spectral-prosody 0.1.0

Spectral graph theory applied to metrical patterns across languages
Documentation 
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141

//! Test the conjecture that breath-constrained meters produce isospectral graphs
//! regardless of language. Iambic pentameter and Sanskrit sloka should be spectrally close
//! because both are optimized for ~1 breath unit.

use crate::laplacian_scan::SpectralSignature;
use crate::metrical_graph::{MetricalLine, MetricalGraph};

/// Estimate breath cost of a line (syllable count as proxy).
pub fn breath_cost(line: &MetricalLine) -> f64 {
    // A single relaxed breath can sustain roughly 10-16 syllables
    // Normalize: 10 syllables = 1.0 breath unit
    line.syllable_count() as f64 / 10.0
}

/// Check whether two traditions are isospectral within tolerance.
pub fn isospectral_check(sig_a: &SpectralSignature, sig_b: &SpectralSignature, tolerance: f64) -> bool {
    let norm_a = sig_a.normalized();
    let norm_b = sig_b.normalized();
    norm_a.distance_to(&norm_b) < tolerance
}

/// Generate a breath-equivalent line in a target meter.
/// Maps stress patterns to preserve breath cadence across traditions.
pub fn breath_equivalent_line(source: &MetricalLine, target_syllables: usize, target_stresses: Vec<bool>, language: &str) -> MetricalLine {
    let source_cost = breath_cost(source);
    let _target_cost = target_syllables as f64 / 10.0;
    // Create line that matches breath cost
    let syllables = vec![source_cost / target_syllables as f64; target_syllables];
    MetricalLine::new(syllables, target_stresses, language.to_string())
}

/// Build a collection of breath-constrained traditions for comparison.
pub fn breath_constrained_traditions() -> Vec<(&'static str, Vec<MetricalLine>)> {
    vec![
        ("English Iambic Pentameter", vec![
            MetricalLine::new(vec![1.0; 10], vec![false, true, false, true, false, true, false, true, false, true], "English".into()),
            MetricalLine::new(vec![1.0; 10], vec![false, true, false, true, false, true, false, true, false, true], "English".into()),
            MetricalLine::new(vec![1.0; 10], vec![false, true, false, true, false, true, false, true, false, true], "English".into()),
        ]),
        ("Sanskrit Sloka", vec![
            MetricalLine::new(vec![0.625; 16], vec![false, true, false, true, false, true, false, false, false, true, false, true, false, true, false, false], "Sanskrit".into()),
            MetricalLine::new(vec![0.625; 16], vec![false, true, false, true, false, true, false, false, false, true, false, true, false, true, false, false], "Sanskrit".into()),
            MetricalLine::new(vec![0.625; 16], vec![false, true, false, true, false, true, false, false, false, true, false, true, false, true, false, false], "Sanskrit".into()),
        ]),
        ("French Alexandrine", vec![
            MetricalLine::new(vec![0.833; 12], vec![false, false, false, true, false, false, false, false, false, true, false, false], "French".into()),
            MetricalLine::new(vec![0.833; 12], vec![false, false, false, true, false, false, false, false, false, true, false, false], "French".into()),
            MetricalLine::new(vec![0.833; 12], vec![false, false, false, true, false, false, false, false, false, true, false, false], "French".into()),
        ]),
        ("Arabic Rajaz", vec![
            // Rajaz: 6+6+6 syllable pattern (3=iambic-like feet)
            MetricalLine::new(vec![0.833; 12], vec![false, true, false, true, false, true, false, true, false, true, false, true], "Arabic".into()),
            MetricalLine::new(vec![0.833; 12], vec![false, true, false, true, false, true, false, true, false, true, false, true], "Arabic".into()),
            MetricalLine::new(vec![0.833; 12], vec![false, true, false, true, false, true, false, true, false, true, false, true], "Arabic".into()),
        ]),
    ]
}

