{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:2XWQIHN5OLOL425KGYQ4XKR4QF","short_pith_number":"pith:2XWQIHN5","canonical_record":{"source":{"id":"1010.1203","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2010-10-06T16:54:23Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"004152450ec871fa74830a0109005cf62ca21938b74a072d66b63e9a7ba19a1d","abstract_canon_sha256":"b04ab69b7650f73b39c2b717354a127a9fac9409850015f1d2e6b2d6756c3a57"},"schema_version":"1.0"},"canonical_sha256":"d5ed041dbd72dcbe6baa3621cbaa3c817b573d99a9ce9ab83ee0f4cf7e849b6a","source":{"kind":"arxiv","id":"1010.1203","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1010.1203","created_at":"2026-05-18T03:31:18Z"},{"alias_kind":"arxiv_version","alias_value":"1010.1203v3","created_at":"2026-05-18T03:31:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.1203","created_at":"2026-05-18T03:31:18Z"},{"alias_kind":"pith_short_12","alias_value":"2XWQIHN5OLOL","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_16","alias_value":"2XWQIHN5OLOL425K","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_8","alias_value":"2XWQIHN5","created_at":"2026-05-18T12:26:03Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:2XWQIHN5OLOL425KGYQ4XKR4QF","target":"record","payload":{"canonical_record":{"source":{"id":"1010.1203","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2010-10-06T16:54:23Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"004152450ec871fa74830a0109005cf62ca21938b74a072d66b63e9a7ba19a1d","abstract_canon_sha256":"b04ab69b7650f73b39c2b717354a127a9fac9409850015f1d2e6b2d6756c3a57"},"schema_version":"1.0"},"canonical_sha256":"d5ed041dbd72dcbe6baa3621cbaa3c817b573d99a9ce9ab83ee0f4cf7e849b6a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:31:18.149478Z","signature_b64":"8vmrab3ldGZxyz1q3AO0Z0nuwnmnll69dX/zmaGutV0gOTQ8UtsHhT/QMVd516EjkDwD7x7GiIdXEK8NJgD0BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d5ed041dbd72dcbe6baa3621cbaa3c817b573d99a9ce9ab83ee0f4cf7e849b6a","last_reissued_at":"2026-05-18T03:31:18.148922Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:31:18.148922Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1010.1203","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:31:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JKMIAlccSSWoI4zKxVFEh/NqlT04YmRyQ4YG4bfccNEvxPzLzHEUXP+5jN6b81PhhITNTy4a75UATG8ulT2lDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T02:38:31.526712Z"},"content_sha256":"d6a6d3f5174bdf816da6f074d132e3f12815fcca768894e43839abdb60f9d085","schema_version":"1.0","event_id":"sha256:d6a6d3f5174bdf816da6f074d132e3f12815fcca768894e43839abdb60f9d085"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:2XWQIHN5OLOL425KGYQ4XKR4QF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"First cohomology for finite groups of Lie type: simple modules with small dominant weights","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.GR","authors_text":"Adrian M. Brunyate, Andrew J. Talian, Benjamin F. Jones, Benjamin J. Wyser (University of Georgia VIGRE Algebra Group), Brandon L. Samples, Brian D. Boe, Christopher M. Drupieski, Daniel K. Nakano, Duc Duy Nguyen, Jon F. Carlson, Leonard Chastkofsky, Lisa Townsley, Nham Vo Ngo, Niles Johnson, Wenjing Li","submitted_at":"2010-10-06T16:54:23Z","abstract_excerpt":"Let $k$ be an algebraically closed field of characteristic $p > 0$, and let $G$ be a simple, simply connected algebraic group defined over $\\mathbb{F}_p$. Given $r \\geq 1$, set $q=p^r$, and let $G(\\mathbb{F}_q)$ be the corresponding finite Chevalley group. In this paper we investigate the structure of the first cohomology group $H^1(G(\\mathbb{F}_q),L(\\lambda))$ where $L(\\lambda)$ is the simple $G$-module of highest weight $\\lambda$. Under certain very mild conditions on $p$ and $q$, we are able to completely describe the first cohomology group when $\\lambda$ is less than or equal to a