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Let $D$ be an effective Cartier divisor on $\\overline X$ whose support is contained in $Z$. Motivated by Hiranouchi's Hermite--Minkowski type theorem for varieties over finite fields, we formulate a finiteness conjecture for continuous semisimple geometric representations\n  $$\n  \\pi_1(X,D)\\longrightarrow \\operatorname{GL}_n(F),\n  $$\n  where $\\pi_1(X,D)$ is "},"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":"2606.31341","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.NT","submitted_at":"2026-06-30T08:41:30Z","cross_cats_sorted":[],"title_canon_sha256":"6bd76b342ad9971d7327f83a7ec566bd45c32344ea5acbac5cde677090800c0d","abstract_canon_sha256":"c56530f562c1ad39df88fe26f847e4e05e68d033ca02c5cc9b6b9216693fcb62"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-01T01:17:59.813307Z","signature_b64":"PV+Rqg992lIR/qEmLuXZC/BL23zcwdcTlioR74RxWpBlgCfMAoaGOKkJ02deMYiW613E1okDP/fcdzU4220/CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4dae2cb55743b1af40523ffee601647d888f0a3f8fbbe5ef273ae59b3eb526ee","last_reissued_at":"2026-07-01T01:17:59.812901Z","signature_status":"signed_v1","first_computed_at":"2026-07-01T01:17:59.812901Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the Finiteness of Geometric Representations for Varieties over Finite Fields","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Yufan Luo","submitted_at":"2026-06-30T08:41:30Z","abstract_excerpt":"Let $p$ be a prime number, and let $k$ be a finite field of characteristic different from $p$. Let $X$ be a normal geometrically connected variety over $k$, let $\\overline X$ be a compactification of $X$, and let $Z=\\overline X\\setminus X$. Let $D$ be an effective Cartier divisor on $\\overline X$ whose support is contained in $Z$. Motivated by Hiranouchi's Hermite--Minkowski type theorem for varieties over finite fields, we formulate a finiteness conjecture for continuous semisimple geometric representations\n  $$\n  \\pi_1(X,D)\\longrightarrow \\operatorname{GL}_n(F),\n  $$\n  where $\\pi_1(X,D)$ is "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.31341","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.31341/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2606.31341","created_at":"2026-07-01T01:17:59.812958+00:00"},{"alias_kind":"arxiv_version","alias_value":"2606.31341v1","created_at":"2026-07-01T01:17:59.812958+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.31341","created_at":"2026-07-01T01:17:59.812958+00:00"},{"alias_kind":"pith_short_12","alias_value":"JWXCZNKXIOY2","created_at":"2026-07-01T01:17:59.812958+00:00"},{"alias_kind":"pith_short_16","alias_value":"JWXCZNKXIOY26QCS","created_at":"2026-07-01T01:17:59.812958+00:00"},{"alias_kind":"pith_short_8","alias_value":"JWXCZNKX","created_at":"2026-07-01T01:17:59.812958+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/JWXCZNKXIOY26QCSH77OMALEPW","json":"https://pith.science/pith/JWXCZNKXIOY26QCSH77OMALEPW.json","graph_json":"https://pith.science/api/pith-number/JWXCZNKXIOY26QCSH77OMALEPW/graph.json","events_json":"https://pith.science/api/pith-number/JWXCZNKXIOY26QCSH77OMALEPW/events.json","paper":"https://pith.science/paper/JWXCZNKX"},"agent_actions":{"view_html":"https://pith.science/pith/JWXCZNKXIOY26QCSH77OMALEPW","download_json":"https://pith.science/pith/JWXCZNKXIOY26QCSH77OMALEPW.json","view_paper":"https://pith.science/paper/JWXCZNKX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2606.31341&json=true","fetch_graph":"https://pith.science/api/pith-number/JWXCZNKXIOY26QCSH77OMALEPW/graph.json","fetch_events":"https://pith.science/api/pith-number/JWXCZNKXIOY26QCSH77OMALEPW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JWXCZNKXIOY26QCSH77OMALEPW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JWXCZNKXIOY26QCSH77OMALEPW/action/storage_attestation","attest_author":"https://pith.science/pith/JWXCZNKXIOY26QCSH77OMALEPW/action/author_attestation","sign_citation":"https://pith.science/pith/JWXCZNKXIOY26QCSH77OMALEPW/action/citation_signature","submit_replication":"https://pith.science/pith/JWXCZNKXIOY26QCSH77OMALEPW/action/replication_record"}},"created_at":"2026-07-01T01:17:59.812958+00:00","updated_at":"2026-07-01T01:17:59.812958+00:00"}