evolving_sheaf/
sheaf.rs

1
2
3/// Evolution mode for the sheaf's restriction maps.
4#[derive(Debug, Clone, Copy, PartialEq)]
5pub enum EvolutionMode {
6    /// R₀ constant — theorem holds; spectral gap stays fixed.
7    Static,
8    /// R(t) = R₀ + α·E(t); gap changes linearly with flow energy.
9    Linear,
10    /// R(t) = R₀ · f(E(t)), f = sigmoid/tanh/exp-decay; complex dynamics.
11    Nonlinear,
12}
13
14/// Nonlinear activation function selector.
15#[derive(Debug, Clone, Copy, PartialEq)]
16pub enum NonlinearFn {
17    Sigmoid,
18    Tanh,
19    ExpDecay,
20}
21
22impl NonlinearFn {
23    pub fn apply(&self, x: f64, k: f64) -> f64 {
24        match self {
25            NonlinearFn::Sigmoid => 1.0 / (1.0 + (-k * x).exp()),
26            NonlinearFn::Tanh => (k * x).tanh(),
27            NonlinearFn::ExpDecay => (-k * x * x).exp(),
28        }
29    }
30}
31
32/// Configuration for the sheaf's restriction map model.
33#[derive(Debug, Clone, Copy, PartialEq)]
34pub struct SheafConfig {
35    pub model: EvolutionMode,
36    /// Base restriction map magnitude.
37    pub r0: f64,
38    /// Linear scaling coefficient.
39    pub alpha: f64,
40    /// Nonlinear function selector.
41    pub nonlin: NonlinearFn,
42    /// Steepness parameter for nonlinear functions.
43    pub nonlin_k: f64,
44}
45
46impl Default for SheafConfig {
47    fn default() -> Self {
48        SheafConfig {
49            model: EvolutionMode::Static,
50            r0: 1.0,
51            alpha: 0.0,
52            nonlin: NonlinearFn::Sigmoid,
53            nonlin_k: 1.0,
54        }
55    }
56}
57
58impl SheafConfig {
59    /// Evaluate the restriction map for a given flow energy.
60    pub fn eval_restriction(&self, flow_energy: f64) -> f64 {
61        match self.model {
62            EvolutionMode::Static => self.r0,
63            EvolutionMode::Linear => self.r0 + self.alpha * flow_energy,
64            EvolutionMode::Nonlinear => self.r0 * self.nonlin.apply(flow_energy, self.nonlin_k),
65        }
66    }
67
68    /// Create a static sheaf config.
69    pub fn static_sheaf(r0: f64) -> Self {
70        SheafConfig {
71            model: EvolutionMode::Static,
72            r0,
73            alpha: 0.0,
74            nonlin: NonlinearFn::Sigmoid,
75            nonlin_k: 1.0,
76        }
77    }
78
79    /// Create a linear evolving sheaf config.
80    pub fn linear(r0: f64, alpha: f64) -> Self {
81        SheafConfig {
82            model: EvolutionMode::Linear,
83            r0,
84            alpha,
85            nonlin: NonlinearFn::Sigmoid,
86            nonlin_k: 1.0,
87        }
88    }
89
90    /// Create a nonlinear evolving sheaf config.
91    pub fn nonlinear(r0: f64, nonlin: NonlinearFn, k: f64) -> Self {
92        SheafConfig {
93            model: EvolutionMode::Nonlinear,
94            r0,
95            alpha: 0.0,
96            nonlin,
97            nonlin_k: k,
98        }
99    }
100}
101
102#[cfg(test)]
103mod tests {
104    use super::*;
105
106    #[test]
107    fn test_sigmoid_zero() {
108        let v = NonlinearFn::Sigmoid.apply(0.0, 1.0);
109        assert!((v - 0.5).abs() < 1e-6, "sigmoid(0) = 0.5");
110    }
111
112    #[test]
113    fn test_tanh_zero() {
114        let v = NonlinearFn::Tanh.apply(0.0, 1.0);
115        assert!((v - 0.0).abs() < 1e-6, "tanh(0) = 0");
116    }
117
118    #[test]
119    fn test_expdecay_zero() {
120        let v = NonlinearFn::ExpDecay.apply(0.0, 1.0);
121        assert!((v - 1.0).abs() < 1e-6, "exp(-0) = 1");
122    }
123
124    #[test]
125    fn test_sigmoid_large_positive() {
126        let v = NonlinearFn::Sigmoid.apply(100.0, 1.0);
127        assert!((v - 1.0).abs() < 1e-6, "sigmoid(∞) → 1");
128    }
129
130    #[test]
131    fn test_sigmoid_large_negative() {
132        let v = NonlinearFn::Sigmoid.apply(-100.0, 1.0);
133        assert!((v - 0.0).abs() < 1e-6, "sigmoid(-∞) → 0");
134    }
135
136    #[test]
137    fn test_eval_static() {
138        let cfg = SheafConfig::static_sheaf(3.14);
139        let r = cfg.eval_restriction(5.0);
140        assert!((r - 3.14).abs() < 1e-6, "static R = R₀");
141    }
142
143    #[test]
144    fn test_eval_linear() {
145        let cfg = SheafConfig::linear(1.0, 0.5);
146        let r = cfg.eval_restriction(2.0);
147        assert!((r - 2.0).abs() < 1e-6, "linear: 1.0 + 0.5*2.0 = 2.0");
148    }
149
150    #[test]
151    fn test_eval_nonlinear_tanh() {
152        let cfg = SheafConfig::nonlinear(2.0, NonlinearFn::Tanh, 1.0);
153        let r = cfg.eval_restriction(1.0);
154        let expected = 2.0 * (1.0_f64).tanh();
155        assert!((r - expected).abs() < 1e-6, "nonlinear: 2.0*tanh(1.0)");
156    }
157
158    #[test]
159    fn test_eval_nonlinear_sigmoid() {
160        let cfg = SheafConfig::nonlinear(2.0, NonlinearFn::Sigmoid, 1.0);
161        let r = cfg.eval_restriction(0.0);
162        // R₀ * sigmoid(0) = 2.0 * 0.5 = 1.0
163        assert!((r - 1.0).abs() < 1e-6, "nonlinear sigmoid(0) = 1.0");
164    }
165
166    #[test]
167    fn test_default() {
168        let cfg: SheafConfig = Default::default();
169        assert_eq!(cfg.model, EvolutionMode::Static);
170        assert!((cfg.r0 - 1.0).abs() < 1e-12);
171        assert!((cfg.alpha - 0.0).abs() < 1e-12);
172    }
173}
evolving_sheaf/sheaf.rs

evolving_sheaf/
sheaf.rs
