{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:PTHBUILNHYPHPA2BG4UOZS3QIS","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":"fc6a51bb903897e732903b240c25dc9c150a3977048fc1a8e5aca21319a90c9e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-08-11T19:14:33Z","title_canon_sha256":"9cf4db37741298aafeadfcdc0ff43aa60445479d20cdc305837de4a4f76a583f"},"schema_version":"1.0","source":{"id":"1508.02694","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.02694","created_at":"2026-05-18T01:21:37Z"},{"alias_kind":"arxiv_version","alias_value":"1508.02694v1","created_at":"2026-05-18T01:21:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.02694","created_at":"2026-05-18T01:21:37Z"},{"alias_kind":"pith_short_12","alias_value":"PTHBUILNHYPH","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_16","alias_value":"PTHBUILNHYPHPA2B","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_8","alias_value":"PTHBUILN","created_at":"2026-05-18T12:29:37Z"}],"graph_snapshots":[{"event_id":"sha256:08cc654680c4e790a9e64f8697bc56bfe49b63b9ad2a4519a3ca6abd087948fc","target":"graph","created_at":"2026-05-18T01:21:37Z","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":"Mordell in 1958 gave a new proof of the three squares theorem. We generalize those techniques to characterize the integers represented by the remaining six \"Ramanujan-Dickson ternaries\" as well as three other ternary forms.","authors_text":"Gabriel Durham, Katherine Thompson, Sarah Blackwell, Tiffany Treece","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-08-11T19:14:33Z","title":"A Generalization of Mordell to Ternary Quadratic Forms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.02694","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":"sha256:0ca9b16185938b4636eecf45285fa31c64b6889030454c9eef4a19084d4b0608","target":"record","created_at":"2026-05-18T01:21:37Z","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":"fc6a51bb903897e732903b240c25dc9c150a3977048fc1a8e5aca21319a90c9e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-08-11T19:14:33Z","title_canon_sha256":"9cf4db37741298aafeadfcdc0ff43aa60445479d20cdc305837de4a4f76a583f"},"schema_version":"1.0","source":{"id":"1508.02694","kind":"arxiv","version":1}},"canonical_sha256":"7cce1a216d3e1e7783413728eccb70449d94b487ea5dcdef5050ef43bb717685","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7cce1a216d3e1e7783413728eccb70449d94b487ea5dcdef5050ef43bb717685","first_computed_at":"2026-05-18T01:21:37.166364Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:21:37.166364Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"iFpUO6Ky3/HXfxk66aAxYgj2STV8Y7wtSA1vjMEQ3EbYnCNFp2QhMtt6d7W2HyRyLPyefgzKGvKGlW9ucaW1CA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:21:37.167065Z","signed_message":"canonical_sha256_bytes"},"source_id":"1508.02694","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0ca9b16185938b4636eecf45285fa31c64b6889030454c9eef4a19084d4b0608","sha256:08cc654680c4e790a9e64f8697bc56bfe49b63b9ad2a4519a3ca6abd087948fc"],"state_sha256":"cec2553d2c47e1697a3454a628e7f5d5eb2208b887749999b792ce0da041c0b0"}