Jue: An Energy-Based Concept Field for Online Relational Memory on Frozen Transformers – What Addressing Suffices For, What Propagation Adds, and a Matched-Interface Protocol for Telling Them Apart

A deployed language model is frozen: retrieval and fine-tuning fetch or overwrite information, but nothing accumulates inside a system that could be said to be learning. We present Jue, an energy-based concept field attached to a frozen transformer that accumulates knowledge online through local Hebbian updates—no gradients reach the base model, and language enters and leaves through explicit provenance contracts. Disabled, the system is exactly the base model. All results are reported under a falsification-first protocol: preregistered thresholds and conclusion wordings, frozen materials, constant provenance with automatic staleness, and a permanent generation-level endpoint CI. The contribution is a three-act mechanism study. Act one: across eight non-conditioned geometric readout variants, accuracy on a divergent multi-relation testbed pins at exactly $0.333$—the first-taught relation permanently captures a concept's output. Act two: relation-conditioned addressing repairs this completely ($1.000$) and, as our own strongest baseline, sweeps the capability matrix—addressing suffices for single-hop disambiguation, and the field adds nothing measurable there. Act three: under isolation-merge teaching, cut-edge causality holds at the string level on $16/18$ blind-registered chains spanning 2–4 hops with zero shortcut contamination ($0/36$), while without isolation chain formation collapses ($3/18$). But soft multi-candidate retrieval reaches $20/20$ where propagation reaches $15/20$, and a matched provenance-aware typed graph memory reproduces every measured property of the field and exceeds it on provenance completeness. That comparison runs under a matched-interface protocol we state separately and consider reusable—identical write contract, readout, provenance and intervention interfaces, matched budget, and blind materials with both architectures frozen at registration—six conditions without which an equivalence result is uninterpretable. Three discriminative probes on the field's native ground returned one tie (a zero-relaxation ablation isolates the dynamics' contribution at $+3/117$) and two instrument blocks we localize here. The energy dynamics are not yet doing irreplaceable work on any surface we could measure; the contribution is accordingly the audit discipline, these measured equivalences, and the complete falsification record—nineteen stop-gates, four hard stops, four retired claims, and the author hypotheses struck down by the project's own data.