{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:XCXLROTPMROES7FYR6U3UEN7HF","short_pith_number":"pith:XCXLROTP","schema_version":"1.0","canonical_sha256":"b8aeb8ba6f645c497cb88fa9ba11bf394e07cffd9daf76755d5d4f29ee859121","source":{"kind":"arxiv","id":"1112.5378","version":1},"attestation_state":"computed","paper":{"title":"Explicit formulas for Drinfeld modules and their periods","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Ahmad El-Guindy, Matthew A. Papanikolas","submitted_at":"2011-12-22T16:57:55Z","abstract_excerpt":"We provide explicit series expansions for the exponential and logarithm functions attached to a rank r Drinfeld module that generalize well known formulas for the Carlitz exponential and logarithm. Using these results we obtain a procedure and an analytic expression for computing the periods of rank 2 Drinfeld modules and also a criterion for supersingularity."},"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":"1112.5378","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-12-22T16:57:55Z","cross_cats_sorted":[],"title_canon_sha256":"5e587fc395a04acc3e1d48e3b8dda006af8f04290a5892361b6502fcb6329e8f","abstract_canon_sha256":"3921b1e2f8e8e083933c1bb520af978f8fe637d1136250b22b7f8c525cc2a96a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:15:07.299688Z","signature_b64":"7lIeq87iI9Xi1wk9YwshWKBCRCkVfQvFar9n7YEIOYQcpYQIQrr0vO5ZoY5Ko6+z2p/PvHhqJwTkdCwzVV3LCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b8aeb8ba6f645c497cb88fa9ba11bf394e07cffd9daf76755d5d4f29ee859121","last_reissued_at":"2026-05-18T01:15:07.298975Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:15:07.298975Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Explicit formulas for Drinfeld modules and their periods","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Ahmad El-Guindy, Matthew A. Papanikolas","submitted_at":"2011-12-22T16:57:55Z","abstract_excerpt":"We provide explicit series expansions for the exponential and logarithm functions attached to a rank r Drinfeld module that generalize well known formulas for the Carlitz exponential and logarithm. Using these results we obtain a procedure and an analytic expression for computing the periods of rank 2 Drinfeld modules and also a criterion for supersingularity."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.5378","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":"1112.5378","created_at":"2026-05-18T01:15:07.299093+00:00"},{"alias_kind":"arxiv_version","alias_value":"1112.5378v1","created_at":"2026-05-18T01:15:07.299093+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.5378","created_at":"2026-05-18T01:15:07.299093+00:00"},{"alias_kind":"pith_short_12","alias_value":"XCXLROTPMROE","created_at":"2026-05-18T12:26:44.992195+00:00"},{"alias_kind":"pith_short_16","alias_value":"XCXLROTPMROES7FY","created_at":"2026-05-18T12:26:44.992195+00:00"},{"alias_kind":"pith_short_8","alias_value":"XCXLROTP","created_at":"2026-05-18T12:26:44.992195+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/XCXLROTPMROES7FYR6U3UEN7HF","json":"https://pith.science/pith/XCXLROTPMROES7FYR6U3UEN7HF.json","graph_json":"https://pith.science/api/pith-number/XCXLROTPMROES7FYR6U3UEN7HF/graph.json","events_json":"https://pith.science/api/pith-number/XCXLROTPMROES7FYR6U3UEN7HF/events.json","paper":"https://pith.science/paper/XCXLROTP"},"agent_actions":{"view_html":"https://pith.science/pith/XCXLROTPMROES7FYR6U3UEN7HF","download_json":"https://pith.science/pith/XCXLROTPMROES7FYR6U3UEN7HF.json","view_paper":"https://pith.science/paper/XCXLROTP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1112.5378&json=true","fetch_graph":"https://pith.science/api/pith-number/XCXLROTPMROES7FYR6U3UEN7HF/graph.json","fetch_events":"https://pith.science/api/pith-number/XCXLROTPMROES7FYR6U3UEN7HF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XCXLROTPMROES7FYR6U3UEN7HF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XCXLROTPMROES7FYR6U3UEN7HF/action/storage_attestation","attest_author":"https://pith.science/pith/XCXLROTPMROES7FYR6U3UEN7HF/action/author_attestation","sign_citation":"https://pith.science/pith/XCXLROTPMROES7FYR6U3UEN7HF/action/citation_signature","submit_replication":"https://pith.science/pith/XCXLROTPMROES7FYR6U3UEN7HF/action/replication_record"}},"created_at":"2026-05-18T01:15:07.299093+00:00","updated_at":"2026-05-18T01:15:07.299093+00:00"}