{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:SPKYNT4JHBJODVCYKMIZRTPSQ6","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":"837eb7e7f6f846023451d247d5bccea79d44d4619d98cc10585d40ddf4449799","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-09-12T08:21:54Z","title_canon_sha256":"a41ec942afd558e8f95fa2da900b05d5e60c3055e8f4ab445a08c9060f6ebad1"},"schema_version":"1.0","source":{"id":"1109.2396","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.2396","created_at":"2026-05-18T04:13:37Z"},{"alias_kind":"arxiv_version","alias_value":"1109.2396v1","created_at":"2026-05-18T04:13:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.2396","created_at":"2026-05-18T04:13:37Z"},{"alias_kind":"pith_short_12","alias_value":"SPKYNT4JHBJO","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_16","alias_value":"SPKYNT4JHBJODVCY","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_8","alias_value":"SPKYNT4J","created_at":"2026-05-18T12:26:41Z"}],"graph_snapshots":[{"event_id":"sha256:a53453ac8350e609da21c990511628401a8711a9a2ff71ce9fab08f5371f256e","target":"graph","created_at":"2026-05-18T04:13:37Z","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 discuss finding large integer solutions of $d=2x^3+y^3+z^3$ by using Elsenhans and Jahnel's adaptation of Elkies' LLL-reduction method. We find 28 first solutions for $|d|<10000$.","authors_text":"Allan J. MacLeod","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-09-12T08:21:54Z","title":"New Solutions of $d=2x^3+y^3+z^3$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.2396","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":"sha256:0949aff8ee786ca3b04f2645521af67e3c5f49e22f917a48528643c5d4ff91ce","target":"record","created_at":"2026-05-18T04:13:37Z","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":"837eb7e7f6f846023451d247d5bccea79d44d4619d98cc10585d40ddf4449799","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-09-12T08:21:54Z","title_canon_sha256":"a41ec942afd558e8f95fa2da900b05d5e60c3055e8f4ab445a08c9060f6ebad1"},"schema_version":"1.0","source":{"id":"1109.2396","kind":"arxiv","version":1}},"canonical_sha256":"93d586cf893852e1d458531198cdf28785def4fa71457e17fccc0340f815a493","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"93d586cf893852e1d458531198cdf28785def4fa71457e17fccc0340f815a493","first_computed_at":"2026-05-18T04:13:37.754696Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:13:37.754696Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LrAyiT0yRWtmfDfAtxYs9WUIQ3qnROQ18yte4rdS9gH53LrsSEKbmF6CgrRrm/pVc4ZVoILpSuswBfSHeHl8Cw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:13:37.755246Z","signed_message":"canonical_sha256_bytes"},"source_id":"1109.2396","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0949aff8ee786ca3b04f2645521af67e3c5f49e22f917a48528643c5d4ff91ce","sha256:a53453ac8350e609da21c990511628401a8711a9a2ff71ce9fab08f5371f256e"],"state_sha256":"a13630458513a065249eeb647717c4124093ed4d93ccd7511c6ad755abf6e9db"}