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We prove that the $L_v$-rational torsion submodule $M(L_v)_{\\mathrm{tors}}$ of $M$ is a finite $A$-module."},"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":"1603.03789","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-03-11T21:24:43Z","cross_cats_sorted":[],"title_canon_sha256":"318412498740673adc202187b07895335989749ed969034ffa1926e9b6865839","abstract_canon_sha256":"c92c23d75f603be055637fa246696a51d56b5d0698f47d876e05a3802994ebc8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:19:10.499859Z","signature_b64":"OjdSe/LcZHWoinjmCvUXXCjcUS6j9hD5AClW+pB9jU86eI4v1DVOb7542Y7opAXlxxe0rH7uU8SjzQredgaMBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"295fd615a8f619c6a72d617f0b9b596e872339a2be89ff705506e6e399144318","last_reissued_at":"2026-05-18T01:19:10.499189Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:19:10.499189Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Finiteness of local torsion for abelian t-modules","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Vesselin Dimitrov","submitted_at":"2016-03-11T21:24:43Z","abstract_excerpt":"Let $C/\\mathbb{F}_q$ be a regular projective curve, $\\infty \\in C$ a closed point, $A := \\Gamma(C - \\{\\infty\\}, \\mathcal{O}_C)$, and $K := K(C)$ the fraction field of $A$. Consider a finite extension $L/K$, a place $v$ of $L$, and an abelian $A$-module $M$ (in the sense of Anderson) over $L_v$. We prove that the $L_v$-rational torsion submodule $M(L_v)_{\\mathrm{tors}}$ of $M$ is a finite $A$-module."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.03789","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":"1603.03789","created_at":"2026-05-18T01:19:10.499275+00:00"},{"alias_kind":"arxiv_version","alias_value":"1603.03789v1","created_at":"2026-05-18T01:19:10.499275+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.03789","created_at":"2026-05-18T01:19:10.499275+00:00"},{"alias_kind":"pith_short_12","alias_value":"FFP5MFNI6YM4","created_at":"2026-05-18T12:30:15.759754+00:00"},{"alias_kind":"pith_short_16","alias_value":"FFP5MFNI6YM4NJZN","created_at":"2026-05-18T12:30:15.759754+00:00"},{"alias_kind":"pith_short_8","alias_value":"FFP5MFNI","created_at":"2026-05-18T12:30:15.759754+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/FFP5MFNI6YM4NJZNMF7QXG2ZN2","json":"https://pith.science/pith/FFP5MFNI6YM4NJZNMF7QXG2ZN2.json","graph_json":"https://pith.science/api/pith-number/FFP5MFNI6YM4NJZNMF7QXG2ZN2/graph.json","events_json":"https://pith.science/api/pith-number/FFP5MFNI6YM4NJZNMF7QXG2ZN2/events.json","paper":"https://pith.science/paper/FFP5MFNI"},"agent_actions":{"view_html":"https://pith.science/pith/FFP5MFNI6YM4NJZNMF7QXG2ZN2","download_json":"https://pith.science/pith/FFP5MFNI6YM4NJZNMF7QXG2ZN2.json","view_paper":"https://pith.science/paper/FFP5MFNI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1603.03789&json=true","fetch_graph":"https://pith.science/api/pith-number/FFP5MFNI6YM4NJZNMF7QXG2ZN2/graph.json","fetch_events":"https://pith.science/api/pith-number/FFP5MFNI6YM4NJZNMF7QXG2ZN2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FFP5MFNI6YM4NJZNMF7QXG2ZN2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FFP5MFNI6YM4NJZNMF7QXG2ZN2/action/storage_attestation","attest_author":"https://pith.science/pith/FFP5MFNI6YM4NJZNMF7QXG2ZN2/action/author_attestation","sign_citation":"https://pith.science/pith/FFP5MFNI6YM4NJZNMF7QXG2ZN2/action/citation_signature","submit_replication":"https://pith.science/pith/FFP5MFNI6YM4NJZNMF7QXG2ZN2/action/replication_record"}},"created_at":"2026-05-18T01:19:10.499275+00:00","updated_at":"2026-05-18T01:19:10.499275+00:00"}