{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:AK2R4N3ZUSKPRGEZIPWAYX4EZB","short_pith_number":"pith:AK2R4N3Z","schema_version":"1.0","canonical_sha256":"02b51e3779a494f8989943ec0c5f84c85ab940f24c43c26a6cbeb53a5dc1748e","source":{"kind":"arxiv","id":"2605.23601","version":1},"attestation_state":"computed","paper":{"title":"Congruence Classes of Supporting the Erd\\\"{o}s-Straus Conjecture I: Tame Solutions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Xiaoping Xu","submitted_at":"2026-05-22T13:11:06Z","abstract_excerpt":"In 1948, Erd\\\"{o}s and Straus formulated a conjecture : for any positive integer $n>2$, there exist positive integers $n_1,n_2$ and $n_3$ such that \\begin{equation}\\frac{4}{n}=\\frac{1}{n_1}+\\frac{1}{n_2}+\\frac{1}{n_3},\\nonumber\\end{equation} which is still open. It is known that one only needs to prove the conjecture for any prime number $n$ such that $n\\equiv 1\\;(\\mbox{mod}\\;24)$. If $n=24m+1$ and $n_1\\leq n_2,n_3$, then $n_1=6m+k$ with $1\\leq k\\leq 12m$. A solution $(n_1,n_2,n_3)$ of the above equation is called a {\\it tame solution} if $n_2$ and $n_3$ are factors of $(6m+k)(24m+1)$. We call"},"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":"2605.23601","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2026-05-22T13:11:06Z","cross_cats_sorted":[],"title_canon_sha256":"a6fea8d84dc6c40c64e1386ef3dc12049a14108d32aaf333bf55889102d4e3fb","abstract_canon_sha256":"01e5c697c1f25cc949d2977c6f25461b6b7d6e5fe8a81e8c0d8bf1b7dc00401e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-25T02:02:21.653792Z","signature_b64":"mPFq9vZGBGVcLhmBNGL11xP6KRZdM2hJJxzJGCldhBN0dDLuypq+z4GPWWgjVOrcSSFS1G4FzvTDmDsLjl1dCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"02b51e3779a494f8989943ec0c5f84c85ab940f24c43c26a6cbeb53a5dc1748e","last_reissued_at":"2026-05-25T02:02:21.653040Z","signature_status":"signed_v1","first_computed_at":"2026-05-25T02:02:21.653040Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Congruence Classes of Supporting the Erd\\\"{o}s-Straus Conjecture I: Tame Solutions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Xiaoping Xu","submitted_at":"2026-05-22T13:11:06Z","abstract_excerpt":"In 1948, Erd\\\"{o}s and Straus formulated a conjecture : for any positive integer $n>2$, there exist positive integers $n_1,n_2$ and $n_3$ such that \\begin{equation}\\frac{4}{n}=\\frac{1}{n_1}+\\frac{1}{n_2}+\\frac{1}{n_3},\\nonumber\\end{equation} which is still open. It is known that one only needs to prove the conjecture for any prime number $n$ such that $n\\equiv 1\\;(\\mbox{mod}\\;24)$. If $n=24m+1$ and $n_1\\leq n_2,n_3$, then $n_1=6m+k$ with $1\\leq k\\leq 12m$. A solution $(n_1,n_2,n_3)$ of the above equation is called a {\\it tame solution} if $n_2$ and $n_3$ are factors of $(6m+k)(24m+1)$. 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