{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:SOJVCCZRK2AMSOI77SFZJQ44JA","short_pith_number":"pith:SOJVCCZR","schema_version":"1.0","canonical_sha256":"9393510b315680c9391ffc8b94c39c480009f3938320d0c7e929b48a17a3ebec","source":{"kind":"arxiv","id":"1506.05914","version":2},"attestation_state":"computed","paper":{"title":"The minimal number of generators of a Togliatti system","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.AG","authors_text":"Emilia Mezzetti, Rosa M. Mir\\'o-Roig","submitted_at":"2015-06-19T08:45:22Z","abstract_excerpt":"We compute the minimal and the maximal bound on the number of generators of a minimal smooth monomial Togliatti system of forms of degree $d$ in $n+1$ variables, for any $d\\ge 2$ and $n\\geq 2$. We classify the Togliatti systems with number of generators reaching the lower bound or close to the lower bound. We then prove that if $n=2$ (resp $n=2,3$) all range between the lower and upper bound is covered, while if $n\\geq 3$ (resp. $n\\ge 4$) there are gaps if we only consider smooth minimal Togliatti systems (resp. if we avoid the smoothness hypothesis). We finally analyze for $n=2$ the Mumford-T"},"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":"1506.05914","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-06-19T08:45:22Z","cross_cats_sorted":["math.AC"],"title_canon_sha256":"865b92de87e2d5204d40130d2c942f702d02b533efbfaa01d8fe0da110bc816a","abstract_canon_sha256":"0e2f800b2c519d01140c6080303a25d5be3c46abdb30f425a0b56993ac45bbba"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:22:01.392258Z","signature_b64":"vmTZCbr2h+gmqYd9F6Ui44EQzzQhgtsNPB4coOmoqNbPNUB3wu07rPpkpKDuRbFqQ0Gya72fIpBmpPILNJ9kDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9393510b315680c9391ffc8b94c39c480009f3938320d0c7e929b48a17a3ebec","last_reissued_at":"2026-05-18T01:22:01.391763Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:22:01.391763Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The minimal number of generators of a Togliatti system","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.AG","authors_text":"Emilia Mezzetti, Rosa M. Mir\\'o-Roig","submitted_at":"2015-06-19T08:45:22Z","abstract_excerpt":"We compute the minimal and the maximal bound on the number of generators of a minimal smooth monomial Togliatti system of forms of degree $d$ in $n+1$ variables, for any $d\\ge 2$ and $n\\geq 2$. We classify the Togliatti systems with number of generators reaching the lower bound or close to the lower bound. We then prove that if $n=2$ (resp $n=2,3$) all range between the lower and upper bound is covered, while if $n\\geq 3$ (resp. $n\\ge 4$) there are gaps if we only consider smooth minimal Togliatti systems (resp. if we avoid the smoothness hypothesis). We finally analyze for $n=2$ the Mumford-T"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.05914","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":"1506.05914","created_at":"2026-05-18T01:22:01.391856+00:00"},{"alias_kind":"arxiv_version","alias_value":"1506.05914v2","created_at":"2026-05-18T01:22:01.391856+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.05914","created_at":"2026-05-18T01:22:01.391856+00:00"},{"alias_kind":"pith_short_12","alias_value":"SOJVCCZRK2AM","created_at":"2026-05-18T12:29:42.218222+00:00"},{"alias_kind":"pith_short_16","alias_value":"SOJVCCZRK2AMSOI7","created_at":"2026-05-18T12:29:42.218222+00:00"},{"alias_kind":"pith_short_8","alias_value":"SOJVCCZR","created_at":"2026-05-18T12:29:42.218222+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/SOJVCCZRK2AMSOI77SFZJQ44JA","json":"https://pith.science/pith/SOJVCCZRK2AMSOI77SFZJQ44JA.json","graph_json":"https://pith.science/api/pith-number/SOJVCCZRK2AMSOI77SFZJQ44JA/graph.json","events_json":"https://pith.science/api/pith-number/SOJVCCZRK2AMSOI77SFZJQ44JA/events.json","paper":"https://pith.science/paper/SOJVCCZR"},"agent_actions":{"view_html":"https://pith.science/pith/SOJVCCZRK2AMSOI77SFZJQ44JA","download_json":"https://pith.science/pith/SOJVCCZRK2AMSOI77SFZJQ44JA.json","view_paper":"https://pith.science/paper/SOJVCCZR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1506.05914&json=true","fetch_graph":"https://pith.science/api/pith-number/SOJVCCZRK2AMSOI77SFZJQ44JA/graph.json","fetch_events":"https://pith.science/api/pith-number/SOJVCCZRK2AMSOI77SFZJQ44JA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/SOJVCCZRK2AMSOI77SFZJQ44JA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/SOJVCCZRK2AMSOI77SFZJQ44JA/action/storage_attestation","attest_author":"https://pith.science/pith/SOJVCCZRK2AMSOI77SFZJQ44JA/action/author_attestation","sign_citation":"https://pith.science/pith/SOJVCCZRK2AMSOI77SFZJQ44JA/action/citation_signature","submit_replication":"https://pith.science/pith/SOJVCCZRK2AMSOI77SFZJQ44JA/action/replication_record"}},"created_at":"2026-05-18T01:22:01.391856+00:00","updated_at":"2026-05-18T01:22:01.391856+00:00"}