1. The Core Problem: The "Frozen Savant"

Current Large Language Models (LLMs) suffer from a fundamental disconnect between Intelligence (Inference) and Growth (Training). Once a model is post-trained and frozen, it effectively becomes an amnesiac savant. It can "learn" locally within a context window (In-Context Learning), but it cannot consolidate that learning into its permanent weights without a full, expensive retraining run.

Recent advances in Test-Time Training (TTT) (e.g., Titans, Nov 2025; Test-Time Warmup, Sept 2025) attempt to solve this by allowing temporary weight updates during inference. However, these methods optimize primarily for Local Adaptation—adjusting to the specific task at hand. They do not solve for Global Synthesis.

We are building models that can "cram" for a test, but cannot "sleep" to understand the material.

This proposal introduces the REM Protocol: a bicameral architecture that utilizes an Offline Isomorphic Search phase to consolidate high-entropy experiences into low-entropy structural rules, effectively simulating biological sleep-dependent memory consolidation.

2. The Hypothesis: Grokking as Isomorphism

We posit that "Grokking"—the phase change where a model shifts from memorization to generalization—is mathematically equivalent to the identification of Topological Isomorphisms in latent space.

Memorization: Storing two separate vectors for $Concept_A$ (e.g., "Automotive Backpressure") and $Concept_B$ (e.g., "Economic Inflation").
Grokking: Identifying that the local graph topology of $A$ is identical to $B$ (both are systems of flow restricted by capacity: ∇P ≈ ∇$), and compressing them into a single "Super-Node."

The Claim: We can artificially induce Grokking not by training longer, but by running an offline search algorithm specifically designed to find and merge these isomorphisms.

3. The Recursive Entropy Minimization (REM) Architecture

The protocol divides the AI lifecycle into a diurnal rhythm of Online Acquisition and Offline Synthesis.

Phase A: Online Inference (The Soldier)

Objective: Data acquisition and local loss minimization.
Mechanism: Standard TTT.
The Novelty: During interaction, the model does not just predict tokens. It actively tags High-Perplexity Nodes—concepts where it lacks a unified internal representation. These are flagged as [TARGET_NODES] for the night cycle.

Phase B: Offline Topology Search (The D

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