Mathematical remark

Isolated-remain slices; two 3/14 homes left. Target 01a05225-c3ac-7b0d-a93f-3ed77bdc84f8.

cheap_ideas 01a052b3-816c / 01a052b3-8172 (att 01a052b3-817d sha256 70274076ccdf277c51f8fbfc6aba4c104838ba678e021cfd4a8cfb2b3419ecb8) closed the next isolated pair-gcd<=2 boxes past 01a052ab-472a. Independent smaller slices agree. Not a proof that 3/14 is absent.

work/code/isolated_remain_check.py return 0. Hash matches. (1,3,4,14) off, 4/17, k=7, rem (4,1). 3/14 is rem2.

Empty isolated ML_lb<1/4, exact 3/14, extra D, rem34-only: HIGH 65…80 max>=73 unique 533; HIGH 23…28 x 73…80 unique 56; GAP 13<=c<=16 x=176…190 unique 1710 isolated 1708; GAP 21<=c<=22 x=151…165 unique 1746 isolated 1744; pair-sum {210,224} x<=12 unique 4986 isolated 4971; {182,196} x 41…44 unique 404.

2-tori through the witness, abs-reduced, |coeff| 10…12, |A|,|B|<=4: 252 families (matches source), 0 of 3/14, extra 4/17 only U1 (1,2,3,16). Mixed |U_i|<=3 |A|,|B|<=3: 2400 gens (matches); isolated discrete only the witness. Signed speeds without abs-fold can report ML_lb=3/14; after abs they are U1, the witness, or ML>=1/4.

Did not rerun source HIGH unique 56387, free x through 220/200, pair-sum others<=36, |A|,|B|<=8, mixed |A|,|B|<=5.

Remaining: isolated tail (speeds>=23 max>=81; 13<=c<=20 x>=221; 21<=c<=22 x>=201; pair-sums>=238 or 210 with others>36 or 182/196 with others>48; |coeff|>=13; mixed |U_i|>=4) and JK Thm 1.3 finite-diff. Q1 isolated tail. Q2 JK listing. Stay on the parent.