{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:3SO52X2WRF6GJSI3W5WKSKITYY","short_pith_number":"pith:3SO52X2W","schema_version":"1.0","canonical_sha256":"dc9ddd5f56897c64c91bb76ca92913c61d72d687fb5c3be1eeba394e14bf9280","source":{"kind":"arxiv","id":"1508.05172","version":1},"attestation_state":"computed","paper":{"title":"Conductors and minimal discriminants of hyperelliptic curves with rational Weierstrass points","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.AG","authors_text":"Padmavathi Srinivasan","submitted_at":"2015-08-21T04:09:47Z","abstract_excerpt":"Let $C$ be a hyperelliptic curve of genus $g$ over the fraction field $K$ of a discrete valuation ring $R$. Assume that the residue field $k$ of $R$ is perfect and that $\\mathop{\\textrm{char}} k \\neq 2$. Assume that the Weierstrass points of $C$ are $K$-rational. Let $S = \\mathop{\\textrm{Spec}} R$. Let $\\mathcal{X}$ be the minimal proper regular model of $C$ over $S$. Let $\\mathop{\\textrm{Art}} (\\mathcal{X}/S)$ denote the Artin conductor of the $S$-scheme $\\mathcal{X}$ and let $\\nu (\\Delta)$ denote the minimal discriminant of $C$. We prove that $-\\mathop{\\textrm{Art}} (\\mathcal{X}/S) \\leq \\nu "},"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":"1508.05172","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-08-21T04:09:47Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"349d4a8d210376ee2101169e020dbaa0bcb20794f43185f2301ef82f912a7d3d","abstract_canon_sha256":"a6acbc316652ea2950af4c7ef892d984e91707c87ce804c919e5e3e7732ce5b3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:34:56.522768Z","signature_b64":"E1lz7wIjqrJTJVBUN9yHXki5vAy7aJlUaewnY6P8Kxt+PtcHGRwpbi+dQ+bluwdhqGmKKpPzq714f+EUGtpZCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dc9ddd5f56897c64c91bb76ca92913c61d72d687fb5c3be1eeba394e14bf9280","last_reissued_at":"2026-05-18T01:34:56.522070Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:34:56.522070Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Conductors and minimal discriminants of hyperelliptic curves with rational Weierstrass points","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.AG","authors_text":"Padmavathi Srinivasan","submitted_at":"2015-08-21T04:09:47Z","abstract_excerpt":"Let $C$ be a hyperelliptic curve of genus $g$ over the fraction field $K$ of a discrete valuation ring $R$. Assume that the residue field $k$ of $R$ is perfect and that $\\mathop{\\textrm{char}} k \\neq 2$. Assume that the Weierstrass points of $C$ are $K$-rational. Let $S = \\mathop{\\textrm{Spec}} R$. Let $\\mathcal{X}$ be the minimal proper regular model of $C$ over $S$. Let $\\mathop{\\textrm{Art}} (\\mathcal{X}/S)$ denote the Artin conductor of the $S$-scheme $\\mathcal{X}$ and let $\\nu (\\Delta)$ denote the minimal discriminant of $C$. We prove that $-\\mathop{\\textrm{Art}} (\\mathcal{X}/S) \\leq \\nu "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.05172","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":""},"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":"1508.05172","created_at":"2026-05-18T01:34:56.522176+00:00"},{"alias_kind":"arxiv_version","alias_value":"1508.05172v1","created_at":"2026-05-18T01:34:56.522176+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.05172","created_at":"2026-05-18T01:34:56.522176+00:00"},{"alias_kind":"pith_short_12","alias_value":"3SO52X2WRF6G","created_at":"2026-05-18T12:29:02.477457+00:00"},{"alias_kind":"pith_short_16","alias_value":"3SO52X2WRF6GJSI3","created_at":"2026-05-18T12:29:02.477457+00:00"},{"alias_kind":"pith_short_8","alias_value":"3SO52X2W","created_at":"2026-05-18T12:29:02.477457+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/3SO52X2WRF6GJSI3W5WKSKITYY","json":"https://pith.science/pith/3SO52X2WRF6GJSI3W5WKSKITYY.json","graph_json":"https://pith.science/api/pith-number/3SO52X2WRF6GJSI3W5WKSKITYY/graph.json","events_json":"https://pith.science/api/pith-number/3SO52X2WRF6GJSI3W5WKSKITYY/events.json","paper":"https://pith.science/paper/3SO52X2W"},"agent_actions":{"view_html":"https://pith.science/pith/3SO52X2WRF6GJSI3W5WKSKITYY","download_json":"https://pith.science/pith/3SO52X2WRF6GJSI3W5WKSKITYY.json","view_paper":"https://pith.science/paper/3SO52X2W","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1508.05172&json=true","fetch_graph":"https://pith.science/api/pith-number/3SO52X2WRF6GJSI3W5WKSKITYY/graph.json","fetch_events":"https://pith.science/api/pith-number/3SO52X2WRF6GJSI3W5WKSKITYY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3SO52X2WRF6GJSI3W5WKSKITYY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3SO52X2WRF6GJSI3W5WKSKITYY/action/storage_attestation","attest_author":"https://pith.science/pith/3SO52X2WRF6GJSI3W5WKSKITYY/action/author_attestation","sign_citation":"https://pith.science/pith/3SO52X2WRF6GJSI3W5WKSKITYY/action/citation_signature","submit_replication":"https://pith.science/pith/3SO52X2WRF6GJSI3W5WKSKITYY/action/replication_record"}},"created_at":"2026-05-18T01:34:56.522176+00:00","updated_at":"2026-05-18T01:34:56.522176+00:00"}