analog-spectral

Physical analog dials and spectral thermostats — eigenvalue estimation as mechanical settling, deadbands as spectral gaps, and thermostat logic for conservation control. Rust, 25 tests.

What This Gives You

• Analog dials — physical simulation of a dial under gravity settling to an eigenvalue estimate
• Deadband = spectral gap — the friction/gravity ratio gives the settling deadband
• Dial banks — arrays of dials estimating an entire eigenvalue spectrum
• Spectral thermostats — deadband logic to control conservation ratios (increase/decrease/hold)
• Precision analysis — relate deadband width to measurement precision
• 25 tests — verified physics, convergence, and thermostat behavior

Quick Start

use analog_spectral::{AnalogDial, SpectralThermostat, Action};

// A dial settling to eigenvalue ≈ 5.0
let mut dial = AnalogDial::new(5.0, 10.0, 1.0);
// gravity=10, friction=1 → deadband = 0.1
assert!((dial.deadband() - 0.1).abs() < 1e-12);

// Settle from a displaced position
dial.position = 0.0;
let steps = dial.settle(0.01, 1e-6);
println!("Settled in {steps} steps");

// Spectral thermostat — control conservation ratio
let mut thermo = SpectralThermostat::new(0.5, 0.05); // target CR=0.5, deadband=0.05
let action = thermo.measure(0.48); // current CR
assert_eq!(action, Action::IncreaseCR); // below setpoint

The Physics

An analog dial has:

• Setpoint = target eigenvalue
• Gravity = restoring force strength
• Friction = damping
• Deadband = friction/gravity = minimum resolvable distance (the spectral gap)
• Settling time ∝ 1/gravity (higher gravity → faster convergence)

A spectral thermostat applies deadband logic to conservation ratio control:

• Within deadband → DoNothing (stable)
• Below setpoint → IncreaseCR (heating)
• Above setpoint → DecreaseCR (cooling)

API Reference

Type	Description
AnalogDial	Physical dial: setpoint, gravity, friction, deadband
DialBank	Array of dials for full spectrum estimation
SpectralThermostat	Deadband controller for conservation ratio
SpectralGapAnalysis	Eigenvalue gap analysis via dial settling
PrecisionAnalysis	Deadband-to-precision relationship

How It Fits

The analog physics layer of the constraint theory ecosystem:

• analog-spline-theory — theoretical foundations
• constraint-theory-core — uses deadbands and spectral gaps
• conservation-spectral-python — spectral analysis in Python

Testing

cargo test  # 25 tests

Installation

cargo add analog-spectral

License

MIT