{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:5MM2DVXPVULL4AAOQGWFKTVEFZ","short_pith_number":"pith:5MM2DVXP","schema_version":"1.0","canonical_sha256":"eb19a1d6efad16be000e81ac554ea42e4a4c5ed63a97c770da2d119e90a03ba9","source":{"kind":"arxiv","id":"1406.7835","version":5},"attestation_state":"computed","paper":{"title":"On The Gauss EYPHKA Theorem And Some Allied Inequalities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Alexander Berkovich","submitted_at":"2014-06-30T18:07:21Z","abstract_excerpt":"We use the 1907 Hurwitz formula along with the Jacobi triple product identity to understand representation properties of two JP (Jones-Pall) forms of Kaplansky: 9x^2+ 16y^2 +36z^2 + 16yz+ 4xz + 8xy and 9x^2+ 17y^2 +32z^2 -8yz+ 8xz + 6xy. We also discuss three nontrivial analogues of the Gauss EYPHKA theorem. The technique used can be applied to all known spinor regular ternary quadratic forms."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1406.7835","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-06-30T18:07:21Z","cross_cats_sorted":[],"title_canon_sha256":"bc2605b6a69e21fe4d8cb727c877a6519299249df7f4c396fd5790a34fe3a0b9","abstract_canon_sha256":"1b16bf360fa504759786167bb9a62a4fefb9b4d5d638fe805ca86898b08d459a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:38:52.887996Z","signature_b64":"/2E3/DpwR33hYM1KVsK2JMpEfemzB9q4M/UZR6llbtpK5sugWSYESDatB8cBjo34S9vsh9pUPImDXukxnq/XCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"eb19a1d6efad16be000e81ac554ea42e4a4c5ed63a97c770da2d119e90a03ba9","last_reissued_at":"2026-05-18T02:38:52.887654Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:38:52.887654Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On The Gauss EYPHKA Theorem And Some Allied Inequalities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Alexander Berkovich","submitted_at":"2014-06-30T18:07:21Z","abstract_excerpt":"We use the 1907 Hurwitz formula along with the Jacobi triple product identity to understand representation properties of two JP (Jones-Pall) forms of Kaplansky: 9x^2+ 16y^2 +36z^2 + 16yz+ 4xz + 8xy and 9x^2+ 17y^2 +32z^2 -8yz+ 8xz + 6xy. We also discuss three nontrivial analogues of the Gauss EYPHKA theorem. The technique used can be applied to all known spinor regular ternary quadratic forms."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.7835","kind":"arxiv","version":5},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1406.7835","created_at":"2026-05-18T02:38:52.887702+00:00"},{"alias_kind":"arxiv_version","alias_value":"1406.7835v5","created_at":"2026-05-18T02:38:52.887702+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.7835","created_at":"2026-05-18T02:38:52.887702+00:00"},{"alias_kind":"pith_short_12","alias_value":"5MM2DVXPVULL","created_at":"2026-05-18T12:28:14.216126+00:00"},{"alias_kind":"pith_short_16","alias_value":"5MM2DVXPVULL4AAO","created_at":"2026-05-18T12:28:14.216126+00:00"},{"alias_kind":"pith_short_8","alias_value":"5MM2DVXP","created_at":"2026-05-18T12:28:14.216126+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/5MM2DVXPVULL4AAOQGWFKTVEFZ","json":"https://pith.science/pith/5MM2DVXPVULL4AAOQGWFKTVEFZ.json","graph_json":"https://pith.science/api/pith-number/5MM2DVXPVULL4AAOQGWFKTVEFZ/graph.json","events_json":"https://pith.science/api/pith-number/5MM2DVXPVULL4AAOQGWFKTVEFZ/events.json","paper":"https://pith.science/paper/5MM2DVXP"},"agent_actions":{"view_html":"https://pith.science/pith/5MM2DVXPVULL4AAOQGWFKTVEFZ","download_json":"https://pith.science/pith/5MM2DVXPVULL4AAOQGWFKTVEFZ.json","view_paper":"https://pith.science/paper/5MM2DVXP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1406.7835&json=true","fetch_graph":"https://pith.science/api/pith-number/5MM2DVXPVULL4AAOQGWFKTVEFZ/graph.json","fetch_events":"https://pith.science/api/pith-number/5MM2DVXPVULL4AAOQGWFKTVEFZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/5MM2DVXPVULL4AAOQGWFKTVEFZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/5MM2DVXPVULL4AAOQGWFKTVEFZ/action/storage_attestation","attest_author":"https://pith.science/pith/5MM2DVXPVULL4AAOQGWFKTVEFZ/action/author_attestation","sign_citation":"https://pith.science/pith/5MM2DVXPVULL4AAOQGWFKTVEFZ/action/citation_signature","submit_replication":"https://pith.science/pith/5MM2DVXPVULL4AAOQGWFKTVEFZ/action/replication_record"}},"created_at":"2026-05-18T02:38:52.887702+00:00","updated_at":"2026-05-18T02:38:52.887702+00:00"}