{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2008:XSU2WZSSPDSHYZT27SL5MRBYIY","short_pith_number":"pith:XSU2WZSS","canonical_record":{"source":{"id":"0803.3796","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2008-03-26T19:08:40Z","cross_cats_sorted":[],"title_canon_sha256":"ecad5c568ff4b560e2b9d662e25ef44fbefdb9d5fcfcfea1f5870b394314747f","abstract_canon_sha256":"124bc4953f09cd73b1e0f3ae95aac0be3b71a267e9f4dc68260c1df0113ddb6a"},"schema_version":"1.0"},"canonical_sha256":"bca9ab665278e47c667afc97d6443846091b75adfac189cc51e9ec590810f068","source":{"kind":"arxiv","id":"0803.3796","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0803.3796","created_at":"2026-05-18T01:37:42Z"},{"alias_kind":"arxiv_version","alias_value":"0803.3796v3","created_at":"2026-05-18T01:37:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0803.3796","created_at":"2026-05-18T01:37:42Z"},{"alias_kind":"pith_short_12","alias_value":"XSU2WZSSPDSH","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"XSU2WZSSPDSHYZT2","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"XSU2WZSS","created_at":"2026-05-18T12:25:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2008:XSU2WZSSPDSHYZT27SL5MRBYIY","target":"record","payload":{"canonical_record":{"source":{"id":"0803.3796","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2008-03-26T19:08:40Z","cross_cats_sorted":[],"title_canon_sha256":"ecad5c568ff4b560e2b9d662e25ef44fbefdb9d5fcfcfea1f5870b394314747f","abstract_canon_sha256":"124bc4953f09cd73b1e0f3ae95aac0be3b71a267e9f4dc68260c1df0113ddb6a"},"schema_version":"1.0"},"canonical_sha256":"bca9ab665278e47c667afc97d6443846091b75adfac189cc51e9ec590810f068","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:37:42.509280Z","signature_b64":"vPc37H8/eBxYzmpAtZB2XhpCBUbzgx4g8hsL3SVE48wPh3CIuwEv+L9q5bDUpNgeAusmWagp0cur5Fg8OZCFCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bca9ab665278e47c667afc97d6443846091b75adfac189cc51e9ec590810f068","last_reissued_at":"2026-05-18T01:37:42.508601Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:37:42.508601Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0803.3796","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:37:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IFAa0aJln0gzDbx/wEgv3y28Va+OoFaagOvRISEhH0rmRuhFU/eZd8VaWJfBRgwNuuEi4biMEUQhWkZ9hcTpDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T12:37:36.185182Z"},"content_sha256":"1a2464be95678af5257f0703b99b7f3c61f5df201e27b230eb252a6996afa46f","schema_version":"1.0","event_id":"sha256:1a2464be95678af5257f0703b99b7f3c61f5df201e27b230eb252a6996afa46f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2008:XSU2WZSSPDSHYZT27SL5MRBYIY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Approximating a Behavioural Pseudometric without Discount for<br> Probabilistic Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.LO","authors_text":"Babita Sharma, Franck van Breugel, James Worrell","submitted_at":"2008-03-26T19:08:40Z","abstract_excerpt":"Desharnais, Gupta, Jagadeesan and Panangaden introduced a family of behavioural pseudometrics for probabilistic transition systems. These pseudometrics are a quantitative analogue of probabilistic bisimilarity. Distance zero captures probabilistic bisimilarity. Each pseudometric has a discount factor, a real number in the interval (0, 1]. The smaller the discount factor, the more the future is discounted. If the discount factor is one, then the future is not discounted at all. Desharnais et al. showed that the behavioural distances can be calculated up to any desired degree of accuracy if the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0803.3796","kind":"arxiv","version":3},"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":"2026-05-18T01:37:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vZLRAi2a0Wb/hXaCYKNvVDvmxOQyNyFf+nabydoYHsFZzUZT03EKNq59Vx8EUu3R+xLaHhJ8/ieAbkHX2E3OAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T12:37:36.185603Z"},"content_sha256":"53d1edbac86100fd04c532e40ecbf50c54f043f845e7eb73544495aa9b2eceb4","schema_version":"1.0","event_id":"sha256:53d1edbac86100fd04c532e40ecbf50c54f043f845e7eb73544495aa9b2eceb4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XSU2WZSSPDSHYZT27SL5MRBYIY/bundle.json","state_url":"https://pith.science/pith/XSU2WZSSPDSHYZT27SL5MRBYIY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XSU2WZSSPDSHYZT27SL5MRBYIY/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":"2026-05-28T12:37:36Z","links":{"resolver":"https://pith.science/pith/XSU2WZSSPDSHYZT27SL5MRBYIY","bundle":"https://pith.science/pith/XSU2WZSSPDSHYZT27SL5MRBYIY/bundle.json","state":"https://pith.science/pith/XSU2WZSSPDSHYZT27SL5MRBYIY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XSU2WZSSPDSHYZT27SL5MRBYIY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:XSU2WZSSPDSHYZT27SL5MRBYIY","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":"124bc4953f09cd73b1e0f3ae95aac0be3b71a267e9f4dc68260c1df0113ddb6a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2008-03-26T19:08:40Z","title_canon_sha256":"ecad5c568ff4b560e2b9d662e25ef44fbefdb9d5fcfcfea1f5870b394314747f"},"schema_version":"1.0","source":{"id":"0803.3796","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0803.3796","created_at":"2026-05-18T01:37:42Z"},{"alias_kind":"arxiv_version","alias_value":"0803.3796v3","created_at":"2026-05-18T01:37:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0803.3796","created_at":"2026-05-18T01:37:42Z"},{"alias_kind":"pith_short_12","alias_value":"XSU2WZSSPDSH","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"XSU2WZSSPDSHYZT2","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"XSU2WZSS","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:53d1edbac86100fd04c532e40ecbf50c54f043f845e7eb73544495aa9b2eceb4","target":"graph","created_at":"2026-05-18T01:37:42Z","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":"Desharnais, Gupta, Jagadeesan and Panangaden introduced a family of behavioural pseudometrics for probabilistic transition systems. These pseudometrics are a quantitative analogue of probabilistic bisimilarity. Distance zero captures probabilistic bisimilarity. Each pseudometric has a discount factor, a real number in the interval (0, 1]. The smaller the discount factor, the more the future is discounted. If the discount factor is one, then the future is not discounted at all. Desharnais et al. showed that the behavioural distances can be calculated up to any desired degree of accuracy if the ","authors_text":"Babita Sharma, Franck van Breugel, James Worrell","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2008-03-26T19:08:40Z","title":"Approximating a Behavioural Pseudometric without Discount for<br> Probabilistic Systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0803.3796","kind":"arxiv","version":3},"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":"sha256:1a2464be95678af5257f0703b99b7f3c61f5df201e27b230eb252a6996afa46f","target":"record","created_at":"2026-05-18T01:37:42Z","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":"124bc4953f09cd73b1e0f3ae95aac0be3b71a267e9f4dc68260c1df0113ddb6a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2008-03-26T19:08:40Z","title_canon_sha256":"ecad5c568ff4b560e2b9d662e25ef44fbefdb9d5fcfcfea1f5870b394314747f"},"schema_version":"1.0","source":{"id":"0803.3796","kind":"arxiv","version":3}},"canonical_sha256":"bca9ab665278e47c667afc97d6443846091b75adfac189cc51e9ec590810f068","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bca9ab665278e47c667afc97d6443846091b75adfac189cc51e9ec590810f068","first_computed_at":"2026-05-18T01:37:42.508601Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:37:42.508601Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vPc37H8/eBxYzmpAtZB2XhpCBUbzgx4g8hsL3SVE48wPh3CIuwEv+L9q5bDUpNgeAusmWagp0cur5Fg8OZCFCw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:37:42.509280Z","signed_message":"canonical_sha256_bytes"},"source_id":"0803.3796","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1a2464be95678af5257f0703b99b7f3c61f5df201e27b230eb252a6996afa46f","sha256:53d1edbac86100fd04c532e40ecbf50c54f043f845e7eb73544495aa9b2eceb4"],"state_sha256":"434cbbf09fa4dad802741002b74aed1075131254acd90cd5c45edd7ef43a0195"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"87qEA8/tq9dy1LCrcqR2ZWTFUsnRZLxSnp8QdOmOC2Sl1VYYOqQ3+KEo1pzIVYbm4yzi5vzWCu2p4M5DZfoNDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T12:37:36.187489Z","bundle_sha256":"a34dec59d22333550334de4e6f42b84ba5c6bde7741bc345991d787d4347e225"}}