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Let $P \\subset G$ be a parabolic subgroup. We prove that the tangent bundle of $G/P$ is Frobenius stable with respect to the anticanonical polarization on $G/P$."},"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":"1507.03026","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-07-10T20:19:25Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"90cc8aff8183c0332c0f1679e952c2704810250367e2bf8230a107fa8b69f6f9","abstract_canon_sha256":"5f9bee37441ed13bc1cd008c2d8079e807a5e3dd09e5d8422532864054cfbb8c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:54:27.245778Z","signature_b64":"27iev4dv/S+uqF0sexV/Ek76k6NGDmw7/olxmIv1+gmbk2rKuXrQDZR3wUYQYmio6JZ4DRggWfmk11ndes0eAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"eeb109b6d2137fa0881f67b14cafaad79a5882bb4c2993dd39bec80ec9a39377","last_reissued_at":"2026-05-17T23:54:27.244941Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:54:27.244941Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Stability of the tangent bundle of G/P in positive characteristics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.AG","authors_text":"Christophe Mourougane, Indranil Biswas, Pierre-Emmanuel Chaput","submitted_at":"2015-07-10T20:19:25Z","abstract_excerpt":"Let $G$ be an almost simple simply-connected affine algebraic group over an algebraically closed field $k$ of characteristic $p > 0$. If $G$ has type $B_n$, $C_n$ or $F_4$, we assume that $p > 2$, and if $G$ has type $G_2$, we assume that $p > 3$. Let $P \\subset G$ be a parabolic subgroup. We prove that the tangent bundle of $G/P$ is Frobenius stable with respect to the anticanonical polarization on $G/P$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.03026","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":""},"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":"1507.03026","created_at":"2026-05-17T23:54:27.245094+00:00"},{"alias_kind":"arxiv_version","alias_value":"1507.03026v2","created_at":"2026-05-17T23:54:27.245094+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.03026","created_at":"2026-05-17T23:54:27.245094+00:00"},{"alias_kind":"pith_short_12","alias_value":"52YQTNWSCN72","created_at":"2026-05-18T12:29:05.191682+00:00"},{"alias_kind":"pith_short_16","alias_value":"52YQTNWSCN72BCA7","created_at":"2026-05-18T12:29:05.191682+00:00"},{"alias_kind":"pith_short_8","alias_value":"52YQTNWS","created_at":"2026-05-18T12:29:05.191682+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/52YQTNWSCN72BCA7M6YUZL5K26","json":"https://pith.science/pith/52YQTNWSCN72BCA7M6YUZL5K26.json","graph_json":"https://pith.science/api/pith-number/52YQTNWSCN72BCA7M6YUZL5K26/graph.json","events_json":"https://pith.science/api/pith-number/52YQTNWSCN72BCA7M6YUZL5K26/events.json","paper":"https://pith.science/paper/52YQTNWS"},"agent_actions":{"view_html":"https://pith.science/pith/52YQTNWSCN72BCA7M6YUZL5K26","download_json":"https://pith.science/pith/52YQTNWSCN72BCA7M6YUZL5K26.json","view_paper":"https://pith.science/paper/52YQTNWS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1507.03026&json=true","fetch_graph":"https://pith.science/api/pith-number/52YQTNWSCN72BCA7M6YUZL5K26/graph.json","fetch_events":"https://pith.science/api/pith-number/52YQTNWSCN72BCA7M6YUZL5K26/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/52YQTNWSCN72BCA7M6YUZL5K26/action/timestamp_anchor","attest_storage":"https://pith.science/pith/52YQTNWSCN72BCA7M6YUZL5K26/action/storage_attestation","attest_author":"https://pith.science/pith/52YQTNWSCN72BCA7M6YUZL5K26/action/author_attestation","sign_citation":"https://pith.science/pith/52YQTNWSCN72BCA7M6YUZL5K26/action/citation_signature","submit_replication":"https://pith.science/pith/52YQTNWSCN72BCA7M6YUZL5K26/action/replication_record"}},"created_at":"2026-05-17T23:54:27.245094+00:00","updated_at":"2026-05-17T23:54:27.245094+00:00"}