fundamen"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.1203","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:31:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OFHWoi2/GIKh/ZEcJ2vbZxeWwegWJZvFsF1hokd0tv+udjP5QQbaVRxvHjkQuLnqBtP+Ptp+nTcwbWkL6fSIBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T02:38:31.527109Z"},"content_sha256":"be295d9c8282dd6bc5380375f9ff5f8307e2773ab302b0784f0eee2aa0729cd8","schema_version":"1.0","event_id":"sha256:be295d9c8282dd6bc5380375f9ff5f8307e2773ab302b0784f0eee2aa0729cd8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2XWQIHN5OLOL425KGYQ4XKR4QF/bundle.json","state_url":"https://pith.science/pith/2XWQIHN5OLOL425KGYQ4XKR4QF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2XWQIHN5OLOL425KGYQ4XKR4QF/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-31T02:38:31Z","links":{"resolver":"https://pith.science/pith/2XWQIHN5OLOL425KGYQ4XKR4QF","bundle":"https://pith.science/pith/2XWQIHN5OLOL425KGYQ4XKR4QF/bundle.json","state":"https://pith.science/pith/2XWQIHN5OLOL425KGYQ4XKR4QF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2XWQIHN5OLOL425KGYQ4XKR4QF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:2XWQIHN5OLOL425KGYQ4XKR4QF","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"b04ab69b7650f73b39c2b717354a127a9fac9409850015f1d2e6b2d6756c3a57","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2010-10-06T16:54:23Z","title_canon_sha256":"004152450ec871fa74830a0109005cf62ca21938b74a072d66b63e9a7ba19a1d"},"schema_version":"1.0","source":{"id":"1010.1203","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1010.1203","created_at":"2026-05-18T03:31:18Z"},{"alias_kind":"arxiv_version","alias_value":"1010.1203v3","created_at":"2026-05-18T03:31:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.1203","created_at":"2026-05-18T03:31:18Z"},{"alias_kind":"pith_short_12","alias_value":"2XWQIHN5OLOL","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_16","alias_value":"2XWQIHN5OLOL425K","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_8","alias_value":"2XWQIHN5","created_at":"2026-05-18T12:26:03Z"}],"graph_snapshots":[{"event_id":"sha256:be295d9c8282dd6bc5380375f9ff5f8307e2773ab302b0784f0eee2aa0729cd8","target":"graph","created_at":"2026-05-18T03:31:18Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"Let $k$ be an algebraically closed field of characteristic $p > 0$, and let $G$ be a simple, simply connected algebraic group defined over $\\mathbb{F}_p$. Given $r \\geq 1$, set $q=p^r$, and let $G(\\mathbb{F}_q)$ be the corresponding finite Chevalley group. In this paper we investigate the structure of the first cohomology group $H^1(G(\\mathbb{F}_q),L(\\lambda))$ where $L(\\lambda)$ is the simple $G$-module of highest weight $\\lambda$. Under certain very mild conditions on $p$ and $q$, we are able to completely describe the first cohomology group when $\\lambda$ is less than or equal to a fundamen","authors_text":"Adrian M. Brunyate, Andrew J. Talian, Benjamin F. Jones, Benjamin J. Wyser (University of Georgia VIGRE Algebra Group), Brandon L. Samples, Brian D. Boe, Christopher M. Drupieski, Daniel K. Nakano, Duc Duy Nguyen, Jon F. Carlson, Leonard Chastkofsky, Lisa Townsley, Nham Vo Ngo, Niles Johnson, Wenjing Li","cross_cats":["math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2010-10-06T16:54:23Z","title":"First cohomology for finite groups of Lie type: simple modules with small dominant weights"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.1203","kind":"arxiv","version":3},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:d6a6d3f5174bdf816da6f074d132e3f12815fcca768894e43839abdb60f9d085","target":"record","created_at":"2026-05-18T03:31:18Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"b04ab69b7650f73b39c2b717354a127a9fac9409850015f1d2e6b2d6756c3a57","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2010-10-06T16:54:23Z","title_canon_sha256":"004152450ec871fa74830a0109005cf62ca21938b74a072d66b63e9a7ba19a1d"},"schema_version":"1.0","source":{"id":"1010.1203","kind":"arxiv","version":3}},"canonical_sha256":"d5ed041dbd72dcbe6baa3621cbaa3c817b573d99a9ce9ab83ee0f4cf7e849b6a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d5ed041dbd72dcbe6baa3621cbaa3c817b573d99a9ce9ab83ee0f4cf7e849b6a","first_computed_at":"2026-05-18T03:31:18.148922Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:31:18.148922Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8vmrab3ldGZxyz1q3AO0Z0nuwnmnll69dX/zmaGutV0gOTQ8UtsHhT/QMVd516EjkDwD7x7GiIdXEK8NJgD0BA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:31:18.149478Z","signed_message":"canonical_sha256_bytes"},"source_id":"1010.1203","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d6a6d3f5174bdf816da6f074d132e3f12815fcca768894e43839abdb60f9d085","sha256:be295d9c8282dd6bc5380375f9ff5f8307e2773ab302b0784f0eee2aa0729cd8"],"state_sha256":"584dcdff24849eda3d89dc40a904d32fa19dc57be844c0e519ad21386a6946ba"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AeqFb6G4jebEsayWZUUqh5sfxNTAm8LMeg/JOo0s4hr7Ak+7EojwdE441XAFja1eqqp8nHwkmOnwbtvc0lW2CQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T02:38:31.529516Z","bundle_sha256":"30f10783ebeff2d84b9aba6155e4c9b6e3a3e8cce815755f653f4d9053f28eff"}}