The Resonance Gate: Endogenous Confidence from Retrieval Geometry in a Vector-Symbolic Memory

Abstract Most systems that give a language model long-term memory or a sense of its own limits add an exogenous confidence estimator: a second model, a trained head, or an LLM judge that inspects an answer after it is produced. We ask whether confidence can instead be endogenous, a structural property of the retrieval operation itself. We build the Resonance Gate (RG), a vector-symbolic (VSA/MAP) memory substrate in which retrieving an answer and scoring confidence in it are one operation, read from the geometry of a cleanup. A small frozen transformer verbalises gate-approved content and is never consulted for facts. No confidence-specific training exists anywhere in the system. We report a pre-registered confirmatory evaluation, a self-commissioned adversarial audit of it, and a harder fair-corpus re-test, all made public before this paper. Three results hold. An untrained closed-form mapping of the retrieval geometry to a belief/disbelief/uncertainty opinion carries essentially all the correctness information a trained logistic readout of the same features extracts (gap 0.013 AUROC2 on the clean corpus, inside a pre-registered 0.02 margin; a gradient-boosted foil does no better). Under a verify-then-speak discipline, ungrounded assertions in templated output are eliminated (0 of 263 templated bodies; 1 of 288 total, in free-text phrasing), measured by a judge validated at unit precision and recall on negation, implication, and temporal assertions. The endogenous signal is a store-membership signal, not an error detector: it separates what is in memory from what is not (gate minus a zero-parameter exact-key oracle, +0.077 AUROC2, CI excludes zero), but among items it answers it ranks correctness at chance (0.516), and membership plus one geometry scalar accounts for its whole advantage. The clean-corpus ambiguity and calibration ceilings we first measured (both 1.00) were artifacts of item construction, which the audit exposed. We give the substrate design, a load- and codebook-normalised resolution statistic with a capacity approximation, a two-geometry encoder, and the transparency process behind the corrections.