PLATFORM PROFILEPrivate
Perplexity
0.95
B-index (V3.1)
TRANSITION
Capture0.675
Escape0.711
Key Structural Insight
Eleven-Parameter Profile
Data Depth5/10
Memory5/10
Action5/10
Process4/10
Network5/10
Closeness7/10
Portability7/10
Substitutability7/10
Human Fallback8/10
Org Depth3/10
Momentum8/10
Capture Escape Extended
V3.1 Decomposition
| Component | Value | Formula |
|---|---|---|
| CES₄ capture core | 0.4740 | CES(d, m, a, p) |
| Knowledge synergy σₖ | 0.5000 | √(d · m) |
| Operability synergy σₒ | 0.4472 | √(a · p) |
| Synergy boost | 1.1421 | 1 + 0.3·(σₖ + σₒ)/2 |
| Org-depth multiplier | 1.1500 | 1 + 0.5·o |
| Momentum multiplier | 1.2400 | 1 + 0.3·t |
| Total Capture | 0.6754 | c·(1+0.5n)·core·syn·org·mom |
| CES₃ escape core | 0.7326 | CES(x, s, h) |
| Feedback attenuation | 0.8341 | max(0.3, 1 − 0.35·core) |
| Total Escape | 0.7111 | ε + escCore · feedback |
| B = Capture / Escape | 0.95 | 0.675 / 0.711 |
Scoring Rationale
Parameter Sensitivity
MARGINAL B-INDEX CHANGE PER ±1 SCORE SHIFT
CLOSE7+0.27
PROC4+0.14
DATA5+0.13
MEM5+0.13
ACT5+0.13
ORG3+0.08
PORT7-0.08
SUB7-0.08
NET5+0.08
FALL8-0.07
MOM8+0.05
+ raises B (deepens lock-in)− lowers B (aids escape)
Comparable Platforms — AI Platforms (9 peers)
| # | Platform | Ticker | B-index | Zone | |
|---|---|---|---|---|---|
| 01 | AI-OS (Theoretical) | - | 7.67 | BLACK HOLE | Profile → |
| 02 | Microsoft Copilot (M365) | MSFT | 5.23 | BLACK HOLE | Profile → |
| 03 | Apple Intelligence | AAPL | 4.43 | BLACK HOLE | Profile → |
| 04 | Google Gemini | GOOG | 3.22 | BLACK HOLE | Profile → |
| 05 | Cursor (Anysphere) | Private | 2.92 | BLACK HOLE | Profile → |
| 06 | ChatGPT | Private | 2.25 | EVENT HORIZON | Profile → |
| 07 | Grok (xAI) | Private | 1.78 | EVENT HORIZON | Profile → |
| 08 | Claude (Anthropic) | Private | 1.66 | EVENT HORIZON | Profile → |
| 09 | Chat LLM (Generic) | - | 0.22 | USEFUL TOOL | Profile → |