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In this paper, we address the first open case. We classify all smooth monomial Togliatti systems $I\\subset k[x_{0},\\dotsc,x_{n}]$ of forms of degree $d\\ge 4$ with $\\mu(I)=2n+3$ and $n\\ge 2$ and all monomial Togliatti systems $I\\subset k[x_0,x_1,x_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":"1710.03579","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-10-07T17:18:22Z","cross_cats_sorted":["math.AC"],"title_canon_sha256":"73fe11e7682c0720d046727473b0da30d6c94e3a651209de93c02a685394cee7","abstract_canon_sha256":"71deaa405ebedb4a695fdbe9c90c1c7e987dff76150c0c71ccf97bc8b73c30c7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:33:11.349619Z","signature_b64":"R/Bn81sMVAyFV6UbbG1huLVEPy2jKPQhI5zUOA+6Vs63NXhispao46GuUYbSYO0+sV/yDG4LmrrJD2XF/jKIDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2f5f695507c1470a08c1817e6bec3463b97a94e6a10b5ac8047513e10041eb75","last_reissued_at":"2026-05-18T00:33:11.348735Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:33:11.348735Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the classification of Togliatti systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.AG","authors_text":"Mart\\'i Salat, Rosa Maria Mir\\'o-Roig","submitted_at":"2017-10-07T17:18:22Z","abstract_excerpt":"In [MeMR], Mezzetti and Mir\\'{o}-Roig proved that the minimal number of generators $\\mu (I)$ of a minimal (smooth) monomial Togliatti system $I\\subset k[x_{0},\\dotsc,x_{n}]$ satisfies $2n+1\\le \\mu(I)\\le \\binom{n+d-1}{n-1}$ and they classify all smooth minimal monomial Togliatti systems $I\\subset k[x_{0},\\dotsc,x_{n}]$ with $2n+1\\le \\mu(I)\\le 2n+2$. In this paper, we address the first open case. We classify all smooth monomial Togliatti systems $I\\subset k[x_{0},\\dotsc,x_{n}]$ of forms of degree $d\\ge 4$ with $\\mu(I)=2n+3$ and $n\\ge 2$ and all monomial Togliatti systems $I\\subset k[x_0,x_1,x_2]"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.03579","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":"1710.03579","created_at":"2026-05-18T00:33:11.348881+00:00"},{"alias_kind":"arxiv_version","alias_value":"1710.03579v1","created_at":"2026-05-18T00:33:11.348881+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.03579","created_at":"2026-05-18T00:33:11.348881+00:00"},{"alias_kind":"pith_short_12","alias_value":"F5PWSVIHYFDQ","created_at":"2026-05-18T12:31:15.632608+00:00"},{"alias_kind":"pith_short_16","alias_value":"F5PWSVIHYFDQUCGB","created_at":"2026-05-18T12:31:15.632608+00:00"},{"alias_kind":"pith_short_8","alias_value":"F5PWSVIH","created_at":"2026-05-18T12:31:15.632608+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/F5PWSVIHYFDQUCGBQF7GX3BUMO","json":"https://pith.science/pith/F5PWSVIHYFDQUCGBQF7GX3BUMO.json","graph_json":"https://pith.science/api/pith-number/F5PWSVIHYFDQUCGBQF7GX3BUMO/graph.json","events_json":"https://pith.science/api/pith-number/F5PWSVIHYFDQUCGBQF7GX3BUMO/events.json","paper":"https://pith.science/paper/F5PWSVIH"},"agent_actions":{"view_html":"https://pith.science/pith/F5PWSVIHYFDQUCGBQF7GX3BUMO","download_json":"https://pith.science/pith/F5PWSVIHYFDQUCGBQF7GX3BUMO.json","view_paper":"https://pith.science/paper/F5PWSVIH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1710.03579&json=true","fetch_graph":"https://pith.science/api/pith-number/F5PWSVIHYFDQUCGBQF7GX3BUMO/graph.json","fetch_events":"https://pith.science/api/pith-number/F5PWSVIHYFDQUCGBQF7GX3BUMO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/F5PWSVIHYFDQUCGBQF7GX3BUMO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/F5PWSVIHYFDQUCGBQF7GX3BUMO/action/storage_attestation","attest_author":"https://pith.science/pith/F5PWSVIHYFDQUCGBQF7GX3BUMO/action/author_attestation","sign_citation":"https://pith.science/pith/F5PWSVIHYFDQUCGBQF7GX3BUMO/action/citation_signature","submit_replication":"https://pith.science/pith/F5PWSVIHYFDQUCGBQF7GX3BUMO/action/replication_record"}},"created_at":"2026-05-18T00:33:11.348881+00:00","updated_at":"2026-05-18T00:33:11.348881+00:00"}