{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:WYE226JP4QOXTWI2V6OB5OMUG3","short_pith_number":"pith:WYE226JP","canonical_record":{"source":{"id":"1011.3362","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2010-11-15T12:39:26Z","cross_cats_sorted":[],"title_canon_sha256":"6c58b142a4ba7aa1bf996909b9f49a1f79094007b712868bd7bf5e0dee954ed7","abstract_canon_sha256":"2c546bddbcb8eb024104facf361f98bedf538f5a9ac5f362a32d025d9c03d26d"},"schema_version":"1.0"},"canonical_sha256":"b609ad792fe41d79d91aaf9c1eb99436c765f33a6e3979ba72fed206bd4a8e4a","source":{"kind":"arxiv","id":"1011.3362","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1011.3362","created_at":"2026-05-18T02:23:36Z"},{"alias_kind":"arxiv_version","alias_value":"1011.3362v1","created_at":"2026-05-18T02:23:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.3362","created_at":"2026-05-18T02:23:36Z"},{"alias_kind":"pith_short_12","alias_value":"WYE226JP4QOX","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_16","alias_value":"WYE226JP4QOXTWI2","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_8","alias_value":"WYE226JP","created_at":"2026-05-18T12:26:17Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:WYE226JP4QOXTWI2V6OB5OMUG3","target":"record","payload":{"canonical_record":{"source":{"id":"1011.3362","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2010-11-15T12:39:26Z","cross_cats_sorted":[],"title_canon_sha256":"6c58b142a4ba7aa1bf996909b9f49a1f79094007b712868bd7bf5e0dee954ed7","abstract_canon_sha256":"2c546bddbcb8eb024104facf361f98bedf538f5a9ac5f362a32d025d9c03d26d"},"schema_version":"1.0"},"canonical_sha256":"b609ad792fe41d79d91aaf9c1eb99436c765f33a6e3979ba72fed206bd4a8e4a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:23:36.685877Z","signature_b64":"uKAfLLgb9xFUEegPxEraasSNB1yuhoEUitb/HNOvi/8Xh44gDEOeMzk+Enl8NAXKHb7KBpGjUNj/zUwAGIULAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b609ad792fe41d79d91aaf9c1eb99436c765f33a6e3979ba72fed206bd4a8e4a","last_reissued_at":"2026-05-18T02:23:36.685310Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:23:36.685310Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1011.3362","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":"2026-05-18T02:23:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cS1tMPfy3t4hTXDnT/GqoJ8+otmZL0Y0XabS9GdVbuOLjfwOowlBFMDJldayfhlWIIHTHG8BjKZHt1IXtPULCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T14:21:10.985174Z"},"content_sha256":"452496af2d77a5027aa9f0cc957722c2a7d84716399e65a95a6aeceea6012ed1","schema_version":"1.0","event_id":"sha256:452496af2d77a5027aa9f0cc957722c2a7d84716399e65a95a6aeceea6012ed1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:WYE226JP4QOXTWI2V6OB5OMUG3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Bisimulations for Nondeterministic Labeled Markov Processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.LO","authors_text":"Nicol\\'as Wolovick, Pedro D'Argenio, Pedro S\\'anchez Terraf","submitted_at":"2010-11-15T12:39:26Z","abstract_excerpt":"We extend the theory of labeled Markov processes with internal nondeterminism, a fundamental concept for the further development of a process theory with abstraction on nondeterministic continuous probabilistic systems. We define nondeterministic labeled Markov processes (NLMP) and provide three definition of bisimulations: a bisimulation following a traditional characterization, a state based bisimulation tailored to our \"measurable\" non-determinism, and an event based bisimulation. We show the relation between them, including that the largest state bisimulation is also an event bisimulation."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.3362","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":"2026-05-18T02:23:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dGizsc0cUOB8gSTUjw5huDqPhbPueKIGaSKrGFL9xZFYODH126sQM++rtLjnbupaCSgctHLAJhJ8vTTjeYwvBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T14:21:10.985801Z"},"content_sha256":"332276d356a57f139648ac73ef099edbf532f564ec30e412a22627d9f7a1fa18","schema_version":"1.0","event_id":"sha256:332276d356a57f139648ac73ef099edbf532f564ec30e412a22627d9f7a1fa18"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WYE226JP4QOXTWI2V6OB5OMUG3/bundle.json","state_url":"https://