"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.2152","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:beee65b921e9e0bf87b3162a1ee21a1fa1190147b72c310030c70e31e2bee9d0","target":"record","created_at":"2026-05-18T04:41:04Z","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":"a4b9af173ad4ff1c4f323d8cd71b76d07cce6982ecd137fa21f908a56ea6f4d0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-09-11T10:28:12Z","title_canon_sha256":"ba60b08c093cd8bca4472157ed8ff91f67211ef55c1e5fc55b217270a5d6c8fc"},"schema_version":"1.0","source":{"id":"1009.2152","kind":"arxiv","version":1}},"canonical_sha256":"309674a791267ecc2d799e6e0fefa19de1ff0ea4f502bc1aeb16bec081bcbab5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"309674a791267ecc2d799e6e0fefa19de1ff0ea4f502bc1aeb16bec081bcbab5","first_computed_at":"2026-05-18T04:41:04.700880Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:41:04.700880Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qb5lVA94AAqNQ792VmcrYdBcg1E+yEuRRfIz95OYnHFOQEFCSe9YBex+GKwRZfuJgJg7mh5PHzQ/Y67m37nQBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:41:04.701359Z","signed_message":"canonical_sha256_bytes"},"source_id":"1009.2152","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:beee65b921e9e0bf87b3162a1ee21a1fa1190147b72c310030c70e31e2bee9d0","sha256:448bbc03ae3e05ad7252bc7cd5a8686c1d1e28013e40a4ea41a44176fcde7604"],"state_sha256":"8c9594d3ff80f1ec7b32bc876ac2976cbac0f175765e80338d60016e65ef2b80"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hWEr3ldx9F/Zk+IEgD9ET5CRFWkBE3fZ0jukYXgEQpWp8iilnSg7Ik8rPj12osHrN0cTstZ+pTOOk3z+wnIpBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-23T22:04:37.267276Z","bundle_sha256":"cdf57401327612797ab017c3975306eb01740d36ca27ddfd16e7c0fb727f80bf"}}