{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:GXNWTJKQOHB2G5QZVEPADD2PDT","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":"99051f137598bdcf7321a03c59de0498f275d260f4bdd41451c0616f5c437ffd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2015-09-06T13:35:07Z","title_canon_sha256":"777ff050a9b65782d8317ba269b4f1403fbe7693516edcc6728e7e15c5a29a17"},"schema_version":"1.0","source":{"id":"1509.01812","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.01812","created_at":"2026-05-18T01:04:57Z"},{"alias_kind":"arxiv_version","alias_value":"1509.01812v4","created_at":"2026-05-18T01:04:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.01812","created_at":"2026-05-18T01:04:57Z"},{"alias_kind":"pith_short_12","alias_value":"GXNWTJKQOHB2","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_16","alias_value":"GXNWTJKQOHB2G5QZ","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_8","alias_value":"GXNWTJKQ","created_at":"2026-05-18T12:29:22Z"}],"graph_snapshots":[{"event_id":"sha256:cec00ff8f71321d4d7f25a1070b073dd8a9e16581bfcd998e84f8d0d17c35fbb","target":"graph","created_at":"2026-05-18T01:04:57Z","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":"We use sets of assignments, a.k.a. teams, and measures on them to define probabilities of first-order formulas in given data. We then axiomatise first-order properties of such probabilities and prove a completeness theorem for our axiomatisation. We use the Hardy-Weinberg Principle of biology and the Bell's Inequalities of quantum physics as examples.","authors_text":"Gianluca Paolini, Jouko V\\\"a\\\"an\\\"anen, Tapani Hyttinen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2015-09-06T13:35:07Z","title":"A Logic for Arguing About Probabilities in Measure Teams"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.01812","kind":"arxiv","version":4},"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:f888b34d249ddf165103e33bb2582ca2efe64c259e5891c831b4f40062907ec9","target":"record","created_at":"2026-05-18T01:04:57Z","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":"99051f137598bdcf7321a03c59de0498f275d260f4bdd41451c0616f5c437ffd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2015-09-06T13:35:07Z","title_canon_sha256":"777ff050a9b65782d8317ba269b4f1403fbe7693516edcc6728e7e15c5a29a17"},"schema_version":"1.0","source":{"id":"1509.01812","kind":"arxiv","version":4}},"canonical_sha256":"35db69a55071c3a37619a91e018f4f1cf730f80c496975464aba918213725096","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"35db69a55071c3a37619a91e018f4f1cf730f80c496975464aba918213725096","first_computed_at":"2026-05-18T01:04:57.838131Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:04:57.838131Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"S1Z1rxyIqXi1/B5jDGM3Gi6Fh99N9/C1Ahfc2eg4Otek/QgcsWBEnLI93H+jglXV63SFCt4qta/9Z4yda1E3CQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:04:57.838713Z","signed_message":"canonical_sha256_bytes"},"source_id":"1509.01812","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f888b34d249ddf165103e33bb2582ca2efe64c259e5891c831b4f40062907ec9","sha256:cec00ff8f71321d4d7f25a1070b073dd8a9e16581bfcd998e84f8d0d17c35fbb"],"state_sha256":"a1e6e05de632207aad8d965aaabde62a089a6eeb03f7708e021245fc4750aae0"}