[noncentral]

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.