fix(kp): place exact angular boundaries on the opening subdivision

Upstream 8eec9a54. Floating accumulation and a 120-degree remainder put star, pada, and sub-lord on different sides of the same boundary. Random longitudes away from those boundaries are unchanged. BUG-1383.

Co-Authored-By: Grok (agent loop)
Co-authored-by: Cursor <cursoragent@cursor.com>

scripts/kp_system.py

@@ -11,7 +11,10 @@ KP (Krishnamurti Paddhati) 占星系统模块
 """
 
 import json
+import math
+from bisect import bisect_right
 from datetime import datetime, timedelta
+from fractions import Fraction
 from pathlib import Path
 from typing import Any, Dict, List, Tuple, Optional
 
@@ -44,6 +47,29 @@ VIMSHOTTARI_YEARS = dict(zip(KP_LORDS, VIMSHOTTARI_DURATION))
 
 NAKSHATRA_SPAN = 360.0 / 27.0  # 13.333... degrees
 
+
+def _angular_partition_starts():
+    """Exact proportional starts, rounded once at the float API boundary."""
+    starts, owners = [], []
+    for star in range(27):
+        sub_start = Fraction(40 * star, 3)
+        for offset in range(9):
+            sub = (star + offset) % 9
+            sub_span = Fraction(40, 3) * VIMSHOTTARI_DURATION[sub] / 120
+            child_start = sub_start
+            for child_offset in range(9):
+                child = (sub + child_offset) % 9
+                starts.append(float(child_start))
+                owners.append((sub, child))
+                child_start += sub_span * VIMSHOTTARI_DURATION[child] / 120
+            sub_start += sub_span
+    return starts, owners
+
+
+_KP_STARTS, _KP_OWNERS = _angular_partition_starts()
+_STAR_STARTS = [float(Fraction(40 * i, 3)) for i in range(27)]
+_PADA_STARTS = [float(Fraction(10 * i, 3)) for i in range(108)]
+
 ROOT = Path(__file__).resolve().parents[1]
 
 
@@ -228,50 +254,25 @@ def get_kp_lords(degree: float) -> Dict:
     Returns:
         KP lords字典
     """
+    if isinstance(degree, bool) or not isinstance(degree, (int, float)) or not math.isfinite(degree):
+        raise ValueError('KP longitude must be a finite number')
     deg = degree % 360
 
     # 1. Sign lord
     sign_index = int(deg // 30)
 
-    # 2. Nakshatra
-    nakshatra_index = int(deg // NAKSHATRA_SPAN) % 27
-    nakshatra_deg = deg % NAKSHATRA_SPAN
-    pada = int(nakshatra_deg // (NAKSHATRA_SPAN / 4)) + 1
-
-    # 3. Sublord & SubSubLord（KP核心算法）
-    # 将Vimshottari 120年周期按比例投影到度数上
-    deg_remainder = deg - 120 * int(deg / 120)
-    deg_cumulative = 0.0
-
-    for i in range(9):
-        deg_nl = NAKSHATRA_SPAN  # 13.333... degrees per nakshatra
-        for j in range(i, i + 9):
-            j_mod = j % 9
-            deg_sl = deg_nl * VIMSHOTTARI_DURATION[j_mod] / 120.0
-            for k in range(j_mod, j_mod + 9):
-                k_mod = k % 9
-                deg_ss = deg_sl * VIMSHOTTARI_DURATION[k_mod] / 120.0
-                deg_cumulative += deg_ss
-                if deg_cumulative >= deg_remainder:
-                    return {
-                        'rasi_lord': SIGN_LORDS.get(SIGNS[sign_index], ''),
-                        'sign': SIGNS[sign_index],
-                        'nakshatra': NAKSHATRAS[nakshatra_index],
-                        'nakshatra_lord': STAR_LORDS[nakshatra_index],
-                        'pada': pada,
-                        'sub_lord': KP_LORDS[j_mod],
-                        'sub_sub_lord': KP_LORDS[k_mod],
-                    }
-
-    # Fallback
+    # 2. Nakshatra. A shared boundary belongs to the subdivision that opens there.
+    nakshatra_index = bisect_right(_STAR_STARTS, deg) - 1
+    pada = (bisect_right(_PADA_STARTS, deg) - 1) % 4 + 1
+    sub, child = _KP_OWNERS[bisect_right(_KP_STARTS, deg) - 1]
     return {
         'rasi_lord': SIGN_LORDS.get(SIGNS[sign_index], ''),
         'sign': SIGNS[sign_index],
         'nakshatra': NAKSHATRAS[nakshatra_index],
         'nakshatra_lord': STAR_LORDS[nakshatra_index],
         'pada': pada,
-        'sub_lord': 'Unknown',
-        'sub_sub_lord': 'Unknown',
+        'sub_lord': KP_LORDS[sub],
+        'sub_sub_lord': KP_LORDS[child],
     }