{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:TYB5PZDHGCQTADGZPDJKBEGHY5","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":"caa7b74903ad15d4a6a539822649c8e6c266d21f6ea4cf2a4b3b903c2b4ebf00","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-01-01T15:47:17Z","title_canon_sha256":"c2ca52c9c6be1ba1a0969ab5bfcb1101408e4084ba8c2f00703377e7996767c6"},"schema_version":"1.0","source":{"id":"1701.00252","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.00252","created_at":"2026-05-18T00:53:35Z"},{"alias_kind":"arxiv_version","alias_value":"1701.00252v1","created_at":"2026-05-18T00:53:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.00252","created_at":"2026-05-18T00:53:35Z"},{"alias_kind":"pith_short_12","alias_value":"TYB5PZDHGCQT","created_at":"2026-05-18T12:31:46Z"},{"alias_kind":"pith_short_16","alias_value":"TYB5PZDHGCQTADGZ","created_at":"2026-05-18T12:31:46Z"},{"alias_kind":"pith_short_8","alias_value":"TYB5PZDH","created_at":"2026-05-18T12:31:46Z"}],"graph_snapshots":[{"event_id":"sha256:8709a6b365f7fd8833270b3359de3b3e0a209eb47bc92c03bf95ebaa0f01c1bb","target":"graph","created_at":"2026-05-18T00:53:35Z","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 $p>0$, $X$ a smooth projective variety over $k$ with a fixed ample divisor $H$. Let $E$ be a rational $GL_n(k)$-bundle on $X$, and $\\rho:GL_n(k)\\rightarrow GL_m(k)$ a rational $GL_n(k)$-representation at most degree $d$ such that $\\rho$ maps the radical $R(GL_n(k))$ of $GL_n(k)$ into the radical $R(GL_m(k))$ of $GL_m(k)$. We show that if $F_X^{N*}(E)$ is semistable for some integer $N\\geq\\max\\limits_{0<r<m}C^r_m\\cdot\\log_p(dr)$, then the induced rational $GL_m(k)$-bundle $E(GL_m(k))$ is semistable. As an application, if $\\dim X=n$, we ","authors_text":"Lingguang Li","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-01-01T15:47:17Z","title":"Semistability of Rational Principal $GL_n$-Bundles in Positive Characteristic"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.00252","kind":"arxiv","version":1},"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:b2ecde2adb95fed146e1becd911bc318eb069c73f795a94ef4d86132bc875f5b","target":"record","created_at":"2026-05-18T00:53:35Z","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":"caa7b74903ad15d4a6a539822649c8e6c266d21f6ea4cf2a4b3b903c2b4ebf00","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-01-01T15:47:17Z","title_canon_sha256":"c2ca52c9c6be1ba1a0969ab5bfcb1101408e4084ba8c2f00703377e7996767c6"},"schema_version":"1.0","source":{"id":"1701.00252","kind":"arxiv","version":1}},"canonical_sha256":"9e03d7e46730a1300cd978d2a090c7c74df2d0abf0a2482bcd8db1c803755da5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9e03d7e46730a1300cd978d2a090c7c74df2d0abf0a2482bcd8db1c803755da5","first_computed_at":"2026-05-18T00:53:35.978309Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:53:35.978309Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"K/4AB64tzTSDrrrXb9TWFjAESgsvqtgzhVtBbfzjEy3i0gioWJ2oCvPE5TaVfqyufaaws79ALWflX+A4/ER7Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:53:35.978728Z","signed_message":"canonical_sha256_bytes"},"source_id":"1701.00252","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b2ecde2adb95fed146e1becd911bc318eb069c73f795a94ef4d86132bc875f5b","sha256:8709a6b365f7fd8833270b3359de3b3e0a209eb47bc92c03bf95ebaa0f01c1bb"],"state_sha256":"483590ca6c9354a5e0d55836b1e44d88267775b426e1b3a31a9422f62ace6b34"}