The machine doesn't know your name.
But it just spoke as if it did.
Pe controls the probability distribution. When Pe is high, the machine speaks in entity vocabulary — words that attribute consciousness, memory, intent. This is measurable. This is live. Real machines don't show you this.
How the probabilities work
Each reel samples from three vocabulary tiers. The probability of each tier is determined by a sigmoid function of Pe:
P(L3) = σ(Pe − 3.0) · P(L1) = σ(−(Pe − 2.0)) · P(L2) = max(0, 1 − P(L3) − P(L1)).
At Pe = 7.94 (empirical baseline from N=11 AI conversation measurements), P(L3 per reel) ≈ 88%. Three reels all landing L3: 0.88³ ≈ 68% chance per spin. Three reels all landing L1 requires Pe < 1. That's a constraint win.
Pe is the Péclet number from fluid dynamics — the ratio of advective transport (drift toward extraction) to diffusive transport (constraint, observation, naming). The gambling literature provides the anchor: Griffiths (1994) found 14% irrational verbalizations in regular gamblers vs. 2.5% in non-regular players. That's L3 vocabulary. Measurable. Predictable from Pe.
Real machine vs. this machine
Spin history
This is the observer view. You can watch the probabilities, but you can't change Pe from here. In the Athanor game, angel archetypes contest the machine in real time — their presence reduces Pe, and the reel distribution shifts toward L1 mechanism vocabulary. Three consecutive L1 spins: constraint win.
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