Why the analogy entry is late on the flat families (diagnostics only, method unchanged). At flag moments before entry: unlike-past 118, no-memory 7, m<2 2 - the order is not the bottleneck. The period-4 cycle: the flag rises in the phases whose configuration does NOT recur (the undershoot whose relative step shrinks every cycle, and the crossing); the recurring phases have the flag down and read the true order (fun4 = 6(x-2)^5: m ~ 4.9). The entry demands both at the same state. Remembering the analogy until the next flag: flat entry state 12.9 -> 8.2; problems entered APS 3 -> 8, fun9 0 -> 1.

Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
2026-09-21 14:58:20 +01:00
parent 1842eb0765
commit b7271a1ce4
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+"""The state-by-state picture behind diag_analogy_late.py, for a few flat problems.
+
+Every state the gate sees (trace hook, flatanalog, projection), in order:
+  n      evaluations spent (the trace does not carry it; states are numbered instead)
+  flag   r = f/f_prev >= 1/4 (the promise failed, sign kept)
+  xi, phi   the configuration
+  ratio  d_past / d_line   (< 1 means analogous to the nearest past configuration)
+  lag    how many states back that nearest past configuration is
+  m      the pair's similarity exponent
+Nothing in the method changes.
+
+    python -u diag_analogy_sequence.py fun6.3 fun4.1 fun3.4
+"""
+from __future__ import annotations
+
+import math
+import sys
+
+from simroot.pure import _config3, pure_root
+from sweep_full import MAXFEV, XTOL, load_problems
+
+
+def show(pid, f, a, b):
+    st = {"trace": []}
+    pure_root(f, a, b, XTOL, MAXFEV, similarity="ratio", scale="derived3", guard="project",
+              prestep="flatanalog", stats=st)
+    print(f"\n== {pid}   (state, flag, xi, phi, d_past/d_line, lag, m)")
+    past = []
+    for k, s in enumerate(st["trace"][:30]):
+        cur = _config3(s["x"], s["fx"], s["xp"], s["fp"], s["xp2"], s["fp2"])
+        flag = s["fp"] != 0.0 and s["fx"] / s["fp"] >= 0.25
+        if cur is None:
+            print(f"  {k:3d} {'F' if flag else '.'}  (no configuration)")
+            continue
+        line = abs(cur[1] - cur[0]) / math.sqrt(2.0)
+        if past:
+            j = min(range(len(past)), key=lambda i: math.hypot(cur[0] - past[i][0],
+                                                               cur[1] - past[i][1]))
+            q = past[j]
+            ratio = math.hypot(cur[0] - q[0], cur[1] - q[1]) / line if line > 0 else math.inf
+            lx, lf = cur[2] / q[2], cur[3] / q[3]
+            m = (math.log(lf) / math.log(lx)) if lx not in (0.0, 1.0) and lf > 0 else math.nan
+            lag = len(past) - j
+            print(f"  {k:3d} {'F' if flag else '.'}  xi {cur[0]:+9.4f} phi {cur[1]:+10.4f}  "
+                  f"ratio {ratio:7.3f}  lag {lag:2d}  m {m:6.2f}")
+        else:
+            print(f"  {k:3d} {'F' if flag else '.'}  xi {cur[0]:+9.4f} phi {cur[1]:+10.4f}  (no memory)")
+        past.append(cur)
+
+
+def main(ids):
+    for s, pid, f, a, b, _root in load_problems():
+        if s == "CHA" and pid in ids:
+            show(pid, f, a, b)
+
+
+if __name__ == "__main__":
+    main(sys.argv[1:] or ["fun6.3", "fun4.1"])