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We study the Frobenius stratification of $\\M^s_X(r,d)$ in terms of Harder-Narasimhan polygons of Frobenius pull backs of stable vector bundles and obtain the irreducibility and dimension of each non-empty Frobenius stratum in case $(p,g,r)=(3,2,3)$."},"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":"1803.03990","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-03-11T17:26:37Z","cross_cats_sorted":[],"title_canon_sha256":"64e6a86f4e5292c835eeaae11fb4cb43e22fcd65d58cbd897314096042ff164b","abstract_canon_sha256":"bfc83cc91cccbabf3a6393fc2729fac4b5235aa3a4b7d19652408a566d17fbd3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:21:33.257623Z","signature_b64":"xEtgSvga2TIBI9MZAlpVSp332SXL18kh8/SWT/2YbjD1P9UbNIDBKu192x7k3Bu6/sfXrO/k5bKowc58weWODA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bd9279c2b5b2b9b8547b052cb1d0f7c707121823ac69ea748ba12c9241e95d2a","last_reissued_at":"2026-05-18T00:21:33.257010Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:21:33.257010Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Frobenius Stratification of Moduli Spaces of Vector Bundles in Positive characteristic. 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We study the Frobenius stratification of $\\M^s_X(r,d)$ in terms of Harder-Narasimhan polygons of Frobenius pull backs of stable vector bundles and obtain the irreducibility and dimension of each non-empty Frobenius stratum in case $(p,g,r)=(3,2,3)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.03990","kind":"arxiv","version":1},"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":"1803.03990","created_at":"2026-05-18T00:21:33.257106+00:00"},{"alias_kind":"arxiv_version","alias_value":"1803.03990v1","created_at":"2026-05-18T00:21:33.257106+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.03990","created_at":"2026-05-18T00:21:33.257106+00:00"},{"alias_kind":"pith_short_12","alias_value":"XWJHTQVVWK43","created_at":"2026-05-18T12:33:01.666342+00:00"},{"alias_kind":"pith_short_16","alias_value":"XWJHTQVVWK43QVD3","created_at":"2026-05-18T12:33:01.666342+00:00"},{"alias_kind":"pith_short_8","alias_value":"XWJHTQVV","created_at":"2026-05-18T12:33:01.666342+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/XWJHTQVVWK43QVD3AUWLDUHXY4","json":"https://pith.science/pith/XWJHTQVVWK43QVD3AUWLDUHXY4.json","graph_json":"https://pith.science/api/pith-number/XWJHTQVVWK43QVD3AUWLDUHXY4/graph.json","events_json":"https://pith.science/api/pith-number/XWJHTQVVWK43QVD3AUWLDUHXY4/events.json","paper":"https://pith.science/paper/XWJHTQVV"},"agent_actions":{"view_html":"https://pith.science/pith/XWJHTQVVWK43QVD3AUWLDUHXY4","download_json":"https://pith.science/pith/XWJHTQVVWK43QVD3AUWLDUHXY4.json","view_paper":"https://pith.science/paper/XWJHTQVV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1803.03990&json=true","fetch_graph":"https://pith.science/api/pith-number/XWJHTQVVWK43QVD3AUWLDUHXY4/graph.json","fetch_events":"https://pith.science/api/pith-number/XWJHTQVVWK43QVD3AUWLDUHXY4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XWJHTQVVWK43QVD3AUWLDUHXY4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XWJHTQVVWK43QVD3AUWLDUHXY4/action/storage_attestation","attest_author":"https://pith.science/pith/XWJHTQVVWK43QVD3AUWLDUHXY4/action/author_attestation","sign_citation":"https://pith.science/pith/XWJHTQVVWK43QVD3AUWLDUHXY4/action/citation_signature","submit_replication":"https://pith.science/pith/XWJHTQVVWK43QVD3AUWLDUHXY4/action/replication_record"}},"created_at":"2026-05-18T00:21:33.257106+00:00","updated_at":"2026-05-18T00:21:33.257106+00:00"}