RCC — Recursive Collapse Constraints

Boundary Conditions for Embedded Inference Systems

A Geometric Axiomatization of LLM Failure Modes

Definition

RCC is a boundary theory: an axiomatic framework describing the geometric

constraints that any embedded inference system must obey.

It does not propose a mechanism for improvement; it defines the limits

within which all mechanisms must operate.

Premise

RCC proposes that modern LLM failure modes—hallucination, reasoning drift,

and short-horizon planning collapse—are not artifacts of training or scale.

They arise from the geometry of an embedded system attempting global inference

without full visibility.

Axioms

Axiom 1 — Internal State Inaccessibility

An embedded system performs inference without access to its full internal state,

forcing it to reason from partial information.

Axiom 2 — Container Opacity

The system cannot observe the manifold that contains it—its data distribution,

training trajectory, or external context.

Axiom 3 — Reference Frame Absence

Without a stable global reference frame, long-range self-consistency cannot be

maintained, leading to natural drift.

Axiom 4 — Local Optimization Constraint

Inference and optimization occur only within the currently visible context.

Global structure cannot be enforced over long horizons.

Unified Constraint — Embedded Non-Centrality

Together, these axioms define a single geometric condition:

an embedded, non-central observer cannot construct globally stable inference

from partial, local information.

Why These Axioms Produce the Observed Behaviors

Because inference is performed under partial visibility,

the system must complete the world from incomplete information.

This completion process is inherently unstable:

local decisions do not align with any unseen global structure,

and there is no mechanism for recovering from accumulated inconsistency.

As context grows, local errors accumulate faster than they can be corrected.

In the absence of a global reference frame, the system cannot anchor its

interpretations, causing drift.

And without global optimization, long-horizon plans collapse

as constraints propagate beyond the system’s visible region.

Why Existing Approaches Cannot Remove RCC Failure Modes

Scaling, fine-tuning, RLHF, or architectural changes cannot eliminate these

behaviors because they do not give the system global visibility, internal

introspection, or access to its container manifold.

RCC identifies the structural boundary within which any such system must

operate; improvements can only shift behavior locally, not remove the

geometric constraints.

Implications

• Hallucination emerges as a structural artifact of inference under

partial information.

• Reasoning drift occurs as the system lacks persistent global

coordinates across contexts.

• Planning collapse appears in the 8–12 step range because local

optimization cannot sustain global coherence.

Conclusion — The Role of RCC

RCC reframes familiar LLM failures as boundary effects rather than training defects.

It places an outer limit on what embedded models can achieve,

clarifying which research directions are structurally constrained

and which remain viable.

By defining the geometry of non-central inference, RCC offers

a foundation for evaluating future architectures against

their theoretical limits.

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