{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:YX5JJFASOLHFTT4BB26NL56JSF","short_pith_number":"pith:YX5JJFAS","schema_version":"1.0","canonical_sha256":"c5fa94941272ce59cf810ebcd5f7c99162ceb007285d04929208b5e1400dc442","source":{"kind":"arxiv","id":"2603.19065","version":2},"attestation_state":"computed","paper":{"title":"Minimal Weierstrass models and regular models of hyperelliptic curves","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Qing Liu","submitted_at":"2026-03-19T15:55:49Z","abstract_excerpt":"Let $C$ be a hyperelliptic curve of genus $g\\ge 2$ over a discrete valuation field $K$ with perfect residue field. We study the minimal Weierstrass models of $C$. When there is more than one such model, we find interesting properties on the minimal regular model and the canonical model of $C$. For curves of genus $2$, we characterize the existence of the stable reduction in terms of the minimal Weierstrass models. When there is more than one such model, we can compute the Euler factor of $\\mathrm{Jac}(C)$ and a volume form of the N\\'eron model of $\\mathrm{Jac}(C)$, using two specific minimal W"},"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":"2603.19065","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2026-03-19T15:55:49Z","cross_cats_sorted":[],"title_canon_sha256":"180d67c61b6038c5532143fc4ff0b60cc0fae5fa372cc428f5af610ee9c5627f","abstract_canon_sha256":"173951d2a3bf73893e4e20d3eae54c52e5dc646daaf0ea951086869c4aea1c2f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-20T00:02:10.679346Z","signature_b64":"yUJGzrXqkWKisLW3yzf/4MFADuSTZO0FVA2KGAxi0XiQ0iFT+ZId+QY/Rncksh2/nhWcURIIGAYe4SpMYK4/Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c5fa94941272ce59cf810ebcd5f7c99162ceb007285d04929208b5e1400dc442","last_reissued_at":"2026-05-20T00:02:10.678675Z","signature_status":"signed_v1","first_computed_at":"2026-05-20T00:02:10.678675Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Minimal Weierstrass models and regular models of hyperelliptic curves","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Qing Liu","submitted_at":"2026-03-19T15:55:49Z","abstract_excerpt":"Let $C$ be a hyperelliptic curve of genus $g\\ge 2$ over a discrete valuation field $K$ with perfect residue field. We study the minimal Weierstrass models of $C$. When there is more than one such model, we find interesting properties on the minimal regular model and the canonical model of $C$. For curves of genus $2$, we characterize the existence of the stable reduction in terms of the minimal Weierstrass models. When there is more than one such model, we can compute the Euler factor of $\\mathrm{Jac}(C)$ and a volume form of the N\\'eron model of $\\mathrm{Jac}(C)$, using two specific minimal W"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2603.19065","kind":"arxiv","version":2},"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/2603.19065/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":"2603.19065","created_at":"2026-05-20T00:02:10.678783+00:00"},{"alias_kind":"arxiv_version","alias_value":"2603.19065v2","created_at":"2026-05-20T00:02:10.678783+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2603.19065","created_at":"2026-05-20T00:02:10.678783+00:00"},{"alias_kind":"pith_short_12","alias_value":"YX5JJFASOLHF","created_at":"2026-05-20T00:02:10.678783+00:00"},{"alias_kind":"pith_short_16","alias_value":"YX5JJFASOLHFTT4B","created_at":"2026-05-20T00:02:10.678783+00:00"},{"alias_kind":"pith_short_8","alias_value":"YX5JJFAS","created_at":"2026-05-20T00:02:10.678783+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/YX5JJFASOLHFTT4BB26NL56JSF","json":"https://pith.science/pith/YX5JJFASOLHFTT4BB26NL56JSF.json","graph_json":"https://pith.science/api/pith-number/YX5JJFASOLHFTT4BB26NL56JSF/graph.json","events_json":"https://pith.science/api/pith-number/YX5JJFASOLHFTT4BB26NL56JSF/events.json","paper":"https://pith.science/paper/YX5JJFAS"},"agent_actions":{"view_html":"https://pith.science/pith/YX5JJFASOLHFTT4BB26NL56JSF","download_json":"https://pith.science/pith/YX5JJFASOLHFTT4BB26NL56JSF.json","view_paper":"https://pith.science/paper/YX5JJFAS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2603.19065&json=true","fetch_graph":"https://pith.science/api/pith-number/YX5JJFASOLHFTT4BB26NL56JSF/graph.json","fetch_events":"https://pith.science/api/pith-number/YX5JJFASOLHFTT4BB26NL56JSF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YX5JJFASOLHFTT4BB26NL56JSF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YX5JJFASOLHFTT4BB26NL56JSF/action/storage_attestation","attest_author":"https://pith.science/pith/YX5JJFASOLHFTT4BB26NL56JSF/action/author_attestation","sign_citation":"https://pith.science/pith/YX5JJFASOLHFTT4BB26NL56JSF/action/citation_signature","submit_replication":"https://pith.science/pith/YX5JJFASOLHFTT4BB26NL56JSF/action/replication_record"}},"created_at":"2026-05-20T00:02:10.678783+00:00","updated_at":"2026-05-20T00:02:10.678783+00:00"}