MB1 — Boundary Estimator Soundness

A measured epsilon-boundary certificate is assumed to warrant the abstract boundary predicate it stands in for.

What decision changes?

Before trusting a boundary-discovery result, ask what sampling, observability, and non-stationarity conditions the estimator needed in order to be sound.

Embedded-agency arguments deny a clean cut between an agent and its environment. The book does not dissolve that problem. It relocates it into a falsifiable, measurable bet: a directed epsilon-boundary can be estimated from traces, and passing the estimator’s certificate is assumed to mean the real, semantic boundary condition holds.

That assumption is MB1. It is not proved. It depends on sampling being adequate, the interface being observable, the estimator being stable under resampling, and the environment not drifting faster than the estimator can track.

This is why boundary discovery is described as a hypothesis rather than a fact: every later step in the book — grounding, correction, successor checks — inherits whatever error MB1 leaves uncaught. An adversary that can decouple the measured boundary from the true one attacks this bridge specifically, not the logic built on top of it.

Formulas

$$I(I_{t+1}; E_{t+1} \mid S_t, A_t) \leq \epsilon$$

What would count as evidence?

Evidence would include estimator stability under resampling, robustness across non-stationary environments, and agreement between independent measurement procedures on the same deployed system.