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We prove the following: Let $E_1$ and $E_2$ be two semistable vector bundles on $C$, with ${\\rm genus}(C)\\, \\geq\\, 2$. If ${\\mathcal F}_n(E_1)\\,= \\, {\\mathcal F}_n(E_2)$ for a fixed $n$, then $E_1 \\,=\\, E_2$."},"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":"1208.3807","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-08-19T04:15:51Z","cross_cats_sorted":[],"title_canon_sha256":"ed2adf75d3ec984c3eb17f8fdf410d8da8ea8843db9be4f5b6829e5267145140","abstract_canon_sha256":"0ff8e28328badc069e36b8f0cf8d79356935d3e9e91dbee8ccbad77b917a7dfc"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:48:26.164326Z","signature_b64":"wLlOQL/B6h88TEUwl2O6YvEhZxhIDm23lwZ1m7vwOM6kBMeMVUPyASHZnqMhiSraggsfc69iW4BZX7fSDlJtAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c6f83b378ee1b31a74b1f6c21f8558e5d346a91fedc82a6f75efcd1653248fe2","last_reissued_at":"2026-05-18T03:48:26.163663Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:48:26.163663Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Reconstructing vector bundles on curves from their direct image on symmetric powers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"D. S. Nagaraj, Indranil Biswas","submitted_at":"2012-08-19T04:15:51Z","abstract_excerpt":"Let $C$ be an irreducible smooth complex projective curve, and let $E$ be an algebraic vector bundle of rank $r$ on $C$. Associated to $E$, there are vector bundles ${\\mathcal F}_n(E)$ of rank $nr$ on $S^n(C)$, where $S^n(C)$ is $ $n$-th symmetric power of $C$. We prove the following: Let $E_1$ and $E_2$ be two semistable vector bundles on $C$, with ${\\rm genus}(C)\\, \\geq\\, 2$. If ${\\mathcal F}_n(E_1)\\,= \\, {\\mathcal F}_n(E_2)$ for a fixed $n$, then $E_1 \\,=\\, E_2$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.3807","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":"1208.3807","created_at":"2026-05-18T03:48:26.163768+00:00"},{"alias_kind":"arxiv_version","alias_value":"1208.3807v1","created_at":"2026-05-18T03:48:26.163768+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.3807","created_at":"2026-05-18T03:48:26.163768+00:00"},{"alias_kind":"pith_short_12","alias_value":"Y34DWN4O4GZR","created_at":"2026-05-18T12:27:27.928770+00:00"},{"alias_kind":"pith_short_16","alias_value":"Y34DWN4O4GZRU5FR","created_at":"2026-05-18T12:27:27.928770+00:00"},{"alias_kind":"pith_short_8","alias_value":"Y34DWN4O","created_at":"2026-05-18T12:27:27.928770+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/Y34DWN4O4GZRU5FR63BB7BKY4X","json":"https://pith.science/pith/Y34DWN4O4GZRU5FR63BB7BKY4X.json","graph_json":"https://pith.science/api/pith-number/Y34DWN4O4GZRU5FR63BB7BKY4X/graph.json","events_json":"https://pith.science/api/pith-number/Y34DWN4O4GZRU5FR63BB7BKY4X/events.json","paper":"https://pith.science/paper/Y34DWN4O"},"agent_actions":{"view_html":"https://pith.science/pith/Y34DWN4O4GZRU5FR63BB7BKY4X","download_json":"https://pith.science/pith/Y34DWN4O4GZRU5FR63BB7BKY4X.json","view_paper":"https://pith.science/paper/Y34DWN4O","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1208.3807&json=true","fetch_graph":"https://pith.science/api/pith-number/Y34DWN4O4GZRU5FR63BB7BKY4X/graph.json","fetch_events":"https://pith.science/api/pith-number/Y34DWN4O4GZRU5FR63BB7BKY4X/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/Y34DWN4O4GZRU5FR63BB7BKY4X/action/timestamp_anchor","attest_storage":"https://pith.science/pith/Y34DWN4O4GZRU5FR63BB7BKY4X/action/storage_attestation","attest_author":"https://pith.science/pith/Y34DWN4O4GZRU5FR63BB7BKY4X/action/author_attestation","sign_citation":"https://pith.science/pith/Y34DWN4O4GZRU5FR63BB7BKY4X/action/citation_signature","submit_replication":"https://pith.science/pith/Y34DWN4O4GZRU5FR63BB7BKY4X/action/replication_record"}},"created_at":"2026-05-18T03:48:26.163768+00:00","updated_at":"2026-05-18T03:48:26.163768+00:00"}