{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:45OLPPTHJNSWTPXSPPDVKVZK22","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":"b9beceb92edb4a09e9f081f2853f21947c63ceb20657855f7347afab738754a2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-08-29T18:17:38Z","title_canon_sha256":"7b339c39a541db058c2ebf9e31f6c6685102a1f0f171ffd984553b9c9653f7a3"},"schema_version":"1.0","source":{"id":"1108.5687","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1108.5687","created_at":"2026-05-18T04:14:36Z"},{"alias_kind":"arxiv_version","alias_value":"1108.5687v1","created_at":"2026-05-18T04:14:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.5687","created_at":"2026-05-18T04:14:36Z"},{"alias_kind":"pith_short_12","alias_value":"45OLPPTHJNSW","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_16","alias_value":"45OLPPTHJNSWTPXS","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_8","alias_value":"45OLPPTH","created_at":"2026-05-18T12:26:20Z"}],"graph_snapshots":[{"event_id":"sha256:b29c0379f8935bac1a09e1028fb7d93c76876e3a86da0dec14a12b735d251657","target":"graph","created_at":"2026-05-18T04:14:36Z","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":"After a brief introduction to the classical theory of binary quadratic forms we use these results for proving (most of) the claims made by P\\'epin in a series of articles on unsolvable quartic diophantine equations, and for constructing families of counterexamples to the Hasse Principle for curves of genus 1 defined by equations of the form $ax^4 + by^4 = z^2$.","authors_text":"Franz Lemmermeyer","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-08-29T18:17:38Z","title":"Binary Quadratic Forms and Counterexamples to Hasse's Local-Global Principle"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.5687","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":"sha256:953b5ce243dd106699bd5148810b3461b22ee0ef3e539e784fa9f41afbcd77e3","target":"record","created_at":"2026-05-18T04:14:36Z","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":"b9beceb92edb4a09e9f081f2853f21947c63ceb20657855f7347afab738754a2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-08-29T18:17:38Z","title_canon_sha256":"7b339c39a541db058c2ebf9e31f6c6685102a1f0f171ffd984553b9c9653f7a3"},"schema_version":"1.0","source":{"id":"1108.5687","kind":"arxiv","version":1}},"canonical_sha256":"e75cb7be674b6569bef27bc755572ad6a02421530edd048a724e44e867fe1299","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e75cb7be674b6569bef27bc755572ad6a02421530edd048a724e44e867fe1299","first_computed_at":"2026-05-18T04:14:36.969501Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:14:36.969501Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UJ+Qx3JhSwxepj2rSoEWWhipd9AQ8/TLh9M/22KkGU55Q2W2XG/e1lA9phCkA7Vq2iU5BdkNNkUqIIhFg4ASAg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:14:36.969913Z","signed_message":"canonical_sha256_bytes"},"source_id":"1108.5687","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:953b5ce243dd106699bd5148810b3461b22ee0ef3e539e784fa9f41afbcd77e3","sha256:b29c0379f8935bac1a09e1028fb7d93c76876e3a86da0dec14a12b735d251657"],"state_sha256":"11a72472d352eca5dec0ae801dc8dc29738fd2cedc66da7202ddd312494c2bfa"}