{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:GIWSPZQNQO5NADVHOOLKULJUGL","short_pith_number":"pith:GIWSPZQN","schema_version":"1.0","canonical_sha256":"322d27e60d83bad00ea77396aa2d3432e97524501e9f703bdc0d0841c4cbde1f","source":{"kind":"arxiv","id":"2507.08652","version":1},"attestation_state":"computed","paper":{"title":"Lower bounds on heights of odd degree points of hyperelliptic curves","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.NT","authors_text":"Jack A. Thorne, Jef Laga","submitted_at":"2025-07-11T14:56:30Z","abstract_excerpt":"We develop a reduction theory for the representation of $\\mathrm{SL}_n$ on pairs of symmetric $n\\times n$ matrices. We apply this theory to the pencils of quadrics arising from divisors on hyperelliptic curves. We use these results to show that, in a density $1$ family, an odd degree point $P$ of degree at most $2g-1$ on the hyperelliptic curve $z^2 = f_0x^{2g+2} + f_1 x^{2g+1} y + \\cdots + f_{2g+2}y^{2g+2}$ cannot have small Weil height."},"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":"2507.08652","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2025-07-11T14:56:30Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"6bc0666c377a40b091a392f37cd62fc41838add497e92768270d2298b05737e6","abstract_canon_sha256":"cccd64f67c4139bbc16b134b8800d5bf83c3feccd471cf3cbc1b2fbe1152f451"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:35:44.417742Z","signature_b64":"9ktr874Ztxpg8IE3MiJn9aP6dfe81mLvRYwa9jcHsvceeNc8DpyoHlIZg2s4we0KUeJPFwezLuSbzOCmT6l2CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"322d27e60d83bad00ea77396aa2d3432e97524501e9f703bdc0d0841c4cbde1f","last_reissued_at":"2026-07-05T11:35:44.417265Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:35:44.417265Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Lower bounds on heights of odd degree points of hyperelliptic curves","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.NT","authors_text":"Jack A. Thorne, Jef Laga","submitted_at":"2025-07-11T14:56:30Z","abstract_excerpt":"We develop a reduction theory for the representation of $\\mathrm{SL}_n$ on pairs of symmetric $n\\times n$ matrices. We apply this theory to the pencils of quadrics arising from divisors on hyperelliptic curves. We use these results to show that, in a density $1$ family, an odd degree point $P$ of degree at most $2g-1$ on the hyperelliptic curve $z^2 = f_0x^{2g+2} + f_1 x^{2g+1} y + \\cdots + f_{2g+2}y^{2g+2}$ cannot have small Weil height."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.08652","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2507.08652/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2507.08652","created_at":"2026-07-05T11:35:44.417343+00:00"},{"alias_kind":"arxiv_version","alias_value":"2507.08652v1","created_at":"2026-07-05T11:35:44.417343+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.08652","created_at":"2026-07-05T11:35:44.417343+00:00"},{"alias_kind":"pith_short_12","alias_value":"GIWSPZQNQO5N","created_at":"2026-07-05T11:35:44.417343+00:00"},{"alias_kind":"pith_short_16","alias_value":"GIWSPZQNQO5NADVH","created_at":"2026-07-05T11:35:44.417343+00:00"},{"alias_kind":"pith_short_8","alias_value":"GIWSPZQN","created_at":"2026-07-05T11:35:44.417343+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/GIWSPZQNQO5NADVHOOLKULJUGL","json":"https://pith.science/pith/GIWSPZQNQO5NADVHOOLKULJUGL.json","graph_json":"https://pith.science/api/pith-number/GIWSPZQNQO5NADVHOOLKULJUGL/graph.json","events_json":"https://pith.science/api/pith-number/GIWSPZQNQO5NADVHOOLKULJUGL/events.json","paper":"https://pith.science/paper/GIWSPZQN"},"agent_actions":{"view_html":"https://pith.science/pith/GIWSPZQNQO5NADVHOOLKULJUGL","download_json":"https://pith.science/pith/GIWSPZQNQO5NADVHOOLKULJUGL.json","view_paper":"https://pith.science/paper/GIWSPZQN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2507.08652&json=true","fetch_graph":"https://pith.science/api/pith-number/GIWSPZQNQO5NADVHOOLKULJUGL/graph.json","fetch_events":"https://pith.science/api/pith-number/GIWSPZQNQO5NADVHOOLKULJUGL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GIWSPZQNQO5NADVHOOLKULJUGL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GIWSPZQNQO5NADVHOOLKULJUGL/action/storage_attestation","attest_author":"https://pith.science/pith/GIWSPZQNQO5NADVHOOLKULJUGL/action/author_attestation","sign_citation":"https://pith.science/pith/GIWSPZQNQO5NADVHOOLKULJUGL/action/citation_signature","submit_replication":"https://pith.science/pith/GIWSPZQNQO5NADVHOOLKULJUGL/action/replication_record"}},"created_at":"2026-07-05T11:35:44.417343+00:00","updated_at":"2026-07-05T11:35:44.417343+00:00"}