| OP here a few folks asked about whether RCC has an actual mathematical backbone, so here’s the compact version of the formal axioms. It’s not meant to be a full derivation, just the minimal structure the argument depends on. RCC can be written as a set of geometric / partial-information constraints: A1. Internal State Inaccessibility
Let Ω denote the full internal state.
The observer only ever sees a projection π(Ω), with
π: Ω → Ω′ and |Ω′| < |Ω|.
All inference happens over Ω′, not Ω. A2. Container Opacity
Let M be the manifold containing the system.
Visibility(M) = 0.
Global properties like ∂M or curvature(M) are, by definition, not accessible from inside. A3. No Global Reference Frame
There is no Γ such that
Γ: Ω′ → globally consistent coordinates.
Inference runs in local frames φᵢ, and the transition φᵢ → φⱼ is not invertible over long distances. A4. Forced Local Optimization
At each step t, the system must produce
x₍ₜ₊₁₎ = argmin L_local(φₜ, π(Ω)),
even when ∂information/∂M = 0. From these, the boundary condition is pretty direct: No embedded inference system can maintain stable, non-drifting long-horizon reasoning when ∂Ω > 0, ∂M > 0, and no Γ exists. This is the sense in which RCC treats hallucination, drift, and multi-step collapse as structural outcomes rather than training failures. If anyone wants the longer derivation or the empirical predictions (e.g., collapse curves tied to effective curvature), I’m happy to share. |