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In this paper, we discuss a case of the EGH conjecture for homogeneous ideals generated by $n+2$ quadrics containing a regular sequence $f_1,\\, \\ldots, \\, f_n$ and give a complete proof for EGH when $n=5$ and $a_1=\\cdots=a_5=2$."},"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":"1812.07539","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2018-12-18T18:16:16Z","cross_cats_sorted":[],"title_canon_sha256":"6f7dc7e6369668604345a9a79db4ee8747c365cf7576904c5c707b7ab727e112","abstract_canon_sha256":"3ccaf7f44a5e9adb0fa695e9caa344f71a932818213c7df3d275e3f841335eec"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:58:00.218156Z","signature_b64":"EubsQZbkAFe++2gTuUqdEt0F12fl2fbeeHu9EvAH4FOqv4YlksaMHc6wW1gc9AOrh24NHiTU+UhLnW/KGdm0AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1fdcb5145594100c022b31926a22f66ee687ee75b23e3f5a9f769543e43fda45","last_reissued_at":"2026-05-17T23:58:00.217485Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:58:00.217485Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Eisenbud-Green-Harris Conjecture for Defect Two Quadratic Ideals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Melvin Hochster, Sema Gunturkun","submitted_at":"2018-12-18T18:16:16Z","abstract_excerpt":"The Eisenbud-Green-Harris (EGH) conjecture states that a homogeneous ideal in a polynomial ring $K[x_1,\\,\\ldots,\\,x_n]$ over a field $K$ that contains a regular sequence $f_1,\\,\\ldots,\\, f_n$ with degrees $a_i$, $i=1,\\,\\ldots,\\,n$ has the same Hilbert function as a lex-plus-powers ideal containing the powers $x_i^{a_i}$, $i=1,\\,\\ldots,\\,n$. 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