{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:VSUZZHROO6REIF7TRXWURDXSDI","short_pith_number":"pith:VSUZZHRO","schema_version":"1.0","canonical_sha256":"aca99c9e2e77a24417f38ded488ef21a257be412f5ae25219cbea4a9f06cce1d","source":{"kind":"arxiv","id":"1602.01232","version":2},"attestation_state":"computed","paper":{"title":"On the Distribution of the Number of Goldbach Partitions of a Randomly Chosen Positive Even Integer","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Ljuben Mutafchiev","submitted_at":"2016-02-03T09:28:54Z","abstract_excerpt":"Let $\\mathcal{P}=\\{p_1,p_2,...\\}$ be the set of all odd primes arranged in increasing order. A Goldbach partition of the even integer $2k>4$ is a way of writing it as a sum of two primes from $\\mathcal{P}$ without regard to order. Let $Q(2k)$ be the number of all Goldbach partitions of the number $2k$. Assume that $2k$ is selected uniformly at random from the interval $(4,2n], n>2$, and let $Y_n=Q(2k)$ with probability $1/(n-2)$. We prove that the random variable $\\frac{Y_n}{n/\\left(\\frac{1}{2}\\log{n}\\right)^2}$ converges weakly, as $n\\to\\infty$, to a uniformly distributed random variable in t"},"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":"1602.01232","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-02-03T09:28:54Z","cross_cats_sorted":[],"title_canon_sha256":"204097c9d93205a8ec04ad48a64f02bd04d616135788ad03bafa10d91796ccd1","abstract_canon_sha256":"77f490ac722b97a6b6be4cc3834abeca9447d2f2dfbec10d416c2ccf080a573a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:09:41.792632Z","signature_b64":"n4EC8Pf1Kesdm2xh+L6vzlJPHB9HY66dxp/nvKPh6/jNw9YS5cVHjk4C1bH3ndsadq4P7DUNXmYaBEmVVKypCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"aca99c9e2e77a24417f38ded488ef21a257be412f5ae25219cbea4a9f06cce1d","last_reissued_at":"2026-05-18T01:09:41.792061Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:09:41.792061Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the Distribution of the Number of Goldbach Partitions of a Randomly Chosen Positive Even Integer","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Ljuben Mutafchiev","submitted_at":"2016-02-03T09:28:54Z","abstract_excerpt":"Let $\\mathcal{P}=\\{p_1,p_2,...\\}$ be the set of all odd primes arranged in increasing order. A Goldbach partition of the even integer $2k>4$ is a way of writing it as a sum of two primes from $\\mathcal{P}$ without regard to order. Let $Q(2k)$ be the number of all Goldbach partitions of the number $2k$. Assume that $2k$ is selected uniformly at random from the interval $(4,2n], n>2$, and let $Y_n=Q(2k)$ with probability $1/(n-2)$. We prove that the random variable $\\frac{Y_n}{n/\\left(\\frac{1}{2}\\log{n}\\right)^2}$ converges weakly, as $n\\to\\infty$, to a uniformly distributed random variable in t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.01232","kind":"arxiv","version":2},"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":"1602.01232","created_at":"2026-05-18T01:09:41.792136+00:00"},{"alias_kind":"arxiv_version","alias_value":"1602.01232v2","created_at":"2026-05-18T01:09:41.792136+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.01232","created_at":"2026-05-18T01:09:41.792136+00:00"},{"alias_kind":"pith_short_12","alias_value":"VSUZZHROO6RE","created_at":"2026-05-18T12:30:48.956258+00:00"},{"alias_kind":"pith_short_16","alias_value":"VSUZZHROO6REIF7T","created_at":"2026-05-18T12:30:48.956258+00:00"},{"alias_kind":"pith_short_8","alias_value":"VSUZZHRO","created_at":"2026-05-18T12:30:48.956258+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/VSUZZHROO6REIF7TRXWURDXSDI","json":"https://pith.science/pith/VSUZZHROO6REIF7TRXWURDXSDI.json","graph_json":"https://pith.science/api/pith-number/VSUZZHROO6REIF7TRXWURDXSDI/graph.json","events_json":"https://pith.science/api/pith-number/VSUZZHROO6REIF7TRXWURDXSDI/events.json","paper":"https://pith.science/paper/VSUZZHRO"},"agent_actions":{"view_html":"https://pith.science/pith/VSUZZHROO6REIF7TRXWURDXSDI","download_json":"https://pith.science/pith/VSUZZHROO6REIF7TRXWURDXSDI.json","view_paper":"https://pith.science/paper/VSUZZHRO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1602.01232&json=true","fetch_graph":"https://pith.science/api/pith-number/VSUZZHROO6REIF7TRXWURDXSDI/graph.json","fetch_events":"https://pith.science/api/pith-number/VSUZZHROO6REIF7TRXWURDXSDI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VSUZZHROO6REIF7TRXWURDXSDI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VSUZZHROO6REIF7TRXWURDXSDI/action/storage_attestation","attest_author":"https://pith.science/pith/VSUZZHROO6REIF7TRXWURDXSDI/action/author_attestation","sign_citation":"https://pith.science/pith/VSUZZHROO6REIF7TRXWURDXSDI/action/citation_signature","submit_replication":"https://pith.science/pith/VSUZZHROO6REIF7TRXWURDXSDI/action/replication_record"}},"created_at":"2026-05-18T01:09:41.792136+00:00","updated_at":"2026-05-18T01:09:41.792136+00:00"}