A withdrawn duplicate of the D4 and E6 cubic counting problems

Definitions and mathematical statement

The complete current mathematical-source entry is: "Question 30. This problem has been withdrawn." No active mathematical question, assumptions, or target statement is supplied. The trailing extracted "Problem/" is layout context. This withdrawal record is preserved under its permanent identity rather than replaced by a conjecture inferred from the attached research aid.

For historical context only, the report says an official pre-withdrawal archive named two cubic surfaces. It identifies the first exactly with Question 5's $D_4$ surface and the second with Question 5(vii)'s $E_6$ surface after $z\mapsto-z$. It additionally gives the projective transformation \[ [x:y:z:t]\longmapsto[y:x:t:-z] \] as a $GL_4({\mathbb{Z}})$ isomorphism from the latter surface to a published standard $E_6$ model. As a signed permutation of primitive integral coordinates, this preserves maximum height $H([x:y:z:t])=\max(|x|,|y|,|z|,|t|)$. The actual surface equations and archive identifier are not included, so the equation equivalence cannot be checked from this record.

Under the report's maximum-height, line-deleted interpretation of the historical point-count questions, it says Le Boudec's 2014 theorem and the 2007 theorem of de la Bretèche--Browning--Derenthal settle the respective problems. No theorem statements or full references are supplied. Exact redundancy is offered as a plausible explanation for withdrawal, but the report explicitly says the editorial motive is undocumented. None of this historical context reactivates the withdrawn question.

Short English statement

This is a withdrawn-question record, not an active mathematical problem. The attached report offers historical duplicate identifications and a height-preserving coordinate map, without the original equations or a documented withdrawal motive.

Sources

• AIM workshop "Rational and integral points on higher dimensional varieties," Question 30: https://aimath.org/WWN/qptsurface2/qptsurface2.pdf. The supplied current text says the problem has been withdrawn; no PDF was accessed here.
• Local canonical registry aim-algebraic-number-theory-notes.json, notes[114], tag question; permanent UnsolvedMath ID $20000463$, source code catalogue entry. Original remarks and literature field are empty.
• Supplied research attempt 1 refers to an unidentified official pre-withdrawal archive, Le Boudec's 2014 result, and de la Bretèche--Browning--Derenthal's 2007 result, without full authoritative citations or surface equations. It is a machine-generated, non-peer-reviewed research aid requiring independent verification before citation.