{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:GSRIZ4XRKVAE3U76YIBMBCQADU","short_pith_number":"pith:GSRIZ4XR","schema_version":"1.0","canonical_sha256":"34a28cf2f155404dd3fec202c08a001d1756ea52af88b4a37d514ee6a0d5fc20","source":{"kind":"arxiv","id":"1404.4209","version":2},"attestation_state":"computed","paper":{"title":"Commutative algebraic groups and $p$-adic linear forms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.NT","authors_text":"Clemens Fuchs, Duc Hiep Pham","submitted_at":"2014-04-16T11:23:23Z","abstract_excerpt":"Let $G$ be a commutative algebraic group defined over a number field $K$ that is disjoint over $K$ to $\\mathbb G_a$ and satisfies the condition of semistability. Consider a linear form $l$ on the Lie algebra of $G$ with algebraic coefficients and an algebraic point $u$ in a $p$-adic neighbourhood of the origin with the condition that $l$ does not vanish at $u$. We give a lower bound for the $p$-adic absolute value of $l(u)$ which depends up to an effectively computable constant only on the height of the linear form, the height of the point $u$ and $p$."},"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":"1404.4209","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-04-16T11:23:23Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"7dc51f0b25b73747fb952ca437e597bead8c8be702753b8dd943325812bde40f","abstract_canon_sha256":"af4451315d0a26d585b8e52695437502c5d0b6765667d2b5e425abe9a7721b5f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:22:19.130175Z","signature_b64":"pzE43EBW/EgkWrYBpQL3ET9QCosmEXOGwhwoL8KpSYebXgOMruqdlsXzROMBGiwSq6Suu1y3M5pDaB3A227BBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"34a28cf2f155404dd3fec202c08a001d1756ea52af88b4a37d514ee6a0d5fc20","last_reissued_at":"2026-05-18T01:22:19.129443Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:22:19.129443Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Commutative algebraic groups and $p$-adic linear forms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.NT","authors_text":"Clemens Fuchs, Duc Hiep Pham","submitted_at":"2014-04-16T11:23:23Z","abstract_excerpt":"Let $G$ be a commutative algebraic group defined over a number field $K$ that is disjoint over $K$ to $\\mathbb G_a$ and satisfies the condition of semistability. Consider a linear form $l$ on the Lie algebra of $G$ with algebraic coefficients and an algebraic point $u$ in a $p$-adic neighbourhood of the origin with the condition that $l$ does not vanish at $u$. We give a lower bound for the $p$-adic absolute value of $l(u)$ which depends up to an effectively computable constant only on the height of the linear form, the height of the point $u$ and $p$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.4209","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":""},"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":"1404.4209","created_at":"2026-05-18T01:22:19.129548+00:00"},{"alias_kind":"arxiv_version","alias_value":"1404.4209v2","created_at":"2026-05-18T01:22:19.129548+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.4209","created_at":"2026-05-18T01:22:19.129548+00:00"},{"alias_kind":"pith_short_12","alias_value":"GSRIZ4XRKVAE","created_at":"2026-05-18T12:28:30.664211+00:00"},{"alias_kind":"pith_short_16","alias_value":"GSRIZ4XRKVAE3U76","created_at":"2026-05-18T12:28:30.664211+00:00"},{"alias_kind":"pith_short_8","alias_value":"GSRIZ4XR","created_at":"2026-05-18T12:28:30.664211+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/GSRIZ4XRKVAE3U76YIBMBCQADU","json":"https://pith.science/pith/GSRIZ4XRKVAE3U76YIBMBCQADU.json","graph_json":"https://pith.science/api/pith-number/GSRIZ4XRKVAE3U76YIBMBCQADU/graph.json","events_json":"https://pith.science/api/pith-number/GSRIZ4XRKVAE3U76YIBMBCQADU/events.json","paper":"https://pith.science/paper/GSRIZ4XR"},"agent_actions":{"view_html":"https://pith.science/pith/GSRIZ4XRKVAE3U76YIBMBCQADU","download_json":"https://pith.science/pith/GSRIZ4XRKVAE3U76YIBMBCQADU.json","view_paper":"https://pith.science/paper/GSRIZ4XR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1404.4209&json=true","fetch_graph":"https://pith.science/api/pith-number/GSRIZ4XRKVAE3U76YIBMBCQADU/graph.json","fetch_events":"https://pith.science/api/pith-number/GSRIZ4XRKVAE3U76YIBMBCQADU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GSRIZ4XRKVAE3U76YIBMBCQADU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GSRIZ4XRKVAE3U76YIBMBCQADU/action/storage_attestation","attest_author":"https://pith.science/pith/GSRIZ4XRKVAE3U76YIBMBCQADU/action/author_attestation","sign_citation":"https://pith.science/pith/GSRIZ4XRKVAE3U76YIBMBCQADU/action/citation_signature","submit_replication":"https://pith.science/pith/GSRIZ4XRKVAE3U76YIBMBCQADU/action/replication_record"}},"created_at":"2026-05-18T01:22:19.129548+00:00","updated_at":"2026-05-18T01:22:19.129548+00:00"}