
We introduce Comfrey GRRM, a framework that makes large language model(LLM) inference geometry-aware, depth-adaptive, and self-correcting at inferencetime and during geometry-aware training. Current transformer architectures areunable to fully utilize the embedding space because their reliance on Euclideangeometry is ill-suited to the inherently hyperbolic structure of language representations.As a result, large regions of the representational landscape remain unexploredduring both training and inference. Our geometry-aware approach provides accessto these previously unreached spaces.The methodological centrepiece is Wavelet-Scale PCA ():, where layers are units,geometric feature signals are distributional variables, and wavelet coefficient distributionsover ordered frequency scales are the bin vectors. The classical Tchebychevinterval step is replaced by an Entropy-Modulated Wavelet Interval whosehalf-width t σij(1+Pij Hij η) is modulated by Shannon entropy of the scale-energydistribution, with a Bayesian logistic probability penalised by λ = −t log N+1N .The wavelet substrate is the Brahimian Wavelet Family: divergence-free curlwavelets in d-dimensional embedding space with exact Z/3Z cyclic symmetry. Fivegeometric signals (Kirchhoff temporal tension, IRQ Ricci curvature, GPS geodesicconsistency, Boltzmann free energy, IRQ algebraic coherence) assemble into a 9-dimensional ManifoldState m ∈ [0, 1]9.A Recursive Thinking Module (, [14]) injects m into the first token embeddingbetween depth steps of an Adaptive Computation Time loop. A Recursive Language1© 2026 CC BY-NC-ND 4.0Model Decomposer (, [11]) breaks hard queries into sub-questions solved independentlyby . A Parallel Engine runs Ollama and HuggingFace backends simultaneouslyand selects the geometrically superior answer. A Verifier (self-consistency,constraint checking, entailment hardening) validates every answer before return. AGeometric Hypernetwork maps m to per-layer LoRA deltas; Geometric uses themanifold signals as label-free reward components. An Episodic Geometric Memoryaccumulates episodes and retrieves the nearest LoRA adapter at inference time.
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