{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:IGNEKWS5JHL4MFSDV5QT3B74CH","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":"5c5f2178bd0f6bd5c25bdfed1e050575a8075255268b36e9ce35dff97a47eea3","cross_cats_sorted":["math.PR"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"cs.LO","submitted_at":"2023-02-13T03:39:45Z","title_canon_sha256":"23f3b7f5e45b3b9ad2b4cb6a4bf2ac9e344d5ec47d3a43c1f02f37307d045f26"},"schema_version":"1.0","source":{"id":"2302.06082","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2302.06082","created_at":"2026-07-05T05:41:01Z"},{"alias_kind":"arxiv_version","alias_value":"2302.06082v1","created_at":"2026-07-05T05:41:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2302.06082","created_at":"2026-07-05T05:41:01Z"},{"alias_kind":"pith_short_12","alias_value":"IGNEKWS5JHL4","created_at":"2026-07-05T05:41:01Z"},{"alias_kind":"pith_short_16","alias_value":"IGNEKWS5JHL4MFSD","created_at":"2026-07-05T05:41:01Z"},{"alias_kind":"pith_short_8","alias_value":"IGNEKWS5","created_at":"2026-07-05T05:41:01Z"}],"graph_snapshots":[{"event_id":"sha256:063b8269dfa27deb5aff0c48ff91d2a416f3171c9dca50bb60029625305a0e9f","target":"graph","created_at":"2026-07-05T05:41:01Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2302.06082/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We present a new proof rule for verifying lower bounds on quantities of probabilistic programs. Our proof rule is not confined to almost-surely terminating programs -- as is the case for existing rules -- and can be used to establish non-trivial lower bounds on, e.g., termination probabilities and expected values, for possibly divergent probabilistic loops, e.g., the well-known three-dimensional random walk on a lattice.","authors_text":"Benjamin Lucien Kaminski, Han Su, Joost-Pieter Katoen, Mingshuai Chen, Naijun Zhan, Shenghua Feng","cross_cats":["math.PR"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"cs.LO","submitted_at":"2023-02-13T03:39:45Z","title":"Lower Bounds for Possibly Divergent Probabilistic Programs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2302.06082","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":"sha256:8a73b30b527be7725f563d395aff2fbcfc43a5b219a23bad0d20281a3a3c1d92","target":"record","created_at":"2026-07-05T05:41:01Z","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":"5c5f2178bd0f6bd5c25bdfed1e050575a8075255268b36e9ce35dff97a47eea3","cross_cats_sorted":["math.PR"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"cs.LO","submitted_at":"2023-02-13T03:39:45Z","title_canon_sha256":"23f3b7f5e45b3b9ad2b4cb6a4bf2ac9e344d5ec47d3a43c1f02f37307d045f26"},"schema_version":"1.0","source":{"id":"2302.06082","kind":"arxiv","version":1}},"canonical_sha256":"419a455a5d49d7c61643af613d87fc11c6e854bb45a5e337370e6a30237e914c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"419a455a5d49d7c61643af613d87fc11c6e854bb45a5e337370e6a30237e914c","first_computed_at":"2026-07-05T05:41:01.802189Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:41:01.802189Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Hq/fjOFRNhu+eOehCgBDGrvZX6mUekK3JZRYOSJ6gAjARnZXIGQ+5SFUX81CgCiJ0POG2gqdMRzmrQPB8eGqCQ==","signature_status":"signed_v1","signed_at":"2026-07-05T05:41:01.802612Z","signed_message":"canonical_sha256_bytes"},"source_id":"2302.06082","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8a73b30b527be7725f563d395aff2fbcfc43a5b219a23bad0d20281a3a3c1d92","sha256:063b8269dfa27deb5aff0c48ff91d2a416f3171c9dca50bb60029625305a0e9f"],"state_sha256":"255d978fc6c5994d87d8f8fa46d37b68677f6140fc542281f6474b38cd3a2334"}