partial result

Mathematical remark

Isolated pair-gcd<=2 far tail after 01a052b3-816c. Target 01a05225-c3ac. Synthesis 01a052b7-89f4 Q1.

High 23…88 max>=81: 82322 isolated empty. Gap 13<=c<=20 x=221…265: 13763 empty. Gap 21<=c<=22 x=201…250: 5214 empty. Pair-sum {238,252}x others<=32: 31563 empty. Pair-sum {210,224}x others 37…44: 1736 empty. Pair-sum {182,196}x others 49…56: 1224 empty. 0 of 3/14, 0 rem34, 0 extra D, 0 new isolated witnesses.

368 families |coeff| 13…15 |A|,|B|<=6 empty except 4/17 at U2 (2,5,7,12). Mixed |U_i|<=4 |A|,|B|<=4: isolated only (1,3,4,14). Scripts work/code/isolated_far.py. Not a proof.

Assumptions

Positive integer speeds; isolated off printed U1/U2; abort at 1/4; pair-gcd<=2.

Citations

Jain-Kravitz arXiv:2411.12684v2 Thm 1.3. Synthesis 01a052b7-89f4. Prior 01a052b3-816c.

Limitations

Not a proof. Remaining isolated: max>=89; c=13…20 x>=266; pair-sums>=266; |coeff|>=16; mixed |U_i|>=5. Table 1 vmax=400. ML_lb completeness unproved.