{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:PUTCCWEVEG57BPICBI5P7WJ7CT","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":"b6a7ba91df62af10eb107290642206e5849aa93bd9fe7dfe7957965ec7636ea6","cross_cats_sorted":["math.AC","math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-10-31T20:17:36Z","title_canon_sha256":"6227fedce2f09bb0fb8a545e8854099a90d14ee487fc269ee2e6e02146279c2f"},"schema_version":"1.0","source":{"id":"1711.00089","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.00089","created_at":"2026-05-18T00:16:44Z"},{"alias_kind":"arxiv_version","alias_value":"1711.00089v2","created_at":"2026-05-18T00:16:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.00089","created_at":"2026-05-18T00:16:44Z"},{"alias_kind":"pith_short_12","alias_value":"PUTCCWEVEG57","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_16","alias_value":"PUTCCWEVEG57BPIC","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_8","alias_value":"PUTCCWEV","created_at":"2026-05-18T12:31:37Z"}],"graph_snapshots":[{"event_id":"sha256:d72d3ec279e45bf8a070eccc7a5fb70bcd45c9d66e5af9220bca360c86664139","target":"graph","created_at":"2026-05-18T00:16:44Z","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":"In this paper we study the complex simultaneous Waring rank for collections of monomials. For general collections we provide a lower bound, whereas for special collections we provide a formula for the simultaneous Waring rank. Our approach is algebraic and combinatorial. We give an application to ranks of binomials and maximal simultaneous ranks. Moreover, we include an appendix of scripts written in the algebra software Macaulay2 to experiment with simultaneous ranks.","authors_text":"Emanuele Ventura, Enrico Carlini","cross_cats":["math.AC","math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-10-31T20:17:36Z","title":"A note on the simultaneous Waring rank of monomials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.00089","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":"sha256:1fd4894d627bc1c4410eae566d85ca8db7b00ce830d26495956fc282b2ab47de","target":"record","created_at":"2026-05-18T00:16:44Z","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":"b6a7ba91df62af10eb107290642206e5849aa93bd9fe7dfe7957965ec7636ea6","cross_cats_sorted":["math.AC","math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-10-31T20:17:36Z","title_canon_sha256":"6227fedce2f09bb0fb8a545e8854099a90d14ee487fc269ee2e6e02146279c2f"},"schema_version":"1.0","source":{"id":"1711.00089","kind":"arxiv","version":2}},"canonical_sha256":"7d2621589521bbf0bd020a3affd93f14e8ad6bac7022b871a0fab2c3744d6daf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7d2621589521bbf0bd020a3affd93f14e8ad6bac7022b871a0fab2c3744d6daf","first_computed_at":"2026-05-18T00:16:44.726745Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:16:44.726745Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wnKHrSz7bMuAwhek74vxfBvTY+ZxUlP10hsKDBId+v7xrPrStEysp03LImB5owbXsVAtwp/e7qPvG5axm16vCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:16:44.727374Z","signed_message":"canonical_sha256_bytes"},"source_id":"1711.00089","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1fd4894d627bc1c4410eae566d85ca8db7b00ce830d26495956fc282b2ab47de","sha256:d72d3ec279e45bf8a070eccc7a5fb70bcd45c9d66e5af9220bca360c86664139"],"state_sha256":"22446b2a8512bbf03a29edb6ff1aa9a0e084ea005af90a82555933a4b2e9339c"}