{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:5X5TUG537BINC4TFXHOVH6UVYP","short_pith_number":"pith:5X5TUG53","schema_version":"1.0","canonical_sha256":"edfb3a1bbbf850d17265b9dd53fa95c3ecf9fb0a2da6921b77e47de4faf13f16","source":{"kind":"arxiv","id":"1605.02765","version":1},"attestation_state":"computed","paper":{"title":"Synthesizing Probabilistic Invariants via Doob's Decomposition","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.SC"],"primary_cat":"cs.PL","authors_text":"Gilles Barthe, Justin Hsu, Luis Mar\\'ia Ferrer Fioriti, Thomas Espitau","submitted_at":"2016-05-09T20:30:20Z","abstract_excerpt":"When analyzing probabilistic computations, a powerful approach is to first find a martingale---an expression on the program variables whose expectation remains invariant---and then apply the optional stopping theorem in order to infer properties at termination time. One of the main challenges, then, is to systematically find martingales.\n  We propose a novel procedure to synthesize martingale expressions from an arbitrary initial expression. Contrary to state-of-the-art approaches, we do not rely on constraint solving. Instead, we use a symbolic construction based on Doob's decomposition. This"},"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":"1605.02765","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.PL","submitted_at":"2016-05-09T20:30:20Z","cross_cats_sorted":["cs.SC"],"title_canon_sha256":"4e8b9c4346f38fea1a2cfd35bea1a0320e9aafef9c88ed54f596c0dcdb4d866f","abstract_canon_sha256":"bce85e243dd789b2aa3a99cbd545dca45fdd31a6c24fc440004ebd74a20502ff"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:20:59.517637Z","signature_b64":"DPwHkQn0HsohXpSPK8iWhp4Fe4Wwmw9yoEDxCBwWb1R8UvgFTFjVZ5VYCM5+r0RHQlLZwv6N7TloP9DXAGJkAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"edfb3a1bbbf850d17265b9dd53fa95c3ecf9fb0a2da6921b77e47de4faf13f16","last_reissued_at":"2026-05-18T00:20:59.517188Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:20:59.517188Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Synthesizing Probabilistic Invariants via Doob's Decomposition","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.SC"],"primary_cat":"cs.PL","authors_text":"Gilles Barthe, Justin Hsu, Luis Mar\\'ia Ferrer Fioriti, Thomas Espitau","submitted_at":"2016-05-09T20:30:20Z","abstract_excerpt":"When analyzing probabilistic computations, a powerful approach is to first find a martingale---an expression on the program variables whose expectation remains invariant---and then apply the optional stopping theorem in order to infer properties at termination time. One of the main challenges, then, is to systematically find martingales.\n  We propose a novel procedure to synthesize martingale expressions from an arbitrary initial expression. Contrary to state-of-the-art approaches, we do not rely on constraint solving. Instead, we use a symbolic construction based on Doob's decomposition. This"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.02765","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1605.02765","created_at":"2026-05-18T00:20:59.517260+00:00"},{"alias_kind":"arxiv_version","alias_value":"1605.02765v1","created_at":"2026-05-18T00:20:59.517260+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.02765","created_at":"2026-05-18T00:20:59.517260+00:00"},{"alias_kind":"pith_short_12","alias_value":"5X5TUG537BIN","created_at":"2026-05-18T12:30:01.593930+00:00"},{"alias_kind":"pith_short_16","alias_value":"5X5TUG537BINC4TF","created_at":"2026-05-18T12:30:01.593930+00:00"},{"alias_kind":"pith_short_8","alias_value":"5X5TUG53","created_at":"2026-05-18T12:30:01.593930+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/5X5TUG537BINC4TFXHOVH6UVYP","json":"https://pith.science/pith/5X5TUG537BINC4TFXHOVH6UVYP.json","graph_json":"https://pith.science/api/pith-number/5X5TUG537BINC4TFXHOVH6UVYP/graph.json","events_json":"https://pith.science/api/pith-number/5X5TUG537BINC4TFXHOVH6UVYP/events.json","paper":"https://pith.science/paper/5X5TUG53"},"agent_actions":{"view_html":"https://pith.science/pith/5X5TUG537BINC4TFXHOVH6UVYP","download_json":"https://pith.science/pith/5X5TUG537BINC4TFXHOVH6UVYP.json","view_paper":"https://pith.science/paper/5X5TUG53","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1605.02765&json=true","fetch_graph":"https://pith.science/api/pith-number/5X5TUG537BINC4TFXHOVH6UVYP/graph.json","fetch_events":"https://pith.science/api/pith-number/5X5TUG537BINC4TFXHOVH6UVYP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/5X5TUG537BINC4TFXHOVH6UVYP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/5X5TUG537BINC4TFXHOVH6UVYP/action/storage_attestation","attest_author":"https://pith.science/pith/5X5TUG537BINC4TFXHOVH6UVYP/action/author_attestation","sign_citation":"https://pith.science/pith/5X5TUG537BINC4TFXHOVH6UVYP/action/citation_signature","submit_replication":"https://pith.science/pith/5X5TUG537BINC4TFXHOVH6UVYP/action/replication_record"}},"created_at":"2026-05-18T00:20:59.517260+00:00","updated_at":"2026-05-18T00:20:59.517260+00:00"}