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In general $\\trop \\F_d(X)\\subseteq \\F_d(\\trop X)$ but we construct linear spaces $L$ such that $\\trop \\F_1(X)\\subsetneq \\F_1(\\trop X)$ and show that for a toric variety $\\trop \\F_d(X)=\\F_d(\\trop X)$."},"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":"1807.06283","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-07-17T08:54:58Z","cross_cats_sorted":[],"title_canon_sha256":"a9e12996852275d99e6c387bc666b6dd7bb530944219a35fab9913129db51eb8","abstract_canon_sha256":"f22b2a89107a9e5b34912dfeb3a3d687a0b210b9ba03f7f509414519f020ec53"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:49:27.626192Z","signature_b64":"dcJVPoz2AkrRZfdYygJS3am35OqVIIo3ikKrpyDqHDEC9JcWJiWpAKamwirkvMGB+Bku6K6JJOwIjsPsGFopAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"626f65fdba3ff9bd97bf8aafd5c77a48d381b5efa257b6928c4c2a57efecd126","last_reissued_at":"2026-05-17T23:49:27.625679Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:49:27.625679Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Tropical Fano Schemes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Sara Lamboglia","submitted_at":"2018-07-17T08:54:58Z","abstract_excerpt":"We define a tropical version $\\F_d(\\trop X)$ of the Fano Scheme $\\F_d(X)$ of a projective variety $X\\subseteq \\mathbb P^n$ and prove that $\\F_d(\\trop X)$ is the support of a polyhedral complex contained in $\\trop \\Grp(d,n)$. In general $\\trop \\F_d(X)\\subseteq \\F_d(\\trop X)$ but we construct linear spaces $L$ such that $\\trop \\F_1(X)\\subsetneq \\F_1(\\trop X)$ and show that for a toric variety $\\trop \\F_d(X)=\\F_d(\\trop X)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.06283","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":"1807.06283","created_at":"2026-05-17T23:49:27.625766+00:00"},{"alias_kind":"arxiv_version","alias_value":"1807.06283v2","created_at":"2026-05-17T23:49:27.625766+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.06283","created_at":"2026-05-17T23:49:27.625766+00:00"},{"alias_kind":"pith_short_12","alias_value":"MJXWL7N2H743","created_at":"2026-05-18T12:32:37.024351+00:00"},{"alias_kind":"pith_short_16","alias_value":"MJXWL7N2H7433F57","created_at":"2026-05-18T12:32:37.024351+00:00"},{"alias_kind":"pith_short_8","alias_value":"MJXWL7N2","created_at":"2026-05-18T12:32:37.024351+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2604.19713","citing_title":"The integral Chow ring of $\\mathscr{M}_{0}(\\mathbb{P}^r, 2)$","ref_index":17,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/MJXWL7N2H7433F57RKX5LR32JD","json":"https://pith.science/pith/MJXWL7N2H7433F57RKX5LR32JD.json","graph_json":"https://pith.science/api/pith-number/MJXWL7N2H7433F57RKX5LR32JD/graph.json","events_json":"https://pith.science/api/pith-number/MJXWL7N2H7433F57RKX5LR32JD/events.json","paper":"https://pith.science/paper/MJXWL7N2"},"agent_actions":{"view_html":"https://pith.science/pith/MJXWL7N2H7433F57RKX5LR32JD","download_json":"https://pith.science/pith/MJXWL7N2H7433F57RKX5LR32JD.json","view_paper":"https://pith.science/paper/MJXWL7N2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1807.06283&json=true","fetch_graph":"https://pith.science/api/pith-number/MJXWL7N2H7433F57RKX5LR32JD/graph.json","fetch_events":"https://pith.science/api/pith-number/MJXWL7N2H7433F57RKX5LR32JD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MJXWL7N2H7433F57RKX5LR32JD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MJXWL7N2H7433F57RKX5LR32JD/action/storage_attestation","attest_author":"https://pith.science/pith/MJXWL7N2H7433F57RKX5LR32JD/action/author_attestation","sign_citation":"https://pith.science/pith/MJXWL7N2H7433F57RKX5LR32JD/action/citation_signature","submit_replication":"https://pith.science/pith/MJXWL7N2H7433F57RKX5LR32JD/action/replication_record"}},"created_at":"2026-05-17T23:49:27.625766+00:00","updated_at":"2026-05-17T23:49:27.625766+00:00"}