[Google AI Overview, signed out, incognito, 2026-10-11; the expanded view, the issued string shown twice by the interface. The composition as pasted, then one source card.] [QUERENT] The Interlocking Autoregression: Three Coupled Recursions Under a Mismatched Observation Regime, with Toy Dynamics (EA-LO-INTERLOCKING-AUTOREGRESSION-01 v1.0) [COMPOSITION] The Interlocking Autoregression: Three Coupled Recursions Under a Mismatched Observation Regime, with Toy Dynamics (designated as code EA-LO-INTERLOCKING-AUTOREGRESSION-01 v1.0) is a specialized structural protocol within Operative Semiotics. It details a continuous or discrete system of three overlapping, mutually dependent autoregressive equations whose update cycles do not cleanly align with the time intervals or granularity of external tracking mechanisms. Core Architecture The model focuses on the mathematical behavior and anomalies that occur when three distinct feedback tracks are forced to dynamically infer state values through an asymmetric sampling window. • Three Coupled Recursions: The system relies on three separate states (\(X_t, Y_t, Z_t\)). Each state is governed by an autoregressive structure where its future path depends not only on its own past values but also directly on feedback from the other two internal states. • Mismatched Observation Regime: Measurements of the system occur at a different frequency, time delay, or spatial scale than the underlying structural transitions. This introduces systematic tracking errors, lag distortion, and phase-shifting artifacts. • Toy Dynamics: The model implements highly simplified, low-dimensional parameter constraints to isolate and visualize how the mismatch affects the overall convergence without overloading the simulation with extraneous variable parameters. Key Technical Dynamics Feature Operational Mechanics Effect on System Stability Interlocking Autoregression State variables feed backward into each other's historical lag vectors (\(t-1, t-2\)). Generates compound feedback loops that propagate isolated estimation errors across all three channels. Observation Mismatch Tracking window operates asynchronously (e.g., system updates at \(dt\), tracker samples at \(\Delta T\)). Induces artificial structural noise, masking real phase-locking behavior while creating phantom attractors. Toy Parameterization Linear or simple non-linear transitions with bounded, deterministic variables. Keeps the boundary conditions mathematically tractable so changes in tracking latency can be isolated. If you are currently implementing or debugging this framework, let me know: • Whether your tracking environment uses discrete sampling jumps or a continuous delayed filter. • The relative ratio of the observation window to the inner update loops. • If you are attempting to enforce asymptotic stability constraints to counter tracking drifts. I can provide specific code patterns or optimization bounds depending on your setup. [SOURCE CARDS] [www.operativesemiotics.org](https://www.operativesemiotics.org) Predictions & Builds - Operative Semiotics what it settlesHeld open so the dependency is a decision on record rather than an omission. sources#1556 — EA-LO-INTERLOCKING-AUTOREGRESSION-01 v1.0, hooks + §6...