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This is a consequence of our main theorem, which states that the restricted tangent bundle f^* T_{P^r} of a general curve of genus g, equipped with a general degree d map f to P^r, satisfies the property of interpolation (i.e.\\ that for a general effective divisor D of any degree on C, either H^0(f^* T_{P^r}(-D)) = 0 or H^1(f^* T_{P^r}(-D)) = 0). We also pr"},"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":"1511.04480","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-11-13T23:33:44Z","cross_cats_sorted":[],"title_canon_sha256":"66759e9697aff0d4bfd9c7f6422c4d937da638edb91d491e48717633181eeaa1","abstract_canon_sha256":"57da67f49feaba4b0b4f707018b0a1e780f6bfbdfd0d586a9329bbdc9a5b3cb3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:11:13.202204Z","signature_b64":"uSyLBlTvXSKgQFUffs+wYJ8BdeyHEG2SXBGEISxhJCuV3qKIRI9LbgzMzmdyCmvOarILHWNC/VTtXXeOwwLFCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"01429490cfdd3fba666b7136af03b4b6a0060810015a77c71bdddf66444a707a","last_reissued_at":"2026-05-18T01:11:13.201696Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:11:13.201696Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Interpolation for Restricted Tangent Bundles of General Curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Eric Larson","submitted_at":"2015-11-13T23:33:44Z","abstract_excerpt":"Let (C, p_1, p_2, \\ldots, p_n) be a general marked curve of genus g, and q_1, q_2, ..., q_n \\in P^r be a general collection of points. We determine when there exists a nondegenerate degree d map f : C \\to P^r so that f(p_i) = q_i for all i. This is a consequence of our main theorem, which states that the restricted tangent bundle f^* T_{P^r} of a general curve of genus g, equipped with a general degree d map f to P^r, satisfies the property of interpolation (i.e.\\ that for a general effective divisor D of any degree on C, either H^0(f^* T_{P^r}(-D)) = 0 or H^1(f^* T_{P^r}(-D)) = 0). We also pr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.04480","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":"1511.04480","created_at":"2026-05-18T01:11:13.201767+00:00"},{"alias_kind":"arxiv_version","alias_value":"1511.04480v2","created_at":"2026-05-18T01:11:13.201767+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.04480","created_at":"2026-05-18T01:11:13.201767+00:00"},{"alias_kind":"pith_short_12","alias_value":"AFBJJEGP3U73","created_at":"2026-05-18T12:29:10.953037+00:00"},{"alias_kind":"pith_short_16","alias_value":"AFBJJEGP3U73UZTL","created_at":"2026-05-18T12:29:10.953037+00:00"},{"alias_kind":"pith_short_8","alias_value":"AFBJJEGP","created_at":"2026-05-18T12:29:10.953037+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/AFBJJEGP3U73UZTLOE3K6A5UW2","json":"https://pith.science/pith/AFBJJEGP3U73UZTLOE3K6A5UW2.json","graph_json":"https://pith.science/api/pith-number/AFBJJEGP3U73UZTLOE3K6A5UW2/graph.json","events_json":"https://pith.science/api/pith-number/AFBJJEGP3U73UZTLOE3K6A5UW2/events.json","paper":"https://pith.science/paper/AFBJJEGP"},"agent_actions":{"view_html":"https://pith.science/pith/AFBJJEGP3U73UZTLOE3K6A5UW2","download_json":"https://pith.science/pith/AFBJJEGP3U73UZTLOE3K6A5UW2.json","view_paper":"https://pith.science/paper/AFBJJEGP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1511.04480&json=true","fetch_graph":"https://pith.science/api/pith-number/AFBJJEGP3U73UZTLOE3K6A5UW2/graph.json","fetch_events":"https://pith.science/api/pith-number/AFBJJEGP3U73UZTLOE3K6A5UW2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/AFBJJEGP3U73UZTLOE3K6A5UW2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/AFBJJEGP3U73UZTLOE3K6A5UW2/action/storage_attestation","attest_author":"https://pith.science/pith/AFBJJEGP3U73UZTLOE3K6A5UW2/action/author_attestation","sign_citation":"https://pith.science/pith/AFBJJEGP3U73UZTLOE3K6A5UW2/action/citation_signature","submit_replication":"https://pith.science/pith/AFBJJEGP3U73UZTLOE3K6A5UW2/action/replication_record"}},"created_at":"2026-05-18T01:11:13.201767+00:00","updated_at":"2026-05-18T01:11:13.201767+00:00"}