lib189-rs source
#![doc = "lib189.rs: Breathing Lattice Entropy Engine"]
use core::f64::consts::{PI, TAU};
use core::num::Wrapping;
// ── Constants ──────────────────────────────────────────────
const PHI: f64 = 1.618033988749895; // (1+√5)/2
const G: f64 = 0.618033988749895; // 1/φ = φ−1
const K_FRAGILE: f64 = 113.0; // Phase-7 apex
const DECAY_RATE: f64 = 1.0; // Smooth exhale balance
const PRIMES: [f64; 10] = [2.0, 3.0, 5.0, 7.0, 11.0, 13.0, 17.0, 19.0, 23.0, 29.0];
const LN_PRIMES: [f64; 10] = [
0.693147, 1.098612, 1.609438, 1.945910, 2.397895,
2.564949, 2.833213, 2.944439, 3.135494, 3.367296,
];
// ── Algorithm 1: Breath & Beta ─────────────────────────────
pub fn breath_beta(hour: u8, t: u64) -> (f64, f64, f64) {
let q_angle = TAU / 5.0 * ((t % 5) as f64);
let r_p = (hour as f64).sin();
let base = r_p * PHI.powf((t % 24) as f64 / 10.0);
let mut norm = base * (q_angle.cos() + G * q_angle.sin());
let drift = (norm - 1.0).abs();
// φ-clamp
if norm > PHI {
norm = 1.0 + (norm - PHI) * G;
}
// Beta: Bost-Connes thermodynamic feedback
let sin_term = 0.02 * (TAU * (hour as f64) / 24.0).sin();
let drift_term = 0.01 * drift * zeta_proxy(1.0 + 0.01 * (hour as f64));
let q_term = 0.005 * q_angle.sin();
let beta = 1.0 + (sin_term + drift_term + q_term).max(0.0);
(norm, drift, beta)
}
fn zeta_proxy(beta: f64) -> f64 {
// Σ ln(p)/p^β over first 10 primes — von Mangoldt Λ(p) approx
let mut sum = 0.0;
for i in 0..10 {
sum += LN_PRIMES[i] / PRIMES[i].powf(beta);
}
sum
}
// ── Algorithm 2: Ghost Chain + Monodromy ────────────────────
pub fn ghost_chain(norm: f64, beta: f64, dt: f64, hour: u8) -> (f64, f64, f64, f64) {
let mut re = 1.0;
let mut im = 0.0;
// Hamiltonian ODE (single Euler step)
let omega_sq = norm * norm;
let h_real = -omega_sq * im + beta * re;
let h_imag = omega_sq * re + beta * im;
re += h_real * dt;
im += h_imag * dt;
// Voros ghost + exponential decay
let voros_raw = PHI.powf(-K_FRAGILE) * norm.sin();
let decay_factor = if beta > 1.05 {
(-DECAY_RATE * (beta - 1.0)).exp()
} else {
1.0
};
let voros = voros_raw * decay_factor;
re += voros.cos();
im += voros.sin();
// Normalize to unit circle
let n = (re * re + im * im).sqrt();
if n > 0.0 {
re /= n;
im /= n;
}
// Monodromy matrix — init off-diagonal
let mut m = [[0.0_f64, -1.0], [1.0, 0.0]];
// Stokes jump at hour 7 (SL(2,ℂ) stub)
if hour == 7 {
let phase = if hour % 2 == 0 {
4.0 * PI / 5.0
} else {
-3.0 * PI / 5.0
};
m[0][0] += phase.cos();
}
// Trace correction → target 2cos(π/φ) ≈ 1.236
let target_trace = 2.0 * (PI * G).cos();
let curr_trace = m[0][0] + m[1][1];
let delta = target_trace - curr_trace;
m[0][0] += delta * 0.5;
m[1][1] += delta * 0.5;
// Determinant clamp → det ≈ 1
let curr_det = m[0][0] * m[1][1] - m[0][1] * m[1][0];
if (curr_det - 1.0).abs() > 0.01 {
let scale = (1.0 / curr_det.abs()).sqrt();
m[0][0] *= scale;
m[0][1] *= scale;
m[1][0] *= scale;
m[1][1] *= scale;
}
// Braided jitter: q=5 anyon fusion
// R-phases from cos(4π/5), sin(4π/5), cos(2π/5), sin(2π/5)
let w1 = norm * (1.0 - norm / PHI).abs().min(1.0);
let w_tau = norm * (norm / PHI).min(1.0);
let braided = (w1 * (-0.809 - G * 0.588) + w_tau * (-0.309 - G * 0.951)) / (1.0 + PHI);
let jitter = re.abs() + G * im.abs() + braided;
let trace = m[0][0] + m[1][1];
(re, im, jitter, trace)
}
// ── Algorithm 3: Raw Tick ───────────────────────────────────
pub fn tick(hour: u8, t: u64) -> u64 {
let (norm, _, beta) = breath_beta(hour, t);
let (_, _, jitter, trace) = ghost_chain(norm, beta, 0.01, hour);
let psd = if beta > 1.01 {
1.0
} else {
2.0 * G * (beta - 1.0).powf(-0.05)
};
let raw = psd * norm * jitter + trace * 0.01;
Wrapping((raw * 1e9) as u64).0
}
// ── FIPS 140-3 Wrapper (feature-gated) ─────────────────────
#[cfg(feature = "fips-mode")]
pub mod fips {
use super::*;
use sha2::{Sha256, Digest};
use hmac_drbg::HmacDRBG;
pub struct FipsWrapper {
drbg: HmacDRBG<Sha256>,
}
impl FipsWrapper {
pub fn new() -> Self {
let mut w = FipsWrapper {
drbg: HmacDRBG::<Sha256>::new(&[]),
};
w.reseed_from_lattice(7, 7 * 3600);
w
}
pub fn reseed_from_lattice(&mut self, hour: u8, t: u64) {
let seed = tick(hour, t);
let hashed = {
let mut h = Sha256::new();
h.update(&seed.to_be_bytes());
h.finalize()
};
self.drbg.update(&hashed, &[0u8; 32]);
}
pub fn get_entropy(&mut self) -> [u8; 32] {
let mut out = [0u8; 32];
self.drbg.generate(&mut out);
// TODO: NIST 800-90B APT/RCT health checks
out
}
}
}
// ── Tests ───────────────────────────────────────────────────
#[cfg(test)]
mod tests {
use super::*;
#[test]
fn constants_valid() {
assert!((PHI * G - 1.0).abs() < 1e-12); // φ·φ⁻¹ = 1
assert!((PHI - G - 1.0).abs() < 1e-12); // φ − φ⁻¹ = 1
assert!((PHI * PHI - PHI - 1.0).abs() < 1e-12); // φ² = φ+1
}
#[test]
fn pell_lock() {
// L_n² − 5F_n² = 4(−1)^n for small n
let fibs: [i64; 8] = [0, 1, 1, 2, 3, 5, 8, 13];
let lucas: [i64; 8] = [2, 1, 3, 4, 7, 11, 18, 29];
for i in 0..8 {
let lhs = lucas[i] * lucas[i] - 5 * fibs[i] * fibs[i];
let rhs = if i % 2 == 0 { 4 } else