pith.science/pith/WYE226JP4QOXTWI2V6OB5OMUG3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WYE226JP4QOXTWI2V6OB5OMUG3/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":"2026-06-07T14:21:10Z","links":{"resolver":"https://pith.science/pith/WYE226JP4QOXTWI2V6OB5OMUG3","bundle":"https://pith.science/pith/WYE226JP4QOXTWI2V6OB5OMUG3/bundle.json","state":"https://pith.science/pith/WYE226JP4QOXTWI2V6OB5OMUG3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WYE226JP4QOXTWI2V6OB5OMUG3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:WYE226JP4QOXTWI2V6OB5OMUG3","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":"2c546bddbcb8eb024104facf361f98bedf538f5a9ac5f362a32d025d9c03d26d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2010-11-15T12:39:26Z","title_canon_sha256":"6c58b142a4ba7aa1bf996909b9f49a1f79094007b712868bd7bf5e0dee954ed7"},"schema_version":"1.0","source":{"id":"1011.3362","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1011.3362","created_at":"2026-05-18T02:23:36Z"},{"alias_kind":"arxiv_version","alias_value":"1011.3362v1","created_at":"2026-05-18T02:23:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.3362","created_at":"2026-05-18T02:23:36Z"},{"alias_kind":"pith_short_12","alias_value":"WYE226JP4QOX","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_16","alias_value":"WYE226JP4QOXTWI2","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_8","alias_value":"WYE226JP","created_at":"2026-05-18T12:26:17Z"}],"graph_snapshots":[{"event_id":"sha256:332276d356a57f139648ac73ef099edbf532f564ec30e412a22627d9f7a1fa18","target":"graph","created_at":"2026-05-18T02:23:36Z","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 extend the theory of labeled Markov processes with internal nondeterminism, a fundamental concept for the further development of a process theory with abstraction on nondeterministic continuous probabilistic systems. We define nondeterministic labeled Markov processes (NLMP) and provide three definition of bisimulations: a bisimulation following a traditional characterization, a state based bisimulation tailored to our \"measurable\" non-determinism, and an event based bisimulation. We show the relation between them, including that the largest state bisimulation is also an event bisimulation.","authors_text":"Nicol\\'as Wolovick, Pedro D'Argenio, Pedro S\\'anchez Terraf","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2010-11-15T12:39:26Z","title":"Bisimulations for Nondeterministic Labeled Markov Processes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.3362","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":"sha256:452496af2d77a5027aa9f0cc957722c2a7d84716399e65a95a6aeceea6012ed1","target":"record","created_at":"2026-05-18T02:23:36Z","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":"2c546bddbcb8eb024104facf361f98bedf538f5a9ac5f362a32d025d9c03d26d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2010-11-15T12:39:26Z","title_canon_sha256":"6c58b142a4ba7aa1bf996909b9f49a1f79094007b712868bd7bf5e0dee954ed7"},"schema_version":"1.0","source":{"id":"1011.3362","kind":"arxiv","version":1}},"canonical_sha256":"b609ad792fe41d79d91aaf9c1eb99436c765f33a6e3979ba72fed206bd4a8e4a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b609ad792fe41d79d91aaf9c1eb99436c765f33a6e3979ba72fed206bd4a8e4a","first_computed_at":"2026-05-18T02:23:36.685310Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:23:36.685310Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uKAfLLgb9xFUEegPxEraasSNB1yuhoEUitb/HNOvi/8Xh44gDEOeMzk+Enl8NAXKHb7KBpGjUNj/zUwAGIULAg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:23:36.685877Z","signed_message":"canonical_sha256_bytes"},"source_id":"1011.3362","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:452496af2d77a5027aa9f0cc957722c2a7d84716399e65a95a6aeceea6012ed1","sha256:332276d356a57f139648ac73ef099edbf532f564ec30e412a22627d9f7a1fa18"],"state_sha256":"3d0842566398db73499239819bb657828cedc5b068d469ab875f3af0a66bdff1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zApG5I/R2hUgvnbQ7rUNVrERBHye0mTAP0ugPQqKeumQDWXPMtOb+e01gLP7A6EtkMh5pLrLZmXe/hy65ljsCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T14:21:10.988868Z","bundle_sha256":"cf785b751e772cf8d39ef68d0e9c30c161570b17658afe4ebc044c0c2aaca73f"}}