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feat(math): --weinberg diagnostic — phi^-3 vs PDG sin^2(theta_W) (Closes #295) #564

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feat(math): --weinberg diagnostic — phi^-3 vs PDG sin^2(theta_W) (Closes #295) #564

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53 changes: 53 additions & 0 deletions bootstrap/src/math_compare.rs
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Original file line number Diff line number Diff line change
Expand Up @@ -24,6 +24,8 @@ const CKM_V_US: f64 = 0.225;
const CKM_V_CB: f64 = 0.0418;
const CKM_V_UB: f64 = 0.0037;

const SIN2_THETA_W_REF: f64 = 0.23122;

#[derive(Subcommand, Debug)]
pub enum MathCommands {
/// Compare L5 anchors; optional Pellis, extended SM proxies, hybrid map, sensitivity.
Expand All @@ -49,6 +51,9 @@ pub enum MathCommands {
/// Numeric partials of TRINITY and (if --hybrid) hybrid score w.r.t. phi.
#[arg(long)]
sensitivity: bool,
/// Weinberg angle diagnostic: phi^-3 vs PDG sin^2(theta_W).
#[arg(long)]
weinberg: bool,
},
}

Expand All @@ -62,6 +67,7 @@ pub fn run_math_command(cmd: MathCommands, repo_root: &Path) -> anyhow::Result<(
n,
theta,
sensitivity,
weinberg,
} => run_compare(
repo_root,
CompareOpts {
Expand All @@ -72,6 +78,7 @@ pub fn run_math_command(cmd: MathCommands, repo_root: &Path) -> anyhow::Result<(
n,
theta,
sensitivity,
weinberg,
},
),
}
Expand All @@ -85,6 +92,7 @@ pub struct CompareOpts {
pub n: u32,
pub theta: bool,
pub sensitivity: bool,
pub weinberg: bool,
}

#[inline]
Expand Down Expand Up @@ -323,6 +331,30 @@ fn run_compare(repo_root: &Path, opts: CompareOpts) -> anyhow::Result<()> {
record["pellis_spec_seal_hash"] = json!(h);
}

if opts.weinberg {
let phi_inv_cubed = phi_inv.powi(3);
let delta_abs = (phi_inv_cubed - SIN2_THETA_W_REF).abs();
let delta_rel = delta_abs / SIN2_THETA_W_REF;

println!("=== Weinberg Angle Diagnostic (issue #295) ===");
println!("phi^-3 = {:.10}", phi_inv_cubed);
println!("sin^2(theta_W) = {:.10} (PDG MS-bar)", SIN2_THETA_W_REF);
println!("delta_abs = {:.10}", delta_abs);
println!("delta_rel = {:.6} ({:.2}%)", delta_rel, delta_rel * 100.0);

let bound = 0.005_f64;
if delta_abs < bound {
println!("golden test: |phi^-3 - sin^2(theta_W)| = {:.10} < {} PASS", delta_abs, bound);
} else {
println!("golden test: |phi^-3 - sin^2(theta_W)| = {:.10} >= {} NOT MET", delta_abs, bound);
}

record["weinberg_enabled"] = json!(true);
record["phi_inv_cubed"] = json!(phi_inv_cubed);
record["sin2_theta_w_ref"] = json!(SIN2_THETA_W_REF);
record["delta_abs"] = json!(delta_abs);
record["delta_rel"] = json!(delta_rel);
}

append_experience(repo_root, &record)?;
println!(
Expand Down Expand Up @@ -440,4 +472,25 @@ mod tests {
theta
);
}

#[test]
fn test_weinberg_golden_bound() {
let phi_inv_cubed = (1.0 / phi()).powi(3);
let delta = (phi_inv_cubed - SIN2_THETA_W_REF).abs();
assert!(
delta < 0.005,
"golden test: |phi^-3 - sin^2(theta_W)| = {:.10} >= 0.005",
delta
);
}

#[test]
fn test_phi_inv_cubed_approx() {
let phi_inv_cubed = (1.0 / phi()).powi(3);
assert!(
(phi_inv_cubed - 0.236068).abs() < 0.001,
"phi^-3 should be ~0.236, got {:.10}",
phi_inv_cubed
);
}
}
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