Why the translation limit fired late on the fun9.5 flank (diagnostics only). The limit itself reads correctly: at x = 10.89 the pair has lx 1.09, lf 1.5e-3 -> m = inf, and the regime is entered at the next flag (10.39), after which the flank is halved (5.19, 2.60, 1.30). It fires late because the flank configurations do NOT recur from 20.25 to 10.89: (1) the near-zero step 20.2502 -> 20.2501 (overconfident S ~ 1 from a slope dominated by f(81) = 1.5e35) makes the next triples degenerate (xi ~ 0, then -1.7e7) and pollutes the memory; (2) our three-point step on exp is not a translation - it alternates long/short (xi -1.43, -0.46, -4.10, -0.03, -13.9) and first repeats at lag 5 (state 10 ~ state 5). 9 evaluations from 20.25 to 10.39 where one halving would do: ~8 of the +10 gap on fun9.5.

Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
2026-09-21 18:49:19 +01:00
parent baa93963cf
commit cc82156cde
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+"""Why the translation limit did not fire on the exp(x) flank of fun9.5 ([2e-4, 81]).
+
+Every state the gate sees (trace hook) under a prestep, in order, with what the analogy
+reads there:
+  flag   r = f/f_prev >= 1/4 (sign kept) - the entry also needs the last step to be the model's
+  xi, phi   the configuration
+  ratio  d_past / d_line  (< 1: analogous to the nearest past configuration)
+  lx, lf the pair's x-scale and f-scale ratios (translation: lf < 1 <= lx)
+  m      the order read with translation=True
+Nothing in the method changes.
+
+    python -u diag_fun9_flank.py [problem] [prestep]
+"""
+from __future__ import annotations
+
+import math
+import sys
+
+from simroot.pure import _analogy_order, _config3, pure_root
+from sweep_full import MAXFEV, XTOL, load_problems
+
+
+def main(pid_want="fun9.5", pre="defect+flatanalogmempt+exp"):
+    for s, pid, f, a, b, _root in load_problems():
+        if pid != pid_want:
+            continue
+        st = {"trace": []}
+        pure_root(f, a, b, XTOL, MAXFEV, similarity="ratio", scale="derived3",
+                  guard="project", prestep=pre, stats=st)
+        print(f"== {pid}  {pre}  entries {st.get('stick_entries', 0)}")
+        past = []
+        for k, t in enumerate(st["trace"]):
+            cur = _config3(t["x"], t["fx"], t["xp"], t["fp"], t["xp2"], t["fp2"])
+            flag = t["fp"] != 0.0 and t["fx"] / t["fp"] >= 0.25
+            head = f"  {k:3d} x {t['x']:9.4f} f {t['fx']:+9.2e} {'F' if flag else '.'}"
+            if cur is None:
+                print(head + "  (no configuration)")
+                continue
+            line = abs(cur[1] - cur[0]) / math.sqrt(2.0)
+            if past:
+                q = min(past, key=lambda p: math.hypot(cur[0] - p[0], cur[1] - p[1]))
+                ratio = math.hypot(cur[0] - q[0], cur[1] - q[1]) / line if line > 0 else math.inf
+                lx = cur[2] / q[2] if q[2] > 0 else math.nan
+                lf = cur[3] / q[3] if q[3] > 0 else math.nan
+                m = _analogy_order(cur, past, translation=True)
+                ms = "none" if m is None else ("inf" if math.isinf(m) else f"{m:.2f}")
+                print(head + f"  xi {cur[0]:+8.3f} phi {cur[1]:+8.3f}  ratio {ratio:7.3f}"
+                      f"  lx {lx:7.3f} lf {lf:9.3e}  m {ms}")
+            else:
+                print(head + f"  xi {cur[0]:+8.3f} phi {cur[1]:+8.3f}  (no memory)")
+            past.append(cur)
+
+
+if __name__ == "__main__":
+    main(*sys.argv[1:3])
@@ -0,0 +1,23 @@
+== fun9.5  defect+flatanalogmempt+exp  entries 1
+    0 x    0.0002 f -1.00e+00 .  (no configuration)
+    1 x   40.5001 f +3.88e+17 .  xi   +0.500 phi   +0.000  (no memory)
+    2 x   20.2502 f +6.23e+08 .  xi   +0.500 phi   +1.000  ratio   2.828  lx   0.500 lf 1.000e+00  m none
+    3 x   20.2501 f +6.23e+08 F  xi   -0.000 phi   -0.000  ratio 220240183.906  lx   0.000 lf 1.044e-16  m none
+    4 x   19.1406 f +2.05e+08 F  xi -17066711.549 phi -10310042.635  ratio   4.173  lx 17066711.549 lf 1.031e+07  m none
+    5 x   17.5571 f +4.22e+07 .  xi   -1.427 phi   -0.391  ratio   2.019  lx 24356112.465 lf 4.030e+06  m none
+    6 x   16.8250 f +2.03e+07 F  xi   -0.462 phi   -0.134  ratio   2.074  lx 11259747.544 lf 5.403e+05  m none
+    7 x   13.8231 f +1.01e+06 .  xi   -4.101 phi   -0.880  ratio   1.194  lx   1.896 lf 1.180e-01  m none
+    8 x   13.7422 f +9.29e+05 F  xi   -0.027 phi   -0.004  ratio   1.684  lx 1244198.603 lf 1.933e+03  m none
+    9 x   12.6156 f +3.01e+05 F  xi  -13.927 phi   -8.022  ratio   2.909  lx   0.375 lf 3.259e-02  m none
+   10 x   10.8903 f +5.36e+04 .  xi   -1.531 phi   -0.394  ratio   0.130  lx   1.090 lf 1.516e-03  m inf
+   11 x   10.3887 f +3.25e+04 F  xi   -0.291 phi   -0.085  ratio   1.229  lx   0.685 lf 9.668e-04  m none
+   12 x    5.1945 f +1.78e+02 .  xi  -10.357 phi   -1.527  ratio   1.007  lx   1.730 lf 1.677e-03  m none
+   13 x    2.5973 f +1.14e+01 .  xi   -0.500 phi   -0.005  ratio   0.384  lx   3.548 lf 7.623e-06  m inf
+   14 x    1.2988 f +1.66e+00 .  xi   -0.500 phi   -0.059  ratio   0.171  lx   0.500 lf 5.854e-02  m 4.09
+   15 x    0.6094 f -1.88e-01 .  xi   -0.531 phi   -0.189  ratio   0.364  lx   0.942 lf 8.437e-08  m 271.20
+   16 x    0.9527 f +5.82e-01 .  xi   +0.498 phi   +0.417  ratio   7.241  lx   0.008 lf 1.982e-18  m none
+   17 x    0.7352 f +6.75e-02 .  xi   +0.633 phi   +0.668  ratio  11.558  lx   0.633 lf 6.684e-01  m none
+   18 x    0.7039 f +1.36e-03 .  xi   -0.144 phi   -0.129  ratio  13.745  lx   0.063 lf 3.125e-06  m none
+   19 x    0.7032 f -2.25e-06 .  xi   -0.021 phi   -0.021  ratio  86.525  lx   0.008 lf 1.744e-08  m none
+   20 x    0.7032 f +1.38e-11 .  xi   +0.002 phi   +0.002  ratio 7135.750  lx  16.646 lf 5.551e-08  m none
+   21 x    0.7032 f +1.74e-16 .  xi   +0.000 phi   +0.000  ratio 165597.494  lx   0.000 lf 3.401e-13  m none