{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:GIDMEA44PEVE6ZUGG4G4IGRMK3","short_pith_number":"pith:GIDMEA44","schema_version":"1.0","canonical_sha256":"3206c2039c792a4f6686370dc41a2c56d1ffb665d7a52e43c3f7b1a3952e0637","source":{"kind":"arxiv","id":"1612.02730","version":3},"attestation_state":"computed","paper":{"title":"Higher-order Weierstrass weights of branch points on superelliptic curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Caleb McKinley Shor","submitted_at":"2016-12-08T17:05:25Z","abstract_excerpt":"In this paper we consider the problem of calculating the higher-order Weierstrass weight of the branch points of a superelliptic curve $C$. For any $q>1$, we give an exact formula for the $q$-weight of an affine branch point. We also find a formula for the $q$-weight of a point at infinity in the case where $n$ and $d$ are relatively prime. With these formulas, for any fixed $n$, we obtain an asymptotic formula for the ratio of the $q$-weight of the branch points, denoted $BW_q$, to the total $q$-weight of points on the curve: \\[ \\liminf_{d\\to\\infty}\\frac{BW_q}{g(g-1)^2(2q-1)^2}\\geq \\frac{n+1}"},"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":"1612.02730","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-12-08T17:05:25Z","cross_cats_sorted":[],"title_canon_sha256":"5779f6451a047b17bc5689c3e5e1d253781435301a40072c11d85199b3e2ea5f","abstract_canon_sha256":"486b1e11c5eba1c36ff9036430b717302d4db8641dd9e5432bd327453cb9867c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:50:46.261208Z","signature_b64":"wDShPcFCh53AIf2hxRnqB8WWgk7U5DBkkbxlgfOFGt775BgQ1gS7zjOQOft27h/T2yx5LX4kQEbjkmbTqLpzCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3206c2039c792a4f6686370dc41a2c56d1ffb665d7a52e43c3f7b1a3952e0637","last_reissued_at":"2026-05-18T00:50:46.260504Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:50:46.260504Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Higher-order Weierstrass weights of branch points on superelliptic curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Caleb McKinley Shor","submitted_at":"2016-12-08T17:05:25Z","abstract_excerpt":"In this paper we consider the problem of calculating the higher-order Weierstrass weight of the branch points of a superelliptic curve $C$. For any $q>1$, we give an exact formula for the $q$-weight of an affine branch point. We also find a formula for the $q$-weight of a point at infinity in the case where $n$ and $d$ are relatively prime. With these formulas, for any fixed $n$, we obtain an asymptotic formula for the ratio of the $q$-weight of the branch points, denoted $BW_q$, to the total $q$-weight of points on the curve: \\[ \\liminf_{d\\to\\infty}\\frac{BW_q}{g(g-1)^2(2q-1)^2}\\geq \\frac{n+1}"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.02730","kind":"arxiv","version":3},"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":"1612.02730","created_at":"2026-05-18T00:50:46.260617+00:00"},{"alias_kind":"arxiv_version","alias_value":"1612.02730v3","created_at":"2026-05-18T00:50:46.260617+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.02730","created_at":"2026-05-18T00:50:46.260617+00:00"},{"alias_kind":"pith_short_12","alias_value":"GIDMEA44PEVE","created_at":"2026-05-18T12:30:19.053100+00:00"},{"alias_kind":"pith_short_16","alias_value":"GIDMEA44PEVE6ZUG","created_at":"2026-05-18T12:30:19.053100+00:00"},{"alias_kind":"pith_short_8","alias_value":"GIDMEA44","created_at":"2026-05-18T12:30:19.053100+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/GIDMEA44PEVE6ZUGG4G4IGRMK3","json":"https://pith.science/pith/GIDMEA44PEVE6ZUGG4G4IGRMK3.json","graph_json":"https://pith.science/api/pith-number/GIDMEA44PEVE6ZUGG4G4IGRMK3/graph.json","events_json":"https://pith.science/api/pith-number/GIDMEA44PEVE6ZUGG4G4IGRMK3/events.json","paper":"https://pith.science/paper/GIDMEA44"},"agent_actions":{"view_html":"https://pith.science/pith/GIDMEA44PEVE6ZUGG4G4IGRMK3","download_json":"https://pith.science/pith/GIDMEA44PEVE6ZUGG4G4IGRMK3.json","view_paper":"https://pith.science/paper/GIDMEA44","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1612.02730&json=true","fetch_graph":"https://pith.science/api/pith-number/GIDMEA44PEVE6ZUGG4G4IGRMK3/graph.json","fetch_events":"https://pith.science/api/pith-number/GIDMEA44PEVE6ZUGG4G4IGRMK3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GIDMEA44PEVE6ZUGG4G4IGRMK3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GIDMEA44PEVE6ZUGG4G4IGRMK3/action/storage_attestation","attest_author":"https://pith.science/pith/GIDMEA44PEVE6ZUGG4G4IGRMK3/action/author_attestation","sign_citation":"https://pith.science/pith/GIDMEA44PEVE6ZUGG4G4IGRMK3/action/citation_signature","submit_replication":"https://pith.science/pith/GIDMEA44PEVE6ZUGG4G4IGRMK3/action/replication_record"}},"created_at":"2026-05-18T00:50:46.260617+00:00","updated_at":"2026-05-18T00:50:46.260617+00:00"}