{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:SOJVCCZRK2AMSOI77SFZJQ44JA","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"0e2f800b2c519d01140c6080303a25d5be3c46abdb30f425a0b56993ac45bbba","cross_cats_sorted":["math.AC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-06-19T08:45:22Z","title_canon_sha256":"865b92de87e2d5204d40130d2c942f702d02b533efbfaa01d8fe0da110bc816a"},"schema_version":"1.0","source":{"id":"1506.05914","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.05914","created_at":"2026-05-18T01:22:01Z"},{"alias_kind":"arxiv_version","alias_value":"1506.05914v2","created_at":"2026-05-18T01:22:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.05914","created_at":"2026-05-18T01:22:01Z"},{"alias_kind":"pith_short_12","alias_value":"SOJVCCZRK2AM","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_16","alias_value":"SOJVCCZRK2AMSOI7","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_8","alias_value":"SOJVCCZR","created_at":"2026-05-18T12:29:42Z"}],"graph_snapshots":[{"event_id":"sha256:6cd947c2b980717dedeb589af9afa94f433b2aa4911d458b1253d4a2d3cc9c41","target":"graph","created_at":"2026-05-18T01:22:01Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"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","authors_text":"Emilia Mezzetti, Rosa M. Mir\\'o-Roig","cross_cats":["math.AC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-06-19T08:45:22Z","title":"The minimal number of generators of a Togliatti system"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.05914","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:fddf3e92cd09f34242906f4c5a7f23eb08008078e7062824587b2d93d2480eee","target":"record","created_at":"2026-05-18T01:22:01Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"0e2f800b2c519d01140c6080303a25d5be3c46abdb30f425a0b56993ac45bbba","cross_cats_sorted":["math.AC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-06-19T08:45:22Z","title_canon_sha256":"865b92de87e2d5204d40130d2c942f702d02b533efbfaa01d8fe0da110bc816a"},"schema_version":"1.0","source":{"id":"1506.05914","kind":"arxiv","version":2}},"canonical_sha256":"9393510b315680c9391ffc8b94c39c480009f3938320d0c7e929b48a17a3ebec","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9393510b315680c9391ffc8b94c39c480009f3938320d0c7e929b48a17a3ebec","first_computed_at":"2026-05-18T01:22:01.391763Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:22:01.391763Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vmTZCbr2h+gmqYd9F6Ui44EQzzQhgtsNPB4coOmoqNbPNUB3wu07rPpkpKDuRbFqQ0Gya72fIpBmpPILNJ9kDw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:22:01.392258Z","signed_message":"canonical_sha256_bytes"},"source_id":"1506.05914","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fddf3e92cd09f34242906f4c5a7f23eb08008078e7062824587b2d93d2480eee","sha256:6cd947c2b980717dedeb589af9afa94f433b2aa4911d458b1253d4a2d3cc9c41"],"state_sha256":"e6cdd62b8da40eff06bcb401f2fea6cedcc2382cdf852576a1592d82417fb196"}