{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:XSTMADUZYPT5HBK7GENQHWJSYY","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":"c26c49157185f51c7fbfcf1fcbeee49259463cb71726407670decda6e2b6a5a1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-05-10T16:25:39Z","title_canon_sha256":"20b39ee9f8531479e8b5cc87acbbfa4cd676a31830006d330f39e184ca847ce7"},"schema_version":"1.0","source":{"id":"1805.04046","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.04046","created_at":"2026-05-18T00:16:15Z"},{"alias_kind":"arxiv_version","alias_value":"1805.04046v1","created_at":"2026-05-18T00:16:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.04046","created_at":"2026-05-18T00:16:15Z"},{"alias_kind":"pith_short_12","alias_value":"XSTMADUZYPT5","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_16","alias_value":"XSTMADUZYPT5HBK7","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_8","alias_value":"XSTMADUZ","created_at":"2026-05-18T12:33:01Z"}],"graph_snapshots":[{"event_id":"sha256:2f4eb56ae5ab23757caa07fb35a7b652e6c24969e2c3ec3fac79413bdc4b6e3a","target":"graph","created_at":"2026-05-18T00:16:15Z","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 study origami $f: C \\rightarrow E$ with $G$-Galois cover $Q_8$. For a point $P \\in E(\\mathbb{Q}) \\backslash \\left\\{ \\mathcal{O} \\right\\}$, we study the field obtained by adjoining to $\\mathbb{Q}$ the coordinates of all of the preimages of $P$ under $f$. We find a defining polynomial, $f_{E, Q_8,P}$, for this field and study its Galois group. We give an isomorphism depending on $P$ between a certain subfield of this field and a certain subfield of the 4-division field of the elliptic curve.","authors_text":"Edray Herber Goins, Rachel Davis","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-05-10T16:25:39Z","title":"Arithmetic of quaternion origami"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.04046","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":"sha256:1d3debebad2c22a1644dcc25b113c945f40c24c47988185f82933a848b75a2a0","target":"record","created_at":"2026-05-18T00:16:15Z","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":"c26c49157185f51c7fbfcf1fcbeee49259463cb71726407670decda6e2b6a5a1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-05-10T16:25:39Z","title_canon_sha256":"20b39ee9f8531479e8b5cc87acbbfa4cd676a31830006d330f39e184ca847ce7"},"schema_version":"1.0","source":{"id":"1805.04046","kind":"arxiv","version":1}},"canonical_sha256":"bca6c00e99c3e7d3855f311b03d932c60fd93e4a62f3b6c3740f553eef8d5f45","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bca6c00e99c3e7d3855f311b03d932c60fd93e4a62f3b6c3740f553eef8d5f45","first_computed_at":"2026-05-18T00:16:15.167105Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:16:15.167105Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"a2cc4tCn2RH1VkcaKmyT4lpuIDu5mJOIonqFx1mN3yutb3nMwGvRTILuv58mzsO45Z0mxANLFE2Ug5IHDf4tCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:16:15.167865Z","signed_message":"canonical_sha256_bytes"},"source_id":"1805.04046","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1d3debebad2c22a1644dcc25b113c945f40c24c47988185f82933a848b75a2a0","sha256:2f4eb56ae5ab23757caa07fb35a7b652e6c24969e2c3ec3fac79413bdc4b6e3a"],"state_sha256":"77b1e170f197b73df6074cbf6f212ee0f49e58cabe79d4baf6f72dcb42035eea"}