{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:PLIPAKZKFHFSJILO4NFP5TYSHO","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":"632ab40410aadad736ae7d0c5e60bd5651074473a47ea333392ca649a75659a8","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-01-15T08:32:26Z","title_canon_sha256":"af294f434a04dda165e8c32d9ba710358542911e9ba04fdd60266513f58d57b3"},"schema_version":"1.0","source":{"id":"1101.2951","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1101.2951","created_at":"2026-05-18T04:30:25Z"},{"alias_kind":"arxiv_version","alias_value":"1101.2951v2","created_at":"2026-05-18T04:30:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.2951","created_at":"2026-05-18T04:30:25Z"},{"alias_kind":"pith_short_12","alias_value":"PLIPAKZKFHFS","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_16","alias_value":"PLIPAKZKFHFSJILO","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_8","alias_value":"PLIPAKZK","created_at":"2026-05-18T12:26:39Z"}],"graph_snapshots":[{"event_id":"sha256:4f605dcbc916427393a9728cc4a4485304e1abe0033d904abe964e4a9ee8475a","target":"graph","created_at":"2026-05-18T04:30:25Z","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":"Let s(n) be the number of representations of n as the sum of three squares. We prove a remarkable new identity for s(p^2n)- ps(n) with p being an odd prime. This identity makes nontrivial use of ternary quadratic forms with discriminants p^2 and 16p^2. These forms are related by Watson's transformations. To prove this identity we employ the Siegel--Weil and the Smith--Minkowski product formulas.","authors_text":"Alexander Berkovich, Will Jagy","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-01-15T08:32:26Z","title":"On representation of an integer as the sum of three squares and the ternary quadratic forms with the discriminants p^2, 16p^2"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.2951","kind":"arxiv","version":2},"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":"sha256:9817d8c3b789c7f5c556bfef80c46c5cdbe6ebec203aac63fa1858562f7aed51","target":"record","created_at":"2026-05-18T04:30:25Z","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":"632ab40410aadad736ae7d0c5e60bd5651074473a47ea333392ca649a75659a8","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-01-15T08:32:26Z","title_canon_sha256":"af294f434a04dda165e8c32d9ba710358542911e9ba04fdd60266513f58d57b3"},"schema_version":"1.0","source":{"id":"1101.2951","kind":"arxiv","version":2}},"canonical_sha256":"7ad0f02b2a29cb24a16ee34afecf123b96125d4c16d240c2bb7615c68ef99c4c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7ad0f02b2a29cb24a16ee34afecf123b96125d4c16d240c2bb7615c68ef99c4c","first_computed_at":"2026-05-18T04:30:25.245878Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:30:25.245878Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1J1Hex/VbzNGuYC+vbwqEo6c65ksDsWjDMgEGuCQuqJ8SkN5ZGiCyIFOWrsUlwC4R+FvNcUAIappo8YMjMa2AA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:30:25.246608Z","signed_message":"canonical_sha256_bytes"},"source_id":"1101.2951","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9817d8c3b789c7f5c556bfef80c46c5cdbe6ebec203aac63fa1858562f7aed51","sha256:4f605dcbc916427393a9728cc4a4485304e1abe0033d904abe964e4a9ee8475a"],"state_sha256":"e9cb9508e521058fe8fa1cc803a9a7c7627e971056d44fed737358e304632a19"}