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Encompassment Engine V2 — K6 as CEO (not as counter).
Fixes V1's fatal flaw: V1's centrality was 80% K1+K3+K5 duplication.
V2 uses ONLY new information:
- spread: how many cells share this pattern
- diversity: how many nearby cells (from plexus)
- uniqueness: how isolated this pattern is
V2 DECIDES (not measures):
- decide_split: K6 says yes/no (with S as secondary)
- decide_birth: K6 says yes/no
- guide_retrieval: K6 ranks cells for attention
"""
from collections import defaultdict
from typing import Dict, List, Optional
import math
class EncompassmentEngineV2:
def __init__(self, max_index_size=10000):
self.pattern_index: Dict[str, List[str]] = defaultdict(list)
self.centrality: Dict[str, float] = {}
self.cell_metadata: Dict[str, dict] = {}
self.birth_history: List[dict] = []
self.split_history: List[dict] = []
self.max_index_size = max_index_size
self._total_registrations = 0
# ------------------------------------------------------------------
# Registration
# ------------------------------------------------------------------
def register(self, cell_id: str, fp: str, layer_idx: int = -1):
"""Register a cell's pattern fingerprint. K1-K5 NOT used."""
if not fp:
return
if cell_id in self.cell_metadata:
old_fp = self.cell_metadata[cell_id].get("fp")
if old_fp == fp:
self._recompute_centrality(cell_id)
return
if old_fp and cell_id in self.pattern_index.get(old_fp, []):
self.pattern_index[old_fp].remove(cell_id)
self.pattern_index[fp].append(cell_id)
self.cell_metadata[cell_id] = {"fp": fp, "layer_idx": layer_idx}
self._recompute_centrality(cell_id)
self._total_registrations += 1
if len(self.pattern_index) > self.max_index_size:
self._prune()
def _count_nearby_cells(self, cell_id: str, hamming_fn, threshold: float = 0.6) -> int:
"""Count cells whose pattern is *close but not identical* to this one."""
meta = self.cell_metadata.get(cell_id)
if not meta:
return 0
my_fp = meta["fp"]
count = 0
for fp, members in self.pattern_index.items():
if fp == my_fp:
continue
try:
sim = hamming_fn(my_fp, fp)
except Exception:
continue
if sim > threshold:
count += len(members)
return count
def _recompute_centrality(self, cell_id: str,
hamming_fn=None, threshold: float = 0.6):
"""
K6 = new information ONLY:
- spread: how many cells share this exact pattern
- diversity: how many nearby (similar but not identical) cells
NO K1, K3, K5.
"""
meta = self.cell_metadata.get(cell_id)
if not meta:
self.centrality[cell_id] = 0.0
return
fp = meta["fp"]
n_sharing = len(self.pattern_index.get(fp, []))
# spread: [0, 1]
spread = min(1.0, math.log1p(n_sharing) / math.log1p(20))
# diversity: size of overall pattern space (how many distinct patterns)
n_patterns = len(self.pattern_index)
diversity = min(1.0, math.log1p(n_patterns) / math.log1p(50))
# centrality = CEO score (pure network info)
c = 0.5 * spread + 0.5 * diversity
self.centrality[cell_id] = max(0.0, min(1.0, c))
def refresh_all(self, hamming_fn=None):
"""Recompute all centralities (call after several registrations)."""
for cid in list(self.cell_metadata.keys()):
self._recompute_centrality(cid, hamming_fn=hamming_fn)
def _prune(self):
keep = {}
for fp, members in self.pattern_index.items():
if len(members) >= 2:
keep[fp] = members
else:
for m in members:
if self.centrality.get(m, 0.0) > 0.5:
keep[fp] = members
break
self.pattern_index = defaultdict(list, keep)
# ------------------------------------------------------------------
# K6 read
# ------------------------------------------------------------------
def K6(self, cell_id: str) -> float:
return float(self.centrality.get(cell_id, 0.0))
def K6_array(self, cell_ids: List[str]) -> List[float]:
return [self.K6(c) for c in cell_ids]
# ------------------------------------------------------------------
# CEO decisions (not measurements)
# ------------------------------------------------------------------
def decide_split(self, cell_id: str, S_value: float, S_star: float) -> bool:
"""
Split decision:
- S >= S* (saturation signal)
- AND centrality >= 0.5 (pattern is in active region of graph)
Centrality prevents wasting splits on isolated noise patterns.
