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We compute the structure of $\\textrm{H}^1(I_1,\\pi)$ as an $\\mathcal{H}$-module, where $\\pi$ is a mod-$p$ principal series representation of $\\textrm{GL}_n(F)$. We also give some partial results about the structure of $\\textrm{H}^1(I_1,\\pi)$ for a general split reductive group with irreducible root system."},"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":"1708.03014","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2017-08-09T21:10:48Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"b00cc6da3939f0b4f27e8b16c3e3b43f79a2e392d3be82c51889e1be6f9648dc","abstract_canon_sha256":"086baa3b61a1665b9a047db895298dd109a94dd872e0105962bf4e16c563a759"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:15:05.450571Z","signature_b64":"byLFKee0QcrgRpFF83CJ7X3uUUWNb9dQwZDipvzMNCgemr0ikLAleemLi8Q5sUOrhE8qv7c/MCatEd8gLKgSCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c8ffe4fe3417438a990bd6ca2d1e77aa26b4a52eaf23a1ae1a45e6f5ce005dd6","last_reissued_at":"2026-05-18T00:15:05.447621Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:15:05.447621Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The first pro-$p$-Iwahori cohomology of mod-$p$ principal series for $p$-adic $\\textrm{GL}_n$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.RT","authors_text":"Karol Koziol","submitted_at":"2017-08-09T21:10:48Z","abstract_excerpt":"Let $p\\geq 3$ be a prime number and $F$ a $p$-adic field. 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We also give some partial results about the structure of $\\textrm{H}^1(I_1,\\pi)$ for a general split reductive group with irreducible root system."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.03014","kind":"arxiv","version":3},"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":"1708.03014","created_at":"2026-05-18T00:15:05.447706+00:00"},{"alias_kind":"arxiv_version","alias_value":"1708.03014v3","created_at":"2026-05-18T00:15:05.447706+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.03014","created_at":"2026-05-18T00:15:05.447706+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZD76J7RUC5BY","created_at":"2026-05-18T12:31:59.375834+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZD76J7RUC5BYVGIL","created_at":"2026-05-18T12:31:59.375834+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZD76J7RU","created_at":"2026-05-18T12:31:59.375834+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/ZD76J7RUC5BYVGIL23FC2HTXVI","json":"https://pith.science/pith/ZD76J7RUC5BYVGIL23FC2HTXVI.json","graph_json":"https://pith.science/api/pith-number/ZD76J7RUC5BYVGIL23FC2HTXVI/graph.json","events_json":"https://pith.science/api/pith-number/ZD76J7RUC5BYVGIL23FC2HTXVI/events.json","paper":"https://pith.science/paper/ZD76J7RU"},"agent_actions":{"view_html":"https://pith.science/pith/ZD76J7RUC5BYVGIL23FC2HTXVI","download_json":"https://pith.science/pith/ZD76J7RUC5BYVGIL23FC2HTXVI.json","view_paper":"https://pith.science/paper/ZD76J7RU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1708.03014&json=true","fetch_graph":"https://pith.science/api/pith-number/ZD76J7RUC5BYVGIL23FC2HTXVI/graph.json","fetch_events":"https://pith.science/api/pith-number/ZD76J7RUC5BYVGIL23FC2HTXVI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZD76J7RUC5BYVGIL23FC2HTXVI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZD76J7RUC5BYVGIL23FC2HTXVI/action/storage_attestation","attest_author":"https://pith.science/pith/ZD76J7RUC5BYVGIL23FC2HTXVI/action/author_attestation","sign_citation":"https://pith.science/pith/ZD76J7RUC5BYVGIL23FC2HTXVI/action/citation_signature","submit_replication":"https://pith.science/pith/ZD76J7RUC5BYVGIL23FC2HTXVI/action/replication_record"}},"created_at":"2026-05-18T00:15:05.447706+00:00","updated_at":"2026-05-18T00:15:05.447706+00:00"}