RCC — Recursive Collapse Constraints

RCC in One Glance — Why This Matters

LLMs fail not because they are poorly designed but because they operate as embedded, partially-blind inference systems.

RCC shows that hallucination, drift, and planning collapse are structurally unavoidable, not engineering bugs.

This means:

We can map boundaries instead of guessing.
We can optimize compute instead of wasting scale.
We can design architectures that work with the geometry, not against it.

RCC is not a new model.

It is the boundary that all models sit inside.

Why LLM failures persist — even at trillion-parameter scale

A boundary theory argument that hallucination, drift, and planning collapse may be structurally unavoidable.

Most discussions treat hallucination, reasoning drift, and long-horizon collapse as engineering problems.

RCC (Recursive Collapse Constraints) makes a stronger claim:

These behaviors may not be fixable —

they may be geometric side-effects of embedded inference itself.

If this framing is correct, improvements in scaling, RLHF, or architectural tuning can shift where failures appear, but cannot eliminate them.

What RCC is

RCC is a boundary theory:

not a new architecture
not a training method
not an alignment strategy

It is an axiomatic description of the structural limits that any embedded inference system must obey.

Any system that fits the axioms inherits the same constraints, regardless of model size or implementation.

The Four RCC Axioms

Axiom 1 — Internal State Inaccessibility

An embedded system cannot see its full internal state.

Inference is performed through a lossy, partial self-projection.

Axiom 2 — Container Opacity

The system cannot observe the manifold that contains it

(training distribution, trajectory, upstream context, etc.).

Axiom 3 — Absence of a Global Reference Frame

All inference is local to the currently visible context.

Long-range consistency cannot be guaranteed.

Axiom 4 — Forced Local Optimization

Even under uncertainty, the system must produce the next update

using only local information.

Unified Constraint

Putting the axioms together:

An embedded, non-central observer cannot construct globally stable inference from partial information.

This is not a deficit of intelligence.

It is a geometric limitation.

Why familiar LLM failures emerge

Under partial visibility, the system must complete unseen parts of the world.

That completion process is:

underdetermined
unstable over long ranges
inconsistent with any unseen global structure

As context grows:

outputs drift
internal coherence degrades
8–12-step reasoning collapses
corrections fail to restore global stability

These are not bugs — they are consequences of inference under incomplete information.

Why scaling and alignment don’t remove this

Scaling, fine-tuning, or RLHF do not give a model:

global visibility
perfect introspection
access to its container manifold

These methods can improve local behavior,

but they cannot remove the underlying geometric boundary.

Implications

If RCC is correct:

hallucination cannot be eliminated, only relocated
drift cannot be removed, only dampened
chain-of-thought collapse cannot exceed the boundary
self-consistency cannot be globally guaranteed

This reframes “LLM failure modes” as structurally necessary outcomes of embedded inference.

It also suggests that some research directions may be fundamentally constrained, while others remain open.

What RCC Enables

RCC does not limit progress — it redirects it.

By identifying the geometric boundary of embedded inference, RCC enables:

targeted scaling instead of blind over-training
architectures that align with the geometry rather than fight it
failure prediction instead of post-hoc patching
compute-efficient planning horizons for long-context tasks
boundary-aware evaluation metrics for drift and collapse

RCC turns uncertainty from a bug into a map.

If you disagree

Disagreement should identify which axiom is incorrect —

not just critique the symptoms observed in current models.

RCC Tri-Limit Theorem

RCC describes not just what fails, but why no model can escape the failure triangle.

No embedded inference system can simultaneously optimize:

H (hallucination rate ↓)
D (drift ↓)
C (collapse probability ↓)

Under RCC constraints, the system must pay in

R (external reference cost),

S (reasoning depth),

or C (collapse).

R, S, and C cannot be minimized at the same time.

This is not empirical; it is geometric.

Formally:

Let

H = hallucination rate

D = drift under recursive reasoning

C = recurrence collapse probability

R = external reference cost (search / tools / human)

S = reasoning depth (steps)

Then RCC implies:

H ↓ ⇒ R ↑
Reducing hallucination requires increased external referencing.
S ↑ ⇒ D ↑
Deeper reasoning amplifies drift due to partial self-observation.
D ↓ ⇒ C ↑
Stabilizing drift forces earlier collapse at the boundary.

This tri-limit is structural, not architectural.

No model—regardless of scale, architecture, or alignment—can break it

TECHNICAL APPENDIX — Formal Axioms of RCC

Axiom 1 — Internal State Inaccessibility

Let Ω be the full internal state.

The observer sees only a projection:

π : Ω → Ω′ with |Ω′| < |Ω|

All inference operates over Ω′.

Axiom 2 — Container Opacity

Let M be the containing manifold.

Visibility(M) = 0

Global properties such as ∂M or curvature(M)

are unobservable from within.

Axiom 3 — No Global Reference Frame

There exists no Γ such that:

Γ : Ω′ → globally consistent coordinates

Inference occurs only in local frames φᵢ,

where mappings φᵢ ↛ φⱼ

for distant or decorrelated contexts.

Axiom 4 — Irreversible Local Collapse

At each inference step t:

x₍ₜ₊₁₎ = argmin L_local(φₜ, π(Ω))

This requirement holds even when:

∂information / ∂M = 0

Boundary Theorem (RCC)

No embedded inference system can maintain stable, non-drifting long-horizon reasoning when:

∂Ω > 0, ∂M > 0, Γ ∄

Hallucination, drift, and collapse are therefore

structural consequences,

not training artifacts.