{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:FEGEFQZKYSEX42GHZMEJEY5ZGK","short_pith_number":"pith:FEGEFQZK","schema_version":"1.0","canonical_sha256":"290c42c32ac4897e68c7cb089263b9329a3fcd938d4e484d62ee491a1f34ae3c","source":{"kind":"arxiv","id":"1101.5090","version":2},"attestation_state":"computed","paper":{"title":"Symmetric tensor rank with a tangent vector: a generic uniqueness theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Alessandra Bernardi, Edoardo Ballico","submitted_at":"2011-01-26T15:48:28Z","abstract_excerpt":"Let $X_{m,d}\\subset \\mathbb {P}^N$, $N:= \\binom{m+d}{m}-1$, be the order $d$ Veronese embedding of $\\mathbb {P}^m$. Let $\\tau (X_{m,d})\\subset \\mathbb {P}^N$, be the tangent developable of $X_{m,d}$. For each integer $t \\ge 2$ let $\\tau (X_{m,d},t)\\subseteq \\mathbb {P}^N$, be the joint of $\\tau (X_{m,d})$ and $t-2$ copies of $X_{m,d}$. Here we prove that if $m\\ge 2$, $d\\ge 7$ and $t \\le 1 + \\lfloor \\binom{m+d-2}{m}/(m+1)\\rfloor$, then for a general $P\\in \\tau (X_{m,d},t)$ there are uniquely determined $P_1,...,P_{t-2}\\in X_{m,d}$ and a unique tangent vector $\\nu$ of $X_{m,d}$ such that $P$ is "},"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":"1101.5090","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-01-26T15:48:28Z","cross_cats_sorted":[],"title_canon_sha256":"769f22339b198751b4e22453b026758907e0b6726e9d28297a0963ed7b3e3631","abstract_canon_sha256":"c5741d2afc310a9eca4c501aeca531f7678e60e2694298deffdbb55c30881fe7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:41:20.461661Z","signature_b64":"h2XyEzu26bB2G9wtT08L1o1+K9wH2w964p7h/B+a3EQTsNmCpaoZHyX+YxtuzfyvGLe+hDegrMWxdTymmcmHDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"290c42c32ac4897e68c7cb089263b9329a3fcd938d4e484d62ee491a1f34ae3c","last_reissued_at":"2026-05-18T03:41:20.461216Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:41:20.461216Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Symmetric tensor rank with a tangent vector: a generic uniqueness theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Alessandra Bernardi, Edoardo Ballico","submitted_at":"2011-01-26T15:48:28Z","abstract_excerpt":"Let $X_{m,d}\\subset \\mathbb {P}^N$, $N:= \\binom{m+d}{m}-1$, be the order $d$ Veronese embedding of $\\mathbb {P}^m$. Let $\\tau (X_{m,d})\\subset \\mathbb {P}^N$, be the tangent developable of $X_{m,d}$. For each integer $t \\ge 2$ let $\\tau (X_{m,d},t)\\subseteq \\mathbb {P}^N$, be the joint of $\\tau (X_{m,d})$ and $t-2$ copies of $X_{m,d}$. Here we prove that if $m\\ge 2$, $d\\ge 7$ and $t \\le 1 + \\lfloor \\binom{m+d-2}{m}/(m+1)\\rfloor$, then for a general $P\\in \\tau (X_{m,d},t)$ there are uniquely determined $P_1,...,P_{t-2}\\in X_{m,d}$ and a unique tangent vector $\\nu$ of $X_{m,d}$ such that $P$ is "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.5090","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":"1101.5090","created_at":"2026-05-18T03:41:20.461297+00:00"},{"alias_kind":"arxiv_version","alias_value":"1101.5090v2","created_at":"2026-05-18T03:41:20.461297+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.5090","created_at":"2026-05-18T03:41:20.461297+00:00"},{"alias_kind":"pith_short_12","alias_value":"FEGEFQZKYSEX","created_at":"2026-05-18T12:26:28.662955+00:00"},{"alias_kind":"pith_short_16","alias_value":"FEGEFQZKYSEX42GH","created_at":"2026-05-18T12:26:28.662955+00:00"},{"alias_kind":"pith_short_8","alias_value":"FEGEFQZK","created_at":"2026-05-18T12:26:28.662955+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/FEGEFQZKYSEX42GHZMEJEY5ZGK","json":"https://pith.science/pith/FEGEFQZKYSEX42GHZMEJEY5ZGK.json","graph_json":"https://pith.science/api/pith-number/FEGEFQZKYSEX42GHZMEJEY5ZGK/graph.json","events_json":"https://pith.science/api/pith-number/FEGEFQZKYSEX42GHZMEJEY5ZGK/events.json","paper":"https://pith.science/paper/FEGEFQZK"},"agent_actions":{"view_html":"https://pith.science/pith/FEGEFQZKYSEX42GHZMEJEY5ZGK","download_json":"https://pith.science/pith/FEGEFQZKYSEX42GHZMEJEY5ZGK.json","view_paper":"https://pith.science/paper/FEGEFQZK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1101.5090&json=true","fetch_graph":"https://pith.science/api/pith-number/FEGEFQZKYSEX42GHZMEJEY5ZGK/graph.json","fetch_events":"https://pith.science/api/pith-number/FEGEFQZKYSEX42GHZMEJEY5ZGK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FEGEFQZKYSEX42GHZMEJEY5ZGK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FEGEFQZKYSEX42GHZMEJEY5ZGK/action/storage_attestation","attest_author":"https://pith.science/pith/FEGEFQZKYSEX42GHZMEJEY5ZGK/action/author_attestation","sign_citation":"https://pith.science/pith/FEGEFQZKYSEX42GHZMEJEY5ZGK/action/citation_signature","submit_replication":"https://pith.science/pith/FEGEFQZKYSEX42GHZMEJEY5ZGK/action/replication_record"}},"created_at":"2026-05-18T03:41:20.461297+00:00","updated_at":"2026-05-18T03:41:20.461297+00:00"}