Generative retrieval reframes information access as sequence generation: a model emits document identifiers that are subsequently mapped to corpus items. Contemporary systems such as DSI-style retrieval and structured approaches like SEATER demonstrate that learned identifiers can act as effective addresses, but they remain only weakly grounded in the actual geometry and topology of the corpus. In this paper we introduce spectral-aware unique identifiers: composite codes that pair a simple integer ID with an order key derived from taumode-a spectral energy and manifold-aware proximity functional computed by ArrowSpace from graph Laplacians and eigenspaces. Rather than treating identifier tokens themselves as the semantic space, we treat taumode as the retrieval-native latent manifold and use external IDs as thin pointers into it. Taumode summarizes each document into spectral coordinates, energy levels, and graph-consistent neighborhoods, yielding a geometry where similarity, locality, and diffusion are explicit rather than emergent, and where the identifier order is aligned with the spectral energy landscape. In this view ArrowSpace serves both vector search and generative retrieval as a spectral index that provides a mathematically grounded geometry for identifier design, constrained decoding, candidate generation, and reranking. We define a concrete identifier scheme (ℓ i , u i) based on λ τ values and prove that it preserves manifold structure more faithfully than sequence-only identifiers, while remaining compatible with autoregressive models. We substantiate the advantages of spectral-aware IDs over current generative retrieval signals in terms of manifold consistency, interpretability, locality preservation, robustness under structural perturbation, and ease of integration into existing vector databases and generative search pipelines.

Classical information retrieval metrics such as Mean Reciprocal Rank (MRR) evaluate only the position of the first relevant item, ignoring both deeper relevant results and the structural quality of the retrieved set within the corpus graph. We introduce MRR-Top0, a novel ranking metric that extends MRR to the entire top-k result list by weighting each relevant item's reciprocal rank with a topology factor T q,i. This factor combines three graph signals computed on the corpus feature graph: Personalized PageRank (random-walk affinity from the query anchor), a conductance penalty (subgraph cohesion), and a modularity gain (community alignment). The resulting score evaluates both relevance order and structural coherence in a single, bounded, label-agnostic quantity. MRR-Top0 is applicable to any retrieval system operating over an embedding space equipped with a graph Laplacianincluding spectral vector databases, RAG pipelines, and topology-aware search enginesand provides a computationally cheap proxy for assessing whether a ranking reflects the learned manifold structure of the dataset, not merely geometric proximity. We present the formal definition, explain every constituent, discuss key properties and practical guidance, and situate the metric within the broader landscape of graph-aware retrieval evaluation.

Having introduced Graph Wiring-(1) a technique that leverages the Graph Laplacian computed in feature space to provide semantically-aware search over high-dimensional vector corpora-and MRR-Top0 (2) as a topology-aware retrieval metric for evaluating it; this paper proceeds to demonstrate formally and empirically that the feature-space Laplacian produced by ArrowSpace (3) carries structural information in the sense of epiplexity (4), so that it is not plain graph metadata but a reusable context-bound semantic artifact. Using the CVE 1999-2025 vulnerability corpus as a case study, we instantiate ArrowSpace as a spectral vector-search engine, wrap its feature-space Laplacian in a Laplacian-constrained Gaussian Markov Random Field (LGMRF), and evaluate the resulting two-part Minimum Description Length (MDL) code. The model achieves a compression ratio of 38.4× over raw float32 storage, passes all three structural-information diagnostic tests. Furthermore it is demonstrated that the same Laplacian object as computed by Graph Wiring supports six distinct algorithm families (search, classification, anomaly detection, diffusion, dimensionality reduction, and data valuation) without additional learning. The two accompanying Jupyter notebooks are intended as a reproducible reference pattern for applying epiplexity measurement in algorithm design for large-scale data engineering for LLMs and ML operations.