{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2000:I6OXRHQY3IBAJ73ZT6TQA4NMHX","short_pith_number":"pith:I6OXRHQY","schema_version":"1.0","canonical_sha256":"479d789e18da0204ff799fa70071ac3de0eff4abd90ce8ffe5798752c5ee7beb","source":{"kind":"arxiv","id":"math/0011102","version":6},"attestation_state":"computed","paper":{"title":"Analogues of Lehmer's conjecture in positive characteristic","license":"","headline":"","cross_cats":["math.AG"],"primary_cat":"math.NT","authors_text":"Amilcar Pacheco","submitted_at":"2000-11-15T19:19:30Z","abstract_excerpt":"Let $C$ be a smooth projective irreducible curve defined over a finite field $\\mathbb{F}_q$ and $K=\\mathbb{F}_q(C)$. Let $A\\subset K$ be the ring of functions regular outside a fixed place $\\infty$ of $K$. Let $\\phi:A\\to\\text{End}(\\mathbb{G}_a)$ be a Drinfeld $A$-module of rank $r$ defined over a finite extension $L$ of $K$ and $\\hat{h}_{\\phi}$ its canonical height. Given a non-torsion point $\\alpha$ of $\\phi$ of degree $d$ over $K$, we prove that $\\hat{h}_{\\phi}(\\alpha)\\ge 1/d$.\n A similar statement is proved for the canonical height of a point of infinite order of a non-constant semi-stable "},"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":"math/0011102","kind":"arxiv","version":6},"metadata":{"license":"","primary_cat":"math.NT","submitted_at":"2000-11-15T19:19:30Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"affff4672af64f4217887661607d77f91c3869c3578b29211df78f03b975ab97","abstract_canon_sha256":"6a9f168d452b618c8cc4ef0adb4717de3edf8da7d6f7fd37cd61d5cac2df7c59"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:05:38.103780Z","signature_b64":"OwhqUT044fd5v4jv+09AkNBN3wz3BLZnb6T2kRrpNiAMF86Wex2t2JITDpgw+w/x5r1lL+mRWd/XRh5Svy9RDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"479d789e18da0204ff799fa70071ac3de0eff4abd90ce8ffe5798752c5ee7beb","last_reissued_at":"2026-05-18T01:05:38.103192Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:05:38.103192Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Analogues of Lehmer's conjecture in positive characteristic","license":"","headline":"","cross_cats":["math.AG"],"primary_cat":"math.NT","authors_text":"Amilcar Pacheco","submitted_at":"2000-11-15T19:19:30Z","abstract_excerpt":"Let $C$ be a smooth projective irreducible curve defined over a finite field $\\mathbb{F}_q$ and $K=\\mathbb{F}_q(C)$. Let $A\\subset K$ be the ring of functions regular outside a fixed place $\\infty$ of $K$. Let $\\phi:A\\to\\text{End}(\\mathbb{G}_a)$ be a Drinfeld $A$-module of rank $r$ defined over a finite extension $L$ of $K$ and $\\hat{h}_{\\phi}$ its canonical height. Given a non-torsion point $\\alpha$ of $\\phi$ of degree $d$ over $K$, we prove that $\\hat{h}_{\\phi}(\\alpha)\\ge 1/d$.\n A similar statement is proved for the canonical height of a point of infinite order of a non-constant semi-stable "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0011102","kind":"arxiv","version":6},"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":"math/0011102","created_at":"2026-05-18T01:05:38.103278+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/0011102v6","created_at":"2026-05-18T01:05:38.103278+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0011102","created_at":"2026-05-18T01:05:38.103278+00:00"},{"alias_kind":"pith_short_12","alias_value":"I6OXRHQY3IBA","created_at":"2026-05-18T12:25:49.631198+00:00"},{"alias_kind":"pith_short_16","alias_value":"I6OXRHQY3IBAJ73Z","created_at":"2026-05-18T12:25:49.631198+00:00"},{"alias_kind":"pith_short_8","alias_value":"I6OXRHQY","created_at":"2026-05-18T12:25:49.631198+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/I6OXRHQY3IBAJ73ZT6TQA4NMHX","json":"https://pith.science/pith/I6OXRHQY3IBAJ73ZT6TQA4NMHX.json","graph_json":"https://pith.science/api/pith-number/I6OXRHQY3IBAJ73ZT6TQA4NMHX/graph.json","events_json":"https://pith.science/api/pith-number/I6OXRHQY3IBAJ73ZT6TQA4NMHX/events.json","paper":"https://pith.science/paper/I6OXRHQY"},"agent_actions":{"view_html":"https://pith.science/pith/I6OXRHQY3IBAJ73ZT6TQA4NMHX","download_json":"https://pith.science/pith/I6OXRHQY3IBAJ73ZT6TQA4NMHX.json","view_paper":"https://pith.science/paper/I6OXRHQY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/0011102&json=true","fetch_graph":"https://pith.science/api/pith-number/I6OXRHQY3IBAJ73ZT6TQA4NMHX/graph.json","fetch_events":"https://pith.science/api/pith-number/I6OXRHQY3IBAJ73ZT6TQA4NMHX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/I6OXRHQY3IBAJ73ZT6TQA4NMHX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/I6OXRHQY3IBAJ73ZT6TQA4NMHX/action/storage_attestation","attest_author":"https://pith.science/pith/I6OXRHQY3IBAJ73ZT6TQA4NMHX/action/author_attestation","sign_citation":"https://pith.science/pith/I6OXRHQY3IBAJ73ZT6TQA4NMHX/action/citation_signature","submit_replication":"https://pith.science/pith/I6OXRHQY3IBAJ73ZT6TQA4NMHX/action/replication_record"}},"created_at":"2026-05-18T01:05:38.103278+00:00","updated_at":"2026-05-18T01:05:38.103278+00:00"}