{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:RQM2XLU7XK6MBUICJTFVVYI3BE","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":"e471144d1778b6aa796de9185a83b12ba0298072440dc50448ecf67dfac2608c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-08-10T05:31:03Z","title_canon_sha256":"acfa6e4fc9fc94378c8946aae77346b8e5549358ca270937a329e39f64e6566e"},"schema_version":"1.0","source":{"id":"1708.03078","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.03078","created_at":"2026-05-18T00:20:56Z"},{"alias_kind":"arxiv_version","alias_value":"1708.03078v2","created_at":"2026-05-18T00:20:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.03078","created_at":"2026-05-18T00:20:56Z"},{"alias_kind":"pith_short_12","alias_value":"RQM2XLU7XK6M","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_16","alias_value":"RQM2XLU7XK6MBUIC","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_8","alias_value":"RQM2XLU7","created_at":"2026-05-18T12:31:39Z"}],"graph_snapshots":[{"event_id":"sha256:6be020fc3bb13d32250c8a1f81ee39bd02677511802533672e047f8625c2e29a","target":"graph","created_at":"2026-05-18T00:20:56Z","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 article we study forbidden loci and typical ranks of forms with respect to the embeddings of $\\mathbb P^1\\times \\mathbb P^1$ given by the line bundles $(2,2d)$. We introduce the Ranestad-Schreyer locus corresponding to supports of non-reduced apolar schemes. We show that, in those cases, this is contained in the forbidden locus. Furthermore, for these embeddings, we give a component of the real rank boundary, the hypersurface dividing the minimal typical rank from higher ones. These results generalize to a class of embeddings of $\\mathbb P^n\\times \\mathbb P^1$. Finally, in connection w","authors_text":"Emanuele Ventura","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-08-10T05:31:03Z","title":"Real rank boundaries and loci of forms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.03078","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:a8c0530397893a09a29757eb720d2e470c14f6b79192aafd8399eec6cbbbed24","target":"record","created_at":"2026-05-18T00:20:56Z","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":"e471144d1778b6aa796de9185a83b12ba0298072440dc50448ecf67dfac2608c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-08-10T05:31:03Z","title_canon_sha256":"acfa6e4fc9fc94378c8946aae77346b8e5549358ca270937a329e39f64e6566e"},"schema_version":"1.0","source":{"id":"1708.03078","kind":"arxiv","version":2}},"canonical_sha256":"8c19abae9fbabcc0d1024ccb5ae11b0927e1a9b53f9b44de5f20c151b20e48d3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8c19abae9fbabcc0d1024ccb5ae11b0927e1a9b53f9b44de5f20c151b20e48d3","first_computed_at":"2026-05-18T00:20:56.316817Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:20:56.316817Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zElkdFHdJjg+2lcnZkXXyds4gKWflJgbmB0/SSr2hP17I350BvC1ESS28HT+wu+49N6ah/R1pfdhqu+FVsmcAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:20:56.317258Z","signed_message":"canonical_sha256_bytes"},"source_id":"1708.03078","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a8c0530397893a09a29757eb720d2e470c14f6b79192aafd8399eec6cbbbed24","sha256:6be020fc3bb13d32250c8a1f81ee39bd02677511802533672e047f8625c2e29a"],"state_sha256":"45743a368be44f5d53b6e00f7f98bb541d587a7c4653cc760c6a2687a6ac72cf"}