{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2007:FDRFTXHY56HQJI74QUDOFGVKV3","short_pith_number":"pith:FDRFTXHY","schema_version":"1.0","canonical_sha256":"28e259dcf8ef8f04a3fc8506e29aaaaef0f1efdd54c9c99c6e7e468e946bf9c8","source":{"kind":"arxiv","id":"0711.0194","version":2},"attestation_state":"computed","paper":{"title":"Coinductive Proof Principles for Stochastic Processes","license":"","headline":"","cross_cats":[],"primary_cat":"cs.LO","authors_text":"Dexter Kozen","submitted_at":"2007-11-01T19:25:13Z","abstract_excerpt":"We give an explicit coinduction principle for recursively-defined stochastic processes. The principle applies to any closed property, not just equality, and works even when solutions are not unique. The rule encapsulates low-level analytic arguments, allowing reasoning about such processes at a higher algebraic level. We illustrate the use of the rule in deriving properties of a simple coin-flip process."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"0711.0194","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"cs.LO","submitted_at":"2007-11-01T19:25:13Z","cross_cats_sorted":[],"title_canon_sha256":"642c4c66bc59f111cb3f593c9c42eea0f3a4565aa3dca2c02e6bae9645980545","abstract_canon_sha256":"02d20fd78bc4218c9315fc9b071f6c672a8053cf52e65779539976d9540460a9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:37:42.593685Z","signature_b64":"sy1+w7DUPyiDSBriICIfd9pK7P7smmTjZ/++HmjO+I7mzyjcWMej+QHZyzZCMrEo+ccPmAytT+4Cagj3/FqaAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"28e259dcf8ef8f04a3fc8506e29aaaaef0f1efdd54c9c99c6e7e468e946bf9c8","last_reissued_at":"2026-05-18T01:37:42.592856Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:37:42.592856Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Coinductive Proof Principles for Stochastic Processes","license":"","headline":"","cross_cats":[],"primary_cat":"cs.LO","authors_text":"Dexter Kozen","submitted_at":"2007-11-01T19:25:13Z","abstract_excerpt":"We give an explicit coinduction principle for recursively-defined stochastic processes. The principle applies to any closed property, not just equality, and works even when solutions are not unique. The rule encapsulates low-level analytic arguments, allowing reasoning about such processes at a higher algebraic level. We illustrate the use of the rule in deriving properties of a simple coin-flip process."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0711.0194","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"0711.0194","created_at":"2026-05-18T01:37:42.592978+00:00"},{"alias_kind":"arxiv_version","alias_value":"0711.0194v2","created_at":"2026-05-18T01:37:42.592978+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0711.0194","created_at":"2026-05-18T01:37:42.592978+00:00"},{"alias_kind":"pith_short_12","alias_value":"FDRFTXHY56HQ","created_at":"2026-05-18T12:25:55.427421+00:00"},{"alias_kind":"pith_short_16","alias_value":"FDRFTXHY56HQJI74","created_at":"2026-05-18T12:25:55.427421+00:00"},{"alias_kind":"pith_short_8","alias_value":"FDRFTXHY","created_at":"2026-05-18T12:25:55.427421+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/FDRFTXHY56HQJI74QUDOFGVKV3","json":"https://pith.science/pith/FDRFTXHY56HQJI74QUDOFGVKV3.json","graph_json":"https://pith.science/api/pith-number/FDRFTXHY56HQJI74QUDOFGVKV3/graph.json","events_json":"https://pith.science/api/pith-number/FDRFTXHY56HQJI74QUDOFGVKV3/events.json","paper":"https://pith.science/paper/FDRFTXHY"},"agent_actions":{"view_html":"https://pith.science/pith/FDRFTXHY56HQJI74QUDOFGVKV3","download_json":"https://pith.science/pith/FDRFTXHY56HQJI74QUDOFGVKV3.json","view_paper":"https://pith.science/paper/FDRFTXHY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0711.0194&json=true","fetch_graph":"https://pith.science/api/pith-number/FDRFTXHY56HQJI74QUDOFGVKV3/graph.json","fetch_events":"https://pith.science/api/pith-number/FDRFTXHY56HQJI74QUDOFGVKV3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FDRFTXHY56HQJI74QUDOFGVKV3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FDRFTXHY56HQJI74QUDOFGVKV3/action/storage_attestation","attest_author":"https://pith.science/pith/FDRFTXHY56HQJI74QUDOFGVKV3/action/author_attestation","sign_citation":"https://pith.science/pith/FDRFTXHY56HQJI74QUDOFGVKV3/action/citation_signature","submit_replication":"https://pith.science/pith/FDRFTXHY56HQJI74QUDOFGVKV3/action/replication_record"}},"created_at":"2026-05-18T01:37:42.592978+00:00","updated_at":"2026-05-18T01:37:42.592978+00:00"}