/// Test the iso-breath conjecture across all breath-constrained traditions.
/// Returns pairwise isospectral comparisons.
pub fn test_iso_breath_conjecture(tolerance: f64) -> Vec<(String, String, f64, bool)> {
    let traditions = breath_constrained_traditions();
    let signatures: Vec<SpectralSignature> = traditions.iter().map(|(name, lines)| {
        SpectralSignature::from_lines(lines, name)
    }).collect();

    let mut results = Vec::new();
    for i in 0..signatures.len() {
        for j in (i + 1)..signatures.len() {
            let dist = signatures[i].normalized().distance_to(&signatures[j].normalized());
            let iso = dist < tolerance;
            results.push((signatures[i].tradition.clone(), signatures[j].tradition.clone(), dist, iso));
        }
    }
    results
}

#[cfg(test)]
mod tests {
    use super::*;

    #[test]
    fn test_breath_cost_iambic() {
        let line = MetricalLine::new(vec![1.0; 10], vec![false, true, false, true, false, true, false, true, false, true], "English".into());
        assert!((breath_cost(&line) - 1.0).abs() < 1e-9);
    }

    #[test]
    fn test_breath_cost_sanskrit() {
        let line = MetricalLine::new(vec![0.625; 16], vec![false; 16], "Sanskrit".into());
        assert!((breath_cost(&line) - 1.6).abs() < 1e-9);
    }

    #[test]
    fn test_isospectral_check_same() {
        let lines = vec![
            MetricalLine::new(vec![1.0; 10], vec![false, true, false, true, false, true, false, true, false, true], "English".into()),
            MetricalLine::new(vec![1.0; 10], vec![false, true, false, true, false, true, false, true, false, true], "English".into()),
        ];
        let sig1 = SpectralSignature::from_lines(&lines, "A");
        let sig2 = SpectralSignature::from_lines(&lines, "B");
        assert!(isospectral_check(&sig1, &sig2, 0.01));
    }

    #[test]
    fn test_iambic_and_sanskrit_spectrally_close() {
        // Core conjecture: iambic pentameter and Sanskrit sloka should be spectrally close
        let en_lines = vec![
            MetricalLine::new(vec![1.0; 10], vec![false, true, false, true, false, true, false, true, false, true], "English".into()),
            MetricalLine::new(vec![1.0; 10], vec![false, true, false, true, false, true, false, true, false, true], "English".into()),
            MetricalLine::new(vec![1.0; 10], vec![false, true, false, true, false, true, false, true, false, true], "English".into()),
        ];
        let sa_lines = vec![
            MetricalLine::new(vec![0.625; 16], vec![false, true, false, true, false, true, false, false, false, true, false, true, false, true, false, false], "Sanskrit".into()),
            MetricalLine::new(vec![0.625; 16], vec![false, true, false, true, false, true, false, false, false, true, false, true, false, true, false, false], "Sanskrit".into()),
            MetricalLine::new(vec![0.625; 16], vec![false, true, false, true, false, true, false, false, false, true, false, true, false, true, false, false], "Sanskrit".into()),
        ];
        let sig_en = SpectralSignature::from_lines(&en_lines, "English");
        let sig_sa = SpectralSignature::from_lines(&sa_lines, "Sanskrit");
        let sim = sig_en.cosine_similarity(&sig_sa);
        // High cosine similarity because internal structure is identical (all same within tradition)
        assert!(sim > 0.5, "Iambic and Sanskrit sloka should be spectrally related, cosine={}", sim);
    }

    #[test]
    fn test_iso_breath_conjecture_runs() {
        let results = test_iso_breath_conjecture(2.0);
        assert!(!results.is_empty());
        // At least some pairs should be isospectral at this tolerance
        let iso_count = results.iter().filter(|&&(_, _, _, iso)| iso).count();
        assert!(iso_count > 0, "Some tradition pairs should be isospectral");
    }

    #[test]
    fn test_breath_equivalent_line() {
        let source = MetricalLine::new(vec![1.0; 10], vec![false, true, false, true, false, true, false, true, false, true], "English".into());
        let eq = breath_equivalent_line(&source, 12, vec![false; 12], "French");
        assert_eq!(eq.syllable_count(), 12);
        assert_eq!(eq.language, "French");
    }
}