{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:5WZDB6NCUHSKY4J3DMSFCSAJXK","short_pith_number":"pith:5WZDB6NC","schema_version":"1.0","canonical_sha256":"edb230f9a2a1e4ac713b1b24514809bab1f52438ce0147c9d0caf2093b2aa64e","source":{"kind":"arxiv","id":"2607.10654","version":1},"attestation_state":"computed","paper":{"title":"The Prime Digit Distribution Conjecture: A Formal Proof of Average Digit Equidistribution in the Prime Numbers","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Mahadee Al Mobin, Md. Shariful Islam","submitted_at":"2026-07-12T08:40:29Z","abstract_excerpt":"Let $S_n=\\{p\\in\\mathbb{P}:p<10^n\\}$, $N_n$ denote the total number of decimal digits occurring in the primes of $S_n$, $C_n(d)$ be the number of occurrences of a digit $d\\in\\{0,\\ldots,9\\}$ among those digits, and $P_n(d)$ be the probability of occurrence of a digit, $d$ among those digits. We prove that\n  \\[\n  P_n(d)=\\frac{C_n(d)}{N_n}\n  =\\frac{1}{10}\n  +O\\!\\left(\\frac{\\log n}{n}\\right),\n  \\qquad n\\to\\infty,\n  \\]\n  uniformly for every decimal digit $d$. The argument is entirely unconditional and combines the Prime Number Theorem, the Erd\\H{o}s--Tur\\'an discrepancy inequality, and classical Vau"},"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":"2607.10654","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.NT","submitted_at":"2026-07-12T08:40:29Z","cross_cats_sorted":[],"title_canon_sha256":"0b1ba3db1c2aa58b57a5b0c1e8805eef7e8d1d5299d6bcb5fcdd468cf1441451","abstract_canon_sha256":"14f7ac33be15352354a7e6c64cda995b8acaed47b6e2d84a31cd573359136276"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-14T01:21:32.751219Z","signature_b64":"+yqqaeUI68ngnR17UjVKE7Uaqkropy+tW2jR59IJ7GEFrbSPhOLsUsK+qLth66Vq9toGx+Fp5NST0hIIEMboDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"edb230f9a2a1e4ac713b1b24514809bab1f52438ce0147c9d0caf2093b2aa64e","last_reissued_at":"2026-07-14T01:21:32.750407Z","signature_status":"signed_v1","first_computed_at":"2026-07-14T01:21:32.750407Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Prime Digit Distribution Conjecture: A Formal Proof of Average Digit Equidistribution in the Prime Numbers","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Mahadee Al Mobin, Md. Shariful Islam","submitted_at":"2026-07-12T08:40:29Z","abstract_excerpt":"Let $S_n=\\{p\\in\\mathbb{P}:p<10^n\\}$, $N_n$ denote the total number of decimal digits occurring in the primes of $S_n$, $C_n(d)$ be the number of occurrences of a digit $d\\in\\{0,\\ldots,9\\}$ among those digits, and $P_n(d)$ be the probability of occurrence of a digit, $d$ among those digits. We prove that\n  \\[\n  P_n(d)=\\frac{C_n(d)}{N_n}\n  =\\frac{1}{10}\n  +O\\!\\left(\\frac{\\log n}{n}\\right),\n  \\qquad n\\to\\infty,\n  \\]\n  uniformly for every decimal digit $d$. The argument is entirely unconditional and combines the Prime Number Theorem, the Erd\\H{o}s--Tur\\'an discrepancy inequality, and classical Vau"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.10654","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.10654/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2607.10654","created_at":"2026-07-14T01:21:32.750832+00:00"},{"alias_kind":"arxiv_version","alias_value":"2607.10654v1","created_at":"2026-07-14T01:21:32.750832+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.10654","created_at":"2026-07-14T01:21:32.750832+00:00"},{"alias_kind":"pith_short_12","alias_value":"5WZDB6NCUHSK","created_at":"2026-07-14T01:21:32.750832+00:00"},{"alias_kind":"pith_short_16","alias_value":"5WZDB6NCUHSKY4J3","created_at":"2026-07-14T01:21:32.750832+00:00"},{"alias_kind":"pith_short_8","alias_value":"5WZDB6NC","created_at":"2026-07-14T01:21:32.750832+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/5WZDB6NCUHSKY4J3DMSFCSAJXK","json":"https://pith.science/pith/5WZDB6NCUHSKY4J3DMSFCSAJXK.json","graph_json":"https://pith.science/api/pith-number/5WZDB6NCUHSKY4J3DMSFCSAJXK/graph.json","events_json":"https://pith.science/api/pith-number/5WZDB6NCUHSKY4J3DMSFCSAJXK/events.json","paper":"https://pith.science/paper/5WZDB6NC"},"agent_actions":{"view_html":"https://pith.science/pith/5WZDB6NCUHSKY4J3DMSFCSAJXK","download_json":"https://pith.science/pith/5WZDB6NCUHSKY4J3DMSFCSAJXK.json","view_paper":"https://pith.science/paper/5WZDB6NC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2607.10654&json=true","fetch_graph":"https://pith.science/api/pith-number/5WZDB6NCUHSKY4J3DMSFCSAJXK/graph.json","fetch_events":"https://pith.science/api/pith-number/5WZDB6NCUHSKY4J3DMSFCSAJXK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/5WZDB6NCUHSKY4J3DMSFCSAJXK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/5WZDB6NCUHSKY4J3DMSFCSAJXK/action/storage_attestation","attest_author":"https://pith.science/pith/5WZDB6NCUHSKY4J3DMSFCSAJXK/action/author_attestation","sign_citation":"https://pith.science/pith/5WZDB6NCUHSKY4J3DMSFCSAJXK/action/citation_signature","submit_replication":"https://pith.science/pith/5WZDB6NCUHSKY4J3DMSFCSAJXK/action/replication_record"}},"created_at":"2026-07-14T01:21:32.750832+00:00","updated_at":"2026-07-14T01:21:32.750832+00:00"}