{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:KXDVIOUCVXGZS43AHMNPOUDHSI","short_pith_number":"pith:KXDVIOUC","canonical_record":{"source":{"id":"1607.03455","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.PL","submitted_at":"2016-07-12T18:19:22Z","cross_cats_sorted":["cs.LO"],"title_canon_sha256":"b1f328a6fa04d8a1e637f22901b5dec2a97b1a15fb9ef4e9458dc2925fcf5fc1","abstract_canon_sha256":"c5d9898f9e98464de96d60a00791167981dfab91d3eea1bfddf3bebe49f6e3d5"},"schema_version":"1.0"},"canonical_sha256":"55c7543a82adcd9973603b1af7506792131e5e485fc3073fda9a4d9acdeb669b","source":{"kind":"arxiv","id":"1607.03455","version":5},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.03455","created_at":"2026-05-18T00:20:59Z"},{"alias_kind":"arxiv_version","alias_value":"1607.03455v5","created_at":"2026-05-18T00:20:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.03455","created_at":"2026-05-18T00:20:59Z"},{"alias_kind":"pith_short_12","alias_value":"KXDVIOUCVXGZ","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_16","alias_value":"KXDVIOUCVXGZS43A","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_8","alias_value":"KXDVIOUC","created_at":"2026-05-18T12:30:29Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:KXDVIOUCVXGZS43AHMNPOUDHSI","target":"record","payload":{"canonical_record":{"source":{"id":"1607.03455","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.PL","submitted_at":"2016-07-12T18:19:22Z","cross_cats_sorted":["cs.LO"],"title_canon_sha256":"b1f328a6fa04d8a1e637f22901b5dec2a97b1a15fb9ef4e9458dc2925fcf5fc1","abstract_canon_sha256":"c5d9898f9e98464de96d60a00791167981dfab91d3eea1bfddf3bebe49f6e3d5"},"schema_version":"1.0"},"canonical_sha256":"55c7543a82adcd9973603b1af7506792131e5e485fc3073fda9a4d9acdeb669b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:20:59.360993Z","signature_b64":"NaN40B2bE5+WAj/23ZXMFaQ7likXxsY8+IWtnYVOkd9gFqwCN27rqtJy0dmCtoIMikXxKoxPf1OAPHP6N3KpBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"55c7543a82adcd9973603b1af7506792131e5e485fc3073fda9a4d9acdeb669b","last_reissued_at":"2026-05-18T00:20:59.360346Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:20:59.360346Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1607.03455","source_version":5,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:20:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vylobnpxapY9Zew4RXmJcTFsRVlpyxVD7vyx/wc5qbjVibCdU+UmC3IQAxcprOyY7InjDgwhOL+14j228HM0BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T08:34:50.892361Z"},"content_sha256":"0718056607ae839ccf1d386b18cef6c1b2bb241980038a8033ab174b113f504c","schema_version":"1.0","event_id":"sha256:0718056607ae839ccf1d386b18cef6c1b2bb241980038a8033ab174b113f504c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:KXDVIOUCVXGZS43AHMNPOUDHSI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Coupling proofs are probabilistic product programs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LO"],"primary_cat":"cs.PL","authors_text":"Benjamin Gr\\'egoire, Gilles Barthe, Justin Hsu, Pierre-Yves Strub","submitted_at":"2016-07-12T18:19:22Z","abstract_excerpt":"Couplings are a powerful mathematical tool for reasoning about pairs of probabilistic processes. Recent developments in formal verification identify a close connection between couplings and pRHL, a relational program logic motivated by applications to provable security, enabling formal construction of couplings from the probability theory literature. However, existing work using pRHL merely shows existence of a coupling and does not give a way to prove quantitative properties about the coupling, which are need to reason about mixing and convergence of probabilistic processes. Furthermore, pRHL"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.03455","kind":"arxiv","version":5},"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":"2026-05-18T00:20:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UW9EhKot6db+spdacHmOgJ5ot7RAAxQX/hXSKiyMTgilojO48kkP+hKetP5fDr7JYMX6AO8ZsGBKiECWGID7AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T08:34:50.892705Z"},"content_sha256":"12a5a1bd3a28a7fdb945b6060b78f55c451382b7307c56ed78f7d9b8b0436dda","schema_version":"1.0","event_id":"sha256:12a5a1bd3a28a7fdb945b6060b78f55c451382b7307c56ed78f7d9b8b0436dda"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KXDVIOUCVXGZS43AHMNPOUDHSI/bundle.json","state_url":"https://pith.science/pith/KXDVIOUCVXGZS43AHMNPOUDHSI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KXDVIOUCVXGZS43AHMNPOUDHSI/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":"2026-06-29T08:34:50Z","links":{"resolver":"https://pith.science/pith/KXDVIOUCVXGZS43AHMNPOUDHSI","bundle":"https://pith.science/pith/KXDVIOUCVXGZS43AHMNPOUDHSI/bundle.json","state":"https://pith.science/pith/KXDVIOUCVXGZS43AHMNPOUDHSI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KXDVIOUCVXGZS43AHMNPOUDHSI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:KXDVIOUCVXGZS43AHMNPOUDHSI","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":"c5d9898f9e98464de96d60a00791167981dfab91d3eea1bfddf3bebe49f6e3d5","cross_cats_sorted":["cs.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.PL","submitted_at":"2016-07-12T18:19:22Z","title_canon_sha256":"b1f328a6fa04d8a1e637f22901b5dec2a97b1a15fb9ef4e9458dc2925fcf5fc1"},"schema_version":"1.0","source":{"id":"1607.03455","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.03455","created_at":"2026-05-18T00:20:59Z"},{"alias_kind":"arxiv_version","alias_value":"1607.03455v5","created_at":"2026-05-18T00:20:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.03455","created_at":"2026-05-18T00:20:59Z"},{"alias_kind":"pith_short_12","alias_value":"KXDVIOUCVXGZ","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_16","alias_value":"KXDVIOUCVXGZS43A","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_8","alias_value":"KXDVIOUC","created_at":"2026-05-18T12:30:29Z"}],"graph_snapshots":[{"event_id":"sha256:12a5a1bd3a28a7fdb945b6060b78f55c451382b7307c56ed78f7d9b8b0436dda","target":"graph","created_at":"2026-05-18T00:20:59Z","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":"Couplings are a powerful mathematical tool for reasoning about pairs of probabilistic processes. Recent developments in formal verification identify a close connection between couplings and pRHL, a relational program logic motivated by applications to provable security, enabling formal construction of couplings from the probability theory literature. However, existing work using pRHL merely shows existence of a coupling and does not give a way to prove quantitative properties about the coupling, which are need to reason about mixing and convergence of probabilistic processes. Furthermore, pRHL","authors_text":"Benjamin Gr\\'egoire, Gilles Barthe, Justin Hsu, Pierre-Yves Strub","cross_cats":["cs.LO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.PL","submitted_at":"2016-07-12T18:19:22Z","title":"Coupling proofs are probabilistic product programs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.03455","kind":"arxiv","version":5},"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":"sha256:0718056607ae839ccf1d386b18cef6c1b2bb241980038a8033ab174b113f504c","target":"record","created_at":"2026-05-18T00:20:59Z","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":"c5d9898f9e98464de96d60a00791167981dfab91d3eea1bfddf3bebe49f6e3d5","cross_cats_sorted":["cs.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.PL","submitted_at":"2016-07-12T18:19:22Z","title_canon_sha256":"b1f328a6fa04d8a1e637f22901b5dec2a97b1a15fb9ef4e9458dc2925fcf5fc1"},"schema_version":"1.0","source":{"id":"1607.03455","kind":"arxiv","version":5}},"canonical_sha256":"55c7543a82adcd9973603b1af7506792131e5e485fc3073fda9a4d9acdeb669b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"55c7543a82adcd9973603b1af7506792131e5e485fc3073fda9a4d9acdeb669b","first_computed_at":"2026-05-18T00:20:59.360346Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:20:59.360346Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NaN40B2bE5+WAj/23ZXMFaQ7likXxsY8+IWtnYVOkd9gFqwCN27rqtJy0dmCtoIMikXxKoxPf1OAPHP6N3KpBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:20:59.360993Z","signed_message":"canonical_sha256_bytes"},"source_id":"1607.03455","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0718056607ae839ccf1d386b18cef6c1b2bb241980038a8033ab174b113f504c","sha256:12a5a1bd3a28a7fdb945b6060b78f55c451382b7307c56ed78f7d9b8b0436dda"],"state_sha256":"e71c84bc5c5cfe75f731ce142e220e66fa0df9d6d11f5e23112a0dd5b0a05aa6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"T6xW2W/HZEpGIMvYbSXFRgjAn7PRlV0sNS0XuWnp0OTc+sX9p9xUOyhjxtO77lRvgH7dTIzLUszr1ee6GYEUAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-29T08:34:50.894869Z","bundle_sha256":"025eaa442301642229172833c62227982dae004725511ca0606362854576a857"}}