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More generally, for a finite collection of points $x_1, ..., x_k \\in X$, let $\\mathrm{Bun}_G^{(\\mathrm{I}; x_1, ..., x_k)}$ be the algebraic stack of principal $G$-bundles on $X$ together with Iwahori level structure at each point $x_j$. We will show that $\\mathrm{D}-\\mathrm{mod}(\\mathrm{Bun}_G^{\\mathrm{I}})$ and $\\mathrm{D}-\\mathrm{mod}(\\mat"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2411.03057","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2024-11-05T12:44:41Z","cross_cats_sorted":[],"title_canon_sha256":"f90b375e887d5594ee4a747e66cdd1c8da4ab5b90ef6a04ceb6bceca205e3edd","abstract_canon_sha256":"7937a54ecc3067c688e8ad1a6b67974fd368a5c3f092558784c13c4fc10d446d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:42:31.939590Z","signature_b64":"LA/hIe1z92xuz10t3tD2hljKTnjlwC0aTWSC5dHdU+tFLVBsDl2umaQjc4lzs2iuBWdSMe2yt6qJvdG73M6RBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"633817e7a6faba0615c3483f9b29e37e6b09db87c27105707a151d29af798023","last_reissued_at":"2026-07-05T09:42:31.939055Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:42:31.939055Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"$\\mathrm{D}-\\mathrm{mod}(\\mathrm{Bun}_G^\\mathrm{I})$ is Compactly Generated","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Taeuk Nam","submitted_at":"2024-11-05T12:44:41Z","abstract_excerpt":"Drinfeld and Gaitsgory proved that $\\mathrm{D}-\\mathrm{mod}(\\mathrm{Bun}_G)$ is compactly generated. Let $\\mathrm{Bun}_G^{\\mathrm{I}}$ be the algebraic stack of principal $G$-bundles on $X$ together with Iwahori level structure at a fixed point $x \\in X$. More generally, for a finite collection of points $x_1, ..., x_k \\in X$, let $\\mathrm{Bun}_G^{(\\mathrm{I}; x_1, ..., x_k)}$ be the algebraic stack of principal $G$-bundles on $X$ together with Iwahori level structure at each point $x_j$. We will show that $\\mathrm{D}-\\mathrm{mod}(\\mathrm{Bun}_G^{\\mathrm{I}})$ and $\\mathrm{D}-\\mathrm{mod}(\\mat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.03057","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2411.03057/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":"2411.03057","created_at":"2026-07-05T09:42:31.939110+00:00"},{"alias_kind":"arxiv_version","alias_value":"2411.03057v2","created_at":"2026-07-05T09:42:31.939110+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.03057","created_at":"2026-07-05T09:42:31.939110+00:00"},{"alias_kind":"pith_short_12","alias_value":"MM4BPZ5G7K5A","created_at":"2026-07-05T09:42:31.939110+00:00"},{"alias_kind":"pith_short_16","alias_value":"MM4BPZ5G7K5AMFOD","created_at":"2026-07-05T09:42:31.939110+00:00"},{"alias_kind":"pith_short_8","alias_value":"MM4BPZ5G","created_at":"2026-07-05T09:42:31.939110+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2608.04207","citing_title":"Iwahori Fundamental Local Equivalence","ref_index":6,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/MM4BPZ5G7K5AMFODJA7ZWKPDPZ","json":"https://pith.science/pith/MM4BPZ5G7K5AMFODJA7ZWKPDPZ.json","graph_json":"https://pith.science/api/pith-number/MM4BPZ5G7K5AMFODJA7ZWKPDPZ/graph.json","events_json":"https://pith.science/api/pith-number/MM4BPZ5G7K5AMFODJA7ZWKPDPZ/events.json","paper":"https://pith.science/paper/MM4BPZ5G"},"agent_actions":{"view_html":"https://pith.science/pith/MM4BPZ5G7K5AMFODJA7ZWKPDPZ","download_json":"https://pith.science/pith/MM4BPZ5G7K5AMFODJA7ZWKPDPZ.json","view_paper":"https://pith.science/paper/MM4BPZ5G","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2411.03057&json=true","fetch_graph":"https://pith.science/api/pith-number/MM4BPZ5G7K5AMFODJA7ZWKPDPZ/graph.json","fetch_events":"https://pith.science/api/pith-number/MM4BPZ5G7K5AMFODJA7ZWKPDPZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MM4BPZ5G7K5AMFODJA7ZWKPDPZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MM4BPZ5G7K5AMFODJA7ZWKPDPZ/action/storage_attestation","attest_author":"https://pith.science/pith/MM4BPZ5G7K5AMFODJA7ZWKPDPZ/action/author_attestation","sign_citation":"https://pith.science/pith/MM4BPZ5G7K5AMFODJA7ZWKPDPZ/action/citation_signature","submit_replication":"https://pith.science/pith/MM4BPZ5G7K5AMFODJA7ZWKPDPZ/action/replication_record"}},"created_at":"2026-07-05T09:42:31.939110+00:00","updated_at":"2026-07-05T09:42:31.939110+00:00"}