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We study the Frobenius stratification of $\\M^s_X(3,0)$ 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 the case $(p,g)=(3,2)$."},"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":"1612.08213","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-12-24T18:02:06Z","cross_cats_sorted":[],"title_canon_sha256":"8c35613e047c6cd2b0b6960942f3a9e79faf7f342439ff7ff24086453cb3862f","abstract_canon_sha256":"9d44c4d7da04cde154a859412fef4fa11ddff5ab0039e80e96d08a60893504dd"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:57:15.890886Z","signature_b64":"YKINVGr0cN8S/jxjsjAd51hzbYj2XuI7yOvYSKW7tkBMO2fPIrCBjG31O5heTnRc3Y9UAJoSTwvuGysPCF8cBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"01e0b76e82e2762ffe9e9adc24f9b9f00da106d95a83c8342ba2df611e758f9d","last_reissued_at":"2026-05-17T23:57:15.890359Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:57:15.890359Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Frobenius Stratification of Moduli Spaces of Rank $3$ Vector Bundles in Characteristic $3$, I","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Lingguang Li","submitted_at":"2016-12-24T18:02:06Z","abstract_excerpt":"Let $X$ be a smooth projective curve of genus $g\\geq 2$ over an algebraically closed field $k$ of characteristic $p>0$, $F_X:X\\rightarrow X$ the absolute Frobenius morphism. Let $\\M^s_X(r,d)$ be the moduli space of stable vector bundles of rank $r$ and degree $d$ on $X$. We study the Frobenius stratification of $\\M^s_X(3,0)$ 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 the case $(p,g)=(3,2)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.08213","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":"1612.08213","created_at":"2026-05-17T23:57:15.890438+00:00"},{"alias_kind":"arxiv_version","alias_value":"1612.08213v3","created_at":"2026-05-17T23:57:15.890438+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.08213","created_at":"2026-05-17T23:57:15.890438+00:00"},{"alias_kind":"pith_short_12","alias_value":"AHQLO3UC4J3C","created_at":"2026-05-18T12:30:07.202191+00:00"},{"alias_kind":"pith_short_16","alias_value":"AHQLO3UC4J3C77U6","created_at":"2026-05-18T12:30:07.202191+00:00"},{"alias_kind":"pith_short_8","alias_value":"AHQLO3UC","created_at":"2026-05-18T12:30:07.202191+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/AHQLO3UC4J3C77U6TLOCJ6NZ6A","json":"https://pith.science/pith/AHQLO3UC4J3C77U6TLOCJ6NZ6A.json","graph_json":"https://pith.science/api/pith-number/AHQLO3UC4J3C77U6TLOCJ6NZ6A/graph.json","events_json":"https://pith.science/api/pith-number/AHQLO3UC4J3C77U6TLOCJ6NZ6A/events.json","paper":"https://pith.science/paper/AHQLO3UC"},"agent_actions":{"view_html":"https://pith.science/pith/AHQLO3UC4J3C77U6TLOCJ6NZ6A","download_json":"https://pith.science/pith/AHQLO3UC4J3C77U6TLOCJ6NZ6A.json","view_paper":"https://pith.science/paper/AHQLO3UC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1612.08213&json=true","fetch_graph":"https://pith.science/api/pith-number/AHQLO3UC4J3C77U6TLOCJ6NZ6A/graph.json","fetch_events":"https://pith.science/api/pith-number/AHQLO3UC4J3C77U6TLOCJ6NZ6A/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/AHQLO3UC4J3C77U6TLOCJ6NZ6A/action/timestamp_anchor","attest_storage":"https://pith.science/pith/AHQLO3UC4J3C77U6TLOCJ6NZ6A/action/storage_attestation","attest_author":"https://pith.science/pith/AHQLO3UC4J3C77U6TLOCJ6NZ6A/action/author_attestation","sign_citation":"https://pith.science/pith/AHQLO3UC4J3C77U6TLOCJ6NZ6A/action/citation_signature","submit_replication":"https://pith.science/pith/AHQLO3UC4J3C77U6TLOCJ6NZ6A/action/replication_record"}},"created_at":"2026-05-17T23:57:15.890438+00:00","updated_at":"2026-05-17T23:57:15.890438+00:00"}