Every large language model conversation traces a path through information space. Velocity accumulates, curvature bends the trajectory, and somewhere ahead — invisible to the model itself — attractors exert pull. The question is whether those dynamics can be measured from the outside, without touching model weights, attention patterns, or provider internals. That constraint turns out to be surprisingly productive.
Information Space Dynamics is a framework for making that measurement rigorous. It treats the prompt-response sequence as a formal trajectory: each turn produces an observable vector of lexical, structural, and semantic quantities, and the sequence of those vectors yields velocity, curvature, torsional accumulation, and stability margin — all computed from text alone. The framework draws a hard line between direct observations, calibrated estimates, and hypothesis-dependent quantities, so the instrument never silently fabricates a value it cannot actually see.
Djehuti Cyberscope AI+ is the empirical workbench that puts ISD into practice. Load a conversation transcript, run the analysis pipeline, and the dashboard renders the full trajectory: a 3D deformation phase-space, per-turn metric timelines, a feature finder that flags high-velocity transitions and structural shifts, and attractor-approach diagnostics that fire when torsional accumulation and stability margin cross calibrated thresholds. An embedded AI analyst — grounded entirely in ISD theory — narrates what the data actually shows, citing turn indices and metric values, not vague impressions.
The Live Lab extends the instrument to real-time experiments. Enter any provider API key directly in the browser — it never leaves client state — start a vanilla conversation, and watch Djehuti collect each completed turn for analysis as the exchange unfolds. The Multi-LLM Moderated Conversation Engine layer supports structured multi-participant sessions with moderator intervention thresholds and pairwise interferometry across model trajectories.
This is early-stage research infrastructure, not a product. The codebase is open, the measurement protocol is documented, and the framework is designed to be extended. If you are studying LLM behavior and want instrumentation that respects the difference between what can be observed and what must remain an estimate, Djehuti is built for that work.
Three-dimensional trajectory plot of velocity, curvature, and torsional accumulation across the full conversation. Attractor-approach events appear as annotated markers at the boundary perimeter.
Per-turn plots of prompt-response alignment, semantic velocity, lexical similarity, word-count delta, and response length over integer logical time.
Indexed markers for high-velocity transitions, low alignment, structural changes, repeated prompts, and attractor-approach events — each with torsional-resistance basis and severity.
The theoretical foundation — velocity, curvature, torsional resistance, and attractor-approach diagnostics for LLM trajectory analysis under strict pure-observability constraints.
Protocol specification for the empirical measurement workbench — ingestion model, observable vector construction, measurement primitives, and analyst boundary.
Shorter-form writing on measurement findings, anomalies, and theoretical extensions — forthcoming.
W. Westlake is an independent AI researcher focused on empirical observability of large language model behavior. The work centers on building rigorous measurement instruments that respect the boundary between what can be directly observed and what must remain a calibrated estimate.
The ISD framework treats conversation as a trajectory through information space — studying velocity, curvature, torsional accumulation, and attractor-approach signatures without requiring access to model internals.
Current work: expanding Djehuti's measurement capabilities, formalizing the zeta-4 observables, and developing multi-LLM interferometry protocols for comparative trajectory analysis across models.