{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:CECMTQSXMVIIXKU3RCQBWWDDOD","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":"c12032404db51b17b3abe92b98b39ec932e3ce0c898255ff787a61e83912b4ca","cross_cats_sorted":["math.AC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2009-12-24T11:15:56Z","title_canon_sha256":"49508f7c24896fc3fa17efb6305d9b6ec81c10c279b7eb606e7b13a142435458"},"schema_version":"1.0","source":{"id":"0912.4834","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0912.4834","created_at":"2026-05-18T04:07:54Z"},{"alias_kind":"arxiv_version","alias_value":"0912.4834v2","created_at":"2026-05-18T04:07:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0912.4834","created_at":"2026-05-18T04:07:54Z"},{"alias_kind":"pith_short_12","alias_value":"CECMTQSXMVII","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_16","alias_value":"CECMTQSXMVIIXKU3","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_8","alias_value":"CECMTQSX","created_at":"2026-05-18T12:25:59Z"}],"graph_snapshots":[{"event_id":"sha256:5b8bc65d59b6e1ae4cc6ed12ccfb95b707f984fb271aa8b7daa09c4baccd0608","target":"graph","created_at":"2026-05-18T04:07:54Z","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 improve the known bound for the $X$-rank $R_{X}(P)$ of an element $P\\in {\\mathbb{P}}^N$ in the case in which $X\\subset {\\mathbb P}^n$ is a projective variety obtained as a linear projection from a general $v$-dimensional subspace $V\\subset {\\mathbb P}^{n+v}$. Then, if $X\\subset {\\mathbb P}^n$ is a curve obtained from a projection of a rational normal curve $C\\subset {\\mathbb P}^{n+1}$ from a point $O\\subset {\\mathbb P}^{n+1}$, we are able to describe the precise value of the $X$-rank for those points $P\\in {\\mathbb P}^n$ such that $R_{X}(P)\\leq R_{C}(O)-1$ and to improve the g","authors_text":"Alessandra Bernardi, Edoardo Ballico","cross_cats":["math.AC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2009-12-24T11:15:56Z","title":"On the X-rank with respect to linear projections of projective varieties"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0912.4834","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":"sha256:1f566ead8eb285533a17beec6003e6e66873fbfe959384fc85634b48c852abc0","target":"record","created_at":"2026-05-18T04:07:54Z","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":"c12032404db51b17b3abe92b98b39ec932e3ce0c898255ff787a61e83912b4ca","cross_cats_sorted":["math.AC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2009-12-24T11:15:56Z","title_canon_sha256":"49508f7c24896fc3fa17efb6305d9b6ec81c10c279b7eb606e7b13a142435458"},"schema_version":"1.0","source":{"id":"0912.4834","kind":"arxiv","version":2}},"canonical_sha256":"1104c9c25765508baa9b88a01b586370fec55c77b68677f06367a0075cd1ba09","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1104c9c25765508baa9b88a01b586370fec55c77b68677f06367a0075cd1ba09","first_computed_at":"2026-05-18T04:07:54.366006Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:07:54.366006Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tes5apPfVi3uAagmKpuCZQGomkX2uERoaeyMqpymhiVft8CkSWIoynkerMLbXz8kRgCIvSMsjJGGgJT3OH0ZBw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:07:54.366467Z","signed_message":"canonical_sha256_bytes"},"source_id":"0912.4834","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1f566ead8eb285533a17beec6003e6e66873fbfe959384fc85634b48c852abc0","sha256:5b8bc65d59b6e1ae4cc6ed12ccfb95b707f984fb271aa8b7daa09c4baccd0608"],"state_sha256":"dc4ae2d3e3b8197ce6954e7d287d15e2087be03a4751625dabae737bc41a16ff"}