{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:PES7YJB35ENDRS26C343GNV3KO","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":"dc0ded6834fbfdf000d0defd3440f55eefb99c4123ba92385395dccc8d940e06","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-06-01T16:54:57Z","title_canon_sha256":"467f53e230806a181dfa3a491adefcb732501033f0b532677d5fe7f52bcbcef7"},"schema_version":"1.0","source":{"id":"1206.0246","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1206.0246","created_at":"2026-05-18T03:37:52Z"},{"alias_kind":"arxiv_version","alias_value":"1206.0246v1","created_at":"2026-05-18T03:37:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.0246","created_at":"2026-05-18T03:37:52Z"},{"alias_kind":"pith_short_12","alias_value":"PES7YJB35END","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_16","alias_value":"PES7YJB35ENDRS26","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_8","alias_value":"PES7YJB3","created_at":"2026-05-18T12:27:18Z"}],"graph_snapshots":[{"event_id":"sha256:dfd98b863116dcb369b067150ae0e19f54638682b0c42ed894f8751d169e76ea","target":"graph","created_at":"2026-05-18T03:37:52Z","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"},"paper":{"abstract_excerpt":"We prove that if $\\lambda_1$, $\\lambda_2$, $\\lambda_3$ and $\\lambda_4$ are non-zero real numbers, not all of the same sign, $\\lambda_1 / \\lambda_2$ is irrational, and $\\varpi$ is any real number then, for any $\\eps > 0$ the inequality $\n  \\bigl|\\lambda_1 p_1 + \\lambda_2 p_2^2 + \\lambda_3 p_3^2 + \\lambda_4 p_4^2 + \\varpi \\bigr| \\le \\bigl(\\max_j p_j \\bigr)^{-1 / 18 + \\eps} $\nhas infinitely many solution in prime variables $p_1$, ..., $p_4$","authors_text":"Alessandro Languasco, Alessandro Zaccagnini","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-06-01T16:54:57Z","title":"A Diophantine problem with a prime and three squares of primes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.0246","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":"sha256:25c7cdea3574d913d66c7bba83559c2b3291fae7516851fd98b08d2fca2a4115","target":"record","created_at":"2026-05-18T03:37:52Z","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":"dc0ded6834fbfdf000d0defd3440f55eefb99c4123ba92385395dccc8d940e06","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-06-01T16:54:57Z","title_canon_sha256":"467f53e230806a181dfa3a491adefcb732501033f0b532677d5fe7f52bcbcef7"},"schema_version":"1.0","source":{"id":"1206.0246","kind":"arxiv","version":1}},"canonical_sha256":"7925fc243be91a38cb5e16f9b336bb538d736394933b14a1047448bf2cf14d0d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7925fc243be91a38cb5e16f9b336bb538d736394933b14a1047448bf2cf14d0d","first_computed_at":"2026-05-18T03:37:52.822518Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:37:52.822518Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ULF2FRwNI18qoEVLRzffiD7WFg4jIKf24CV7RXMdPEp419jAhc04OkBRxQSln3rwyKFlGc/lUk5q4RcZE5iXCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:37:52.823347Z","signed_message":"canonical_sha256_bytes"},"source_id":"1206.0246","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:25c7cdea3574d913d66c7bba83559c2b3291fae7516851fd98b08d2fca2a4115","sha256:dfd98b863116dcb369b067150ae0e19f54638682b0c42ed894f8751d169e76ea"],"state_sha256":"c6fa4add0b98ebc43ecf1d77cd10671e7dbaf053a72d06455ae13353abc11d63"}