{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:IBEKKEQ2SO6F3CXRAWQRNR3SX4","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":"61633b25632226a84646a191a9bc87d0143a7112164d35619afc7c7d2df22216","cross_cats_sorted":["math.AG"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2025-07-09T14:07:04Z","title_canon_sha256":"59642299445472af2dc070874282ccea79a8377c327124605a28b6595ffff35c"},"schema_version":"1.0","source":{"id":"2507.06865","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2507.06865","created_at":"2026-07-05T11:34:24Z"},{"alias_kind":"arxiv_version","alias_value":"2507.06865v1","created_at":"2026-07-05T11:34:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.06865","created_at":"2026-07-05T11:34:24Z"},{"alias_kind":"pith_short_12","alias_value":"IBEKKEQ2SO6F","created_at":"2026-07-05T11:34:24Z"},{"alias_kind":"pith_short_16","alias_value":"IBEKKEQ2SO6F3CXR","created_at":"2026-07-05T11:34:24Z"},{"alias_kind":"pith_short_8","alias_value":"IBEKKEQ2","created_at":"2026-07-05T11:34:24Z"}],"graph_snapshots":[{"event_id":"sha256:0d4a75612365fcedd0ad2ca9f6cd39c03d83c2447ba5626dcb9c5c1c198f69b0","target":"graph","created_at":"2026-07-05T11:34:24Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2507.06865/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $f(x) = x^{2g+1} + c_1 x^{2g} + \\dots + c_{2g+1} \\in k[x]$ be a polynomial of nonzero discriminant, and let $J$ denote the Jacobian of the odd hyperelliptic curve $C : y^2 = f(x)$. We show that the morphism $J \\to \\mathbb{P}^{2^g-1}$ associated to the linear system $|2 \\Theta|$ may be described explicitly, for any $g \\geq 1$, using the theory of pure spinors.\n  We apply this theory to study the heights of rational points in $J(k)$, when $k$ is a number field. As a particular consequence, we show that $100\\%$ of monic, degree $2g+1$ polynomials $f(x) \\in \\mathbb{Z}[x]$ of nonzero discrimina","authors_text":"Jack A. Thorne, Jef Laga","cross_cats":["math.AG"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2025-07-09T14:07:04Z","title":"Kummers, spinors, and heights"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.06865","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:d62940905a1b9cb3d8ee14b651f160d3a4e149dfa6cce48479431ed6a5e5f4a1","target":"record","created_at":"2026-07-05T11:34:24Z","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":"61633b25632226a84646a191a9bc87d0143a7112164d35619afc7c7d2df22216","cross_cats_sorted":["math.AG"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2025-07-09T14:07:04Z","title_canon_sha256":"59642299445472af2dc070874282ccea79a8377c327124605a28b6595ffff35c"},"schema_version":"1.0","source":{"id":"2507.06865","kind":"arxiv","version":1}},"canonical_sha256":"4048a5121a93bc5d8af105a116c772bf186b35493065b255e2e1c004cf558e8f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4048a5121a93bc5d8af105a116c772bf186b35493065b255e2e1c004cf558e8f","first_computed_at":"2026-07-05T11:34:24.269100Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:34:24.269100Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0w51BsibYdmg6ADFHzcPeiDAJiqqXM+Wg5lLV0ZjxqoPn1kRjIb8XxKcuIO/J6MBczsz7gvkVj2xSKFG984dAg==","signature_status":"signed_v1","signed_at":"2026-07-05T11:34:24.269549Z","signed_message":"canonical_sha256_bytes"},"source_id":"2507.06865","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d62940905a1b9cb3d8ee14b651f160d3a4e149dfa6cce48479431ed6a5e5f4a1","sha256:0d4a75612365fcedd0ad2ca9f6cd39c03d83c2447ba5626dcb9c5c1c198f69b0"],"state_sha256":"65c2cf67600dd465b71aa7f403ac8a6add278678d9dba8e3be80c276c9ad829e"}