{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:XSMSI5YOIFGZHD7FMPIFMMIQ7K","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":"9935a3af0f0cb0ce20c48e314b061bd4fa71869ddb8a2b22ad2287f29f2e8139","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.OT","submitted_at":"2025-02-10T16:26:01Z","title_canon_sha256":"cc36b845266b2a71762bd781af642860de02cddcf075ef7f921a736cf4cee129"},"schema_version":"1.0","source":{"id":"2502.06628","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2502.06628","created_at":"2026-07-05T10:12:09Z"},{"alias_kind":"arxiv_version","alias_value":"2502.06628v1","created_at":"2026-07-05T10:12:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2502.06628","created_at":"2026-07-05T10:12:09Z"},{"alias_kind":"pith_short_12","alias_value":"XSMSI5YOIFGZ","created_at":"2026-07-05T10:12:09Z"},{"alias_kind":"pith_short_16","alias_value":"XSMSI5YOIFGZHD7F","created_at":"2026-07-05T10:12:09Z"},{"alias_kind":"pith_short_8","alias_value":"XSMSI5YO","created_at":"2026-07-05T10:12:09Z"}],"graph_snapshots":[{"event_id":"sha256:158f7573313821817547f0d48a2503edcca8e6d9a9fb352e49a2f8738ec1d087","target":"graph","created_at":"2026-07-05T10:12:09Z","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/2502.06628/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This paper examines the foundational concept of random variables in probability theory and statistical inference, demonstrating that their mathematical definition requires no reference to randomization or hypothetical repeated sampling. We show how measure-theoretic probability provides a framework for modeling populations through distributions, leading to three key contributions. First, we establish that random variables, properly understood as measurable functions, can be fully characterized without appealing to infinite hypothetical samples. Second, we demonstrate how this perspective enabl","authors_text":"Paul W. Vos","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.OT","submitted_at":"2025-02-10T16:26:01Z","title":"Random Variables aren't Random"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.06628","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":"sha256:3b950e0221be39184ab9ad620a3fd8092580016af7ba638dd20173c25ec3e704","target":"record","created_at":"2026-07-05T10:12:09Z","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":"9935a3af0f0cb0ce20c48e314b061bd4fa71869ddb8a2b22ad2287f29f2e8139","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.OT","submitted_at":"2025-02-10T16:26:01Z","title_canon_sha256":"cc36b845266b2a71762bd781af642860de02cddcf075ef7f921a736cf4cee129"},"schema_version":"1.0","source":{"id":"2502.06628","kind":"arxiv","version":1}},"canonical_sha256":"bc9924770e414d938fe563d0563110fa9215b4225536d936ffe821822168d700","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bc9924770e414d938fe563d0563110fa9215b4225536d936ffe821822168d700","first_computed_at":"2026-07-05T10:12:09.711427Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:12:09.711427Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VGTB5CXDhhtydaqwvlZlrHnVcwq5JM8v0vsVV5XWauVPUByiGOrjnsis/49RO95FtwgDzpCH5+drfKYAF4uvBg==","signature_status":"signed_v1","signed_at":"2026-07-05T10:12:09.712020Z","signed_message":"canonical_sha256_bytes"},"source_id":"2502.06628","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3b950e0221be39184ab9ad620a3fd8092580016af7ba638dd20173c25ec3e704","sha256:158f7573313821817547f0d48a2503edcca8e6d9a9fb352e49a2f8738ec1d087"],"state_sha256":"f1fbbe6c0be27a83af0d5488fe4144cfbcab1b091a83a781a0c87468ca50df7d"}