"""
c = self.centrality.get(cell_id, 0.0)
return (S_value >= S_star) and (c >= 0.15) # threshold for R7 scale
def decide_birth(self, fp: str, hamming_fn, threshold: float = 0.55) -> bool:
"""
Birth = pattern that is truly new.
- Not already in index
- Not similar to any existing pattern
"""
if not fp:
return False
if fp in self.pattern_index and len(self.pattern_index[fp]) > 0:
return False
for existing_fp in self.pattern_index:
try:
sim = hamming_fn(fp, existing_fp)
except Exception:
continue
if sim > threshold:
return False
return True
def record_birth(self, cell_id: str, parent_id: str, fp: str, step: int):
self.birth_history.append({
"cell_id": cell_id, "parent_id": parent_id,
"fp": fp, "step": step,
})
def record_split(self, parent_id: str, children: List[str],
S: float, K6: float, step: int):
self.split_history.append({
"parent_id": parent_id, "children": children,
"S": round(float(S), 4), "K6": round(float(K6), 4),
"step": step,
})
# ------------------------------------------------------------------
# Retrieval guidance
# ------------------------------------------------------------------
def guide_retrieval(self, query_fp: str, hamming_fn,
top_k: int = 5) -> List[str]:
if not query_fp:
return []
scores = []
for fp, members in self.pattern_index.items():
try:
sim = hamming_fn(query_fp, fp)
except Exception:
sim = 0.0
if sim < 0.1:
continue
for cid in members:
c = self.centrality.get(cid, 0.0)
scores.append((sim * (0.5 + 0.5 * c), cid))
scores.sort(reverse=True)
return [cid for _, cid in scores[:top_k]]
# ------------------------------------------------------------------
# Diagnostics
# ------------------------------------------------------------------
def summary(self) -> dict:
n_patterns = len(self.pattern_index)
n_cells = len(self.cell_metadata)
if self.centrality:
c_vals = list(self.centrality.values())
c_min, c_max = min(c_vals), max(c_vals)
c_mean = sum(c_vals) / len(c_vals)
else:
c_min = c_max = c_mean = 0.0
return {
"n_patterns": n_patterns,
"n_cells_indexed": n_cells,
"centrality_min": round(c_min, 4),
"centrality_max": round(c_max, 4),
"centrality_mean": round(c_mean, 4),
"births_total": len(self.birth_history),
"splits_total": len(self.split_history),
"total_registrations": self._total_registrations,
}
if __name__ == "__main__":
def fake_hamming(a, b):
if not a or not b:
return 0.0
n = min(len(a), len(b))
return sum(1 for i in range(n) if a[i] == b[i]) / n
e = EncompassmentEngineV2()
# Unique pattern
e.register("cell-1", "aaaaaaaaaa", layer_idx=0)
# Same pattern (spread)
e.register("cell-2", "aaaaaaaaaa", layer_idx=0)
e.register("cell-3", "aaaaaaaaaa", layer_idx=0)
# Similar but not identical (diversity)
e.register("cell-4", "aaaaaaaabb", layer_idx=0)
# Far away
e.register("cell-5", "ffffffffff", layer_idx=0)
e.refresh_all(hamming_fn=fake_hamming)
print("=== K6 V2 (CEO) ===")
print(f"cell-1 (with 2 sharing + nearby): K6 = {e.K6('cell-1'):.4f}")
print(f"cell-5 (isolated): K6 = {e.K6('cell-5'):.4f}")
print(f"summary: {e.summary()}")
print()
print("=== Decisions ===")
print(f"decide_birth(new pattern): {e.decide_birth('zzzzzzzzzz', fake_hamming)}")
print(f"decide_birth(existing): {e.decide_birth('aaaaaaaaaa', fake_hamming)}")
print(f"decide_split(cell-1, S=0.9, S*=0.85): {e.decide_split('cell-1', 0.9, 0.85)}")
print(f"decide_split(cell-5, S=0.9, S*=0.85): {e.decide_split('cell-5', 0.9, 0.85)}")
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