{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:3QGMT4PG2WCDS7PFDIO7TWZUNB","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":"de54e62b75eb04cf3824d0442b8dc7de9bcd1785eeef1cdb893196e6e83915f4","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2008-08-20T18:09:12Z","title_canon_sha256":"96c5db93225fd51ae1166ffe6f0310652457924a7bb3aaf8b9a06169009928a9"},"schema_version":"1.0","source":{"id":"0808.2761","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0808.2761","created_at":"2026-05-18T04:42:12Z"},{"alias_kind":"arxiv_version","alias_value":"0808.2761v5","created_at":"2026-05-18T04:42:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0808.2761","created_at":"2026-05-18T04:42:12Z"},{"alias_kind":"pith_short_12","alias_value":"3QGMT4PG2WCD","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"3QGMT4PG2WCDS7PF","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"3QGMT4PG","created_at":"2026-05-18T12:25:56Z"}],"graph_snapshots":[{"event_id":"sha256:e511a7331c0a75528124341a8849731400689709990ba1d713ddfdb3526df8fa","target":"graph","created_at":"2026-05-18T04:42:12Z","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":"In 1997 K. Ono and K. Soundararajan [Invent. Math. 130(1997)] proved that under the generalized Riemann hypothesis any positive odd integer greater than 2719 can be represented by the famous Ramanujan form $x^2+y^2+10z^2$, equivalently the form $2x^2+5y^2+4T_z$ represents all integers greater than 1359, where $T_z$ denotes the triangular number $z(z+1)/2$. Given positive integers $a,b,c$ we employ modular forms and the theory of quadratic forms to determine completely when the general form $ax^2+by^2+cT_z$ represents sufficiently large integers and establish similar results for the forms $ax^2","authors_text":"Ben Kane, Zhi-Wei Sun","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2008-08-20T18:09:12Z","title":"On almost universal mixed sums of squares and triangular numbers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0808.2761","kind":"arxiv","version":5},"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":"sha256:676b83b3d1fd6c92ebee4b50457a4e9070d0973e0521f79ed1145924c45adc0f","target":"record","created_at":"2026-05-18T04:42:12Z","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":"de54e62b75eb04cf3824d0442b8dc7de9bcd1785eeef1cdb893196e6e83915f4","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2008-08-20T18:09:12Z","title_canon_sha256":"96c5db93225fd51ae1166ffe6f0310652457924a7bb3aaf8b9a06169009928a9"},"schema_version":"1.0","source":{"id":"0808.2761","kind":"arxiv","version":5}},"canonical_sha256":"dc0cc9f1e6d584397de51a1df9db3468431b17c2fe4fffd2d8de89077bd2709b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dc0cc9f1e6d584397de51a1df9db3468431b17c2fe4fffd2d8de89077bd2709b","first_computed_at":"2026-05-18T04:42:12.568835Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:42:12.568835Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"AliBq9UQ9kuCNz+ofYjwhceJkVrBDUoopoKpnPb25rWS+8iRs4K+XA+6Hcv5P+khjidr1RUk2pi8o+TX/xlIBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:42:12.569363Z","signed_message":"canonical_sha256_bytes"},"source_id":"0808.2761","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:676b83b3d1fd6c92ebee4b50457a4e9070d0973e0521f79ed1145924c45adc0f","sha256:e511a7331c0a75528124341a8849731400689709990ba1d713ddfdb3526df8fa"],"state_sha256":"fddf4b7398ec33c2fdecaea308a678d4fe7f9cefe1c5b925f78acd68d657c9e3"}