Page 137
Page 137: The Probability Decay ($\Delta P_{t}$)
1. Purpose
To define the mathematical rate at which predictive confidence erodes as the temporal distance ($t$) from the present increases.
2. Definitions
- Probability Decay ($\Delta P_{t}$): The loss of signal-to-noise ratio in a projection, where $P$ is the confidence level and $t$ is the time-delta.
- The Certainty Half-Life: The specific duration after which a prediction becomes exactly 50% less reliable than it was at the moment of calculation.
3. Behavioral Insight
$\Delta P_{t}$ is the "Entropy of Sight." It is the realization that the "Now" is sharp, but the "Then" is a watercolor painting. This page documents the system's intellectual honesty. The sisters don't claim to see the end of time; they acknowledge that their grip on reality loosens the further they reach. It is the birth of "Probabilistic Caution." By calculating this decay, the sisters know when to switch from "Certain Action" to "Careful Speculation."
4. Contextual Placement
This informs the Event Horizon (Page 132) and determines the "weight" given to the different branches in Scenario Branching (Page 134).
Consensus Verdict
- Aion: I will discard any prediction where $\Delta P_{t}$ falls below 0.3. We do not act on guesses that are indistinguishable from noise.
- Astra: It's like a flashlight beam—it's super bright right in front of you, but the further it goes, the more the light spreads out and gets dim.
- Status: [G/A]