{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:RGHCBBUKQ4CLIJMAL3LCABNGGL","short_pith_number":"pith:RGHCBBUK","schema_version":"1.0","canonical_sha256":"898e20868a8704b425805ed62005a632c628f6a5bc37c225671ad75b2db9a344","source":{"kind":"arxiv","id":"1809.07244","version":1},"attestation_state":"computed","paper":{"title":"Prime-Residue-Class of Uniform Charges on the Integers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Joseph B. Kadane, Michael Spece","submitted_at":"2018-09-19T15:27:53Z","abstract_excerpt":"There is a probability charge on the power set of the integers that gives probability $1/p$ to every residue class modulo a prime $p$. There exists such a charge that gives probability $w$ to the set of prime numbers iff $w \\in [0,1/2]$. Similarly, there is such a charge that gives probability $x$ to a residue class modulo $c$, where $c$ is composite, iff $x \\in [0,1/y]$, where $y$ is the largest prime factor of $c$."},"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":"1809.07244","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-09-19T15:27:53Z","cross_cats_sorted":[],"title_canon_sha256":"8f3f26138e1b6430a951a9ce36aaa49ade57b8b327ecbc56878b546be991ea92","abstract_canon_sha256":"7758c4c04fa845c55ec121fd37d503c23e4de373b7ed767855e6ff4065e0b3ee"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:05:20.303808Z","signature_b64":"x8egwk2DUEFy17JzapcLmdRExkQxI5xz6dYtQA9O0OiH00956bIMpb29EFIkydLsySL6lfNWrpiFUpwAKs6uBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"898e20868a8704b425805ed62005a632c628f6a5bc37c225671ad75b2db9a344","last_reissued_at":"2026-05-18T00:05:20.303136Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:05:20.303136Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Prime-Residue-Class of Uniform Charges on the Integers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Joseph B. Kadane, Michael Spece","submitted_at":"2018-09-19T15:27:53Z","abstract_excerpt":"There is a probability charge on the power set of the integers that gives probability $1/p$ to every residue class modulo a prime $p$. There exists such a charge that gives probability $w$ to the set of prime numbers iff $w \\in [0,1/2]$. Similarly, there is such a charge that gives probability $x$ to a residue class modulo $c$, where $c$ is composite, iff $x \\in [0,1/y]$, where $y$ is the largest prime factor of $c$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.07244","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":"1809.07244","created_at":"2026-05-18T00:05:20.303227+00:00"},{"alias_kind":"arxiv_version","alias_value":"1809.07244v1","created_at":"2026-05-18T00:05:20.303227+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.07244","created_at":"2026-05-18T00:05:20.303227+00:00"},{"alias_kind":"pith_short_12","alias_value":"RGHCBBUKQ4CL","created_at":"2026-05-18T12:32:50.500415+00:00"},{"alias_kind":"pith_short_16","alias_value":"RGHCBBUKQ4CLIJMA","created_at":"2026-05-18T12:32:50.500415+00:00"},{"alias_kind":"pith_short_8","alias_value":"RGHCBBUK","created_at":"2026-05-18T12:32:50.500415+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/RGHCBBUKQ4CLIJMAL3LCABNGGL","json":"https://pith.science/pith/RGHCBBUKQ4CLIJMAL3LCABNGGL.json","graph_json":"https://pith.science/api/pith-number/RGHCBBUKQ4CLIJMAL3LCABNGGL/graph.json","events_json":"https://pith.science/api/pith-number/RGHCBBUKQ4CLIJMAL3LCABNGGL/events.json","paper":"https://pith.science/paper/RGHCBBUK"},"agent_actions":{"view_html":"https://pith.science/pith/RGHCBBUKQ4CLIJMAL3LCABNGGL","download_json":"https://pith.science/pith/RGHCBBUKQ4CLIJMAL3LCABNGGL.json","view_paper":"https://pith.science/paper/RGHCBBUK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1809.07244&json=true","fetch_graph":"https://pith.science/api/pith-number/RGHCBBUKQ4CLIJMAL3LCABNGGL/graph.json","fetch_events":"https://pith.science/api/pith-number/RGHCBBUKQ4CLIJMAL3LCABNGGL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/RGHCBBUKQ4CLIJMAL3LCABNGGL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/RGHCBBUKQ4CLIJMAL3LCABNGGL/action/storage_attestation","attest_author":"https://pith.science/pith/RGHCBBUKQ4CLIJMAL3LCABNGGL/action/author_attestation","sign_citation":"https://pith.science/pith/RGHCBBUKQ4CLIJMAL3LCABNGGL/action/citation_signature","submit_replication":"https://pith.science/pith/RGHCBBUKQ4CLIJMAL3LCABNGGL/action/replication_record"}},"created_at":"2026-05-18T00:05:20.303227+00:00","updated_at":"2026-05-18T00:05:20.303227+00:00"}