Syntonic Engine: one formula, three facts about the machine, no tuning

One formula, three facts about the machine, no tuning: the engine sets the time window of a correction or an estimate from statistics measured in the signal, by a law derived from first principles (Theorem U' of the Syntony Principle); its only machine-specific inputs are three facts measured once: the loop timing and delay, the actuator's authority in a correction loop (which since 0.2.8 also sets the correction limit) or the fast sensor's drift in an estimator, and access to the read noise. The law sets a window, not a loop gain; stability stays with the machine. Implemented in Python, C++ and Rust, which agree to 5e-14 rad. On synthetic benches it is at parity with hardened Bayesian Kalman banks within its class and behind them where a second-order model applies; on the simulated MAESTRO 1 joint bench, against a tuned PID given the same correction limit, its baton-tip error under steady noise is at parity on one excerpt and 20 % higher on the other, and 17 to 31 % lower when the noise jumps; its larger joint errors cancel at the tip because they carry the gesture's planned acceleration, seen through the lightly damped loop the correction forms with the servo; in a simulated quadrotor attitude estimator, with the gyro's drift measured once at rest, it lands within a few percent of the best fixed window under moderate changes of the vibration (it overshoots it when the vibration rises x256), at parity with a tuned Kalman filter under steady vibration, and beats a fixed-noise Kalman filter when the vibration rises; in simulation, on gyro drifts drawn from the laws the theory assumes, the optimal exponent from nominal to x256 vibration follows 1/(2H+1) across H for a fractional drift (its gain in error over the square root resolved at H = 0.9, not at 0.75), and the law's local form, fed the drift's structure function measured once at rest, predicts the optimal window and its exponent through crossovers of the drift and a jump of the optimum, from predictions frozen before the evaluation; on logs of a real quadrotor on the ground, the measured noise and drift matrices predict that estimating roll and pitch jointly, as an EKF does, would gain under 0.5 % (RMS) over the law axis by axis. The law has not yet run as an estimator on hardware. The hypothesis under test is portability across machines of different physics and, for the law, the living.

New in 0.2.8: the correction limit, a fixed 5 degrees that no list of design constants declared, is derived from the authority fact (per joint, the servo's time constant times its no-load speed, the largest lag the servo itself can produce). Pre-registered on fresh seeds, it never binds, and the tip error at the published tempo falls 7 to 8 % on excerpt A and 32 to 34 % on excerpt B. The bench's PID now gets the same clip, which moves the published comparison against the engine on excerpt B (tip ratio under steady noise 1.20 instead of 1.06, ten paired draws). Simulation only.