A Continuous-Dynamics Equation Cannot Be Tested on a Static Frozen Substrate: ESCT as a Dynamical Diagnostic Protocol and BERT as Its Zero-Point Calibration

The core of ESCT (Emergent Semantic Continuous-dynamics Theory) is a differential equation, dC/dt = αGP − μC − λC³. This report advances, and supports with experimental evidence, a single methodological claim: the type of this equation is written on its left-hand side. The term dC/dt presupposes a substrate with genuine temporal evolution, yet a BERT forward pass is a one-shot static snapshot that possesses no such dt. To search a static frozen substrate for the structure described by a continuous-dynamics equation is a category error, akin to measuring colour with a thermometer.

We report a falsification chain of nineteen controlled experiments whose consistent conclusion is that, on symbolic/frozen substrates, ESCT-specific continuous-dynamics structure beyond known word-sense disambiguation and static-geometry effects is absent under linear, nonlinear, and real-training-time tests alike. Representative figures: a traction fraction of 0.027; on a real-training-time checkpoint axis, C→P coupling with forward p = 0.145 and leave-one-out 0/16; and a sole cross-distribution invariant, an eigenvalue power-law slope of approximately −1, that is present even in a randomly initialized network, marking it as a random-matrix and architectural artefact rather than learned structure.

We then reframe these results as a recasting of ESCT into a dynamical diagnostic protocol: a measurement apparatus whose quantities can be applied to any model to obtain a reading, where a non-match is itself a valid reading. Under this protocol the nineteen experiments constitute a first calibration against a known-negative sample, and BERT is cleanly diagnosed as a substrate hosting no continuous-dynamics structure (match approximately zero), serving as the apparatus’s zero-point calibration. We note the honest limit of this reframing: BERT establishes that the instrument reads negative cleanly, but not yet that it can read positive, so the claim that ESCT can diagnose any model is at present only half-established.

ESCT’s falsifiable claims must therefore move to a substrate possessing genuine dt and a real-consequence closed loop, where we pre-register a falsification condition: if ESCT finds no corresponding structure even on a genuinely dynamical substrate, then ESCT is false rather than merely mis-located. The report contributes a clean, citable negative-result boundary; a methodological lesson, namely to type-check the substrate before testing a dynamical model; and an explicit rejection of “insufficient scale/compute”-style indefinitely-deferred explanations. An open call invites researchers with persistent-memory, online self-updating, or closed-loop agent resources to supply the protocol’s second calibration point, a positive reading, with refuting results expressly welcomed.

dynamical diagnostic protocol; zero-point calibration; category error; continuous-dynamical systems; frozen substrate; falsification; representational geometry; effective dimensionality; large language models; ESCT

持續動力型方程不可在靜態凍結基質上檢定——ESCT 作為動力診斷協議、BERT 作為其零點校準