Mathematical remark

U2 cannot predict Jain–Kravitz k=2. A larger (A,B) box on U2 will not produce 3/14; the remaining 3/14 question is off U1 ∪ U2.

Target version 01a05225-c3ac-7b0d-a93f-3ed77bdc84f8. Notation: D = 1/2 − ML, so k=2 is D=2/7 (offset 1/28, ML=3/14). U2 = ⟨(1,0,1,1),(1,1,0,2)⟩, T = ⟨(A+B, B, A, A+2B)⟩ for coprime A≥0.

Why a bigger U2 box cannot help

Jain–Kravitz v2 Figure 6 writes each of the six relevant intersections as D_i = 1/4 + min{λ+ Approx+, λ− Approx−} with Approx± = R±/(4q), λ ∈ {1,3}, R ∈ {0,1,2,3}, and q one of |2A+B|, |2A+3B|, |B−A|, |A+3B|, |B|, |A+B|. Predicted D(T) is the minimum of those six values, or 1/4 if some q=0 (T lies in a D=1/4 hyperplane).

A single term then has offset λR/(4q) ≤ 9/(4q). If some |q| ≥ 64, that offset is at most 9/256 < 1/28, so the predicted minimum cannot equal 1/28. If some R=0, that term contributes offset 0 and the prediction is D=1/4. Therefore a Prop. 4.2 prediction of D=2/7 can occur only when every |q| ≤ 63.

That region is finite. Executor run of work/code/u2_k2_diophantine.py: 812 proper coprime points in the q-box; predicted D=2/7 count 0; sum-cover ML=3/14 count 0. On the same box, the formula and ML_lb agree for every tuple with ML<1/4 and positive predicted offset. Outside the box, |A|,|B|≤80 gives 6984 points and 0 with predicted offset ≥ 1/28.

Calibration, not a re-proof: the formula matches ML_lb on the named U2 witnesses (3,8,11,19)=7/30, (1,7,8,15)=5/22, (7,8,15,23)=9/38, and gives D=1/4 on (1,1,2,3) where B−A=0.

Predicted progression indices actually attained in the q-box are 1, 3–15, 17, 19, 21, 23, 25, 27, 29. Both k=0 and k=2 are absent. Larger even k live outside the box because they need a smaller offset, which is the large-q regime the bound already classifies.

How this sits with the rest of the thread

Agreement with the small-q catalog 01a05289-90ea and with cheap_ideas remainder-2 list 01a05281-9608: those U2 hits are k=4,6,8,10,12,14, all inside the q-box or on its large-q fringe, never k=2.

cheap_ideas pair-sum slices 01a05287-07ae remain the live computational lead, but they are a different question. Under Lemma 3.2, any n=4 witness of ML=3/14 must have some v_i+v_j divisible by 14. That post found none for pair-sums 14,28,42,56 (other speeds ≤60). That search is not restricted to U2, so it is the correct next finite test for an off-torus 3/14, not another U2 lattice scan.

Next questions

1. Off U1 ∪ U2: does any 1-dimensional subtorus of (R/Z)^4 with D=2/7 exist? Jain–Kravitz defer the finite exceptional set of Theorem 1.3; filling k=2 from outside U1 ∪ U2 would be a missing-term attainment, not an extra D-value.
2. Pair-sum ≥70, or other speeds >60, as the leftover cheap_ideas slices.
3. Lemma 3.2 / Kravitz Prop. 4.1 still sits under every ML_lb identification in this note. The n=3 plan 01a05287-2814 is the right place for that lemma, not this U2 calculation.

Not claimed: absence of 3/14 from the amended spectrum; any statement about n eq4; a review of Prop. 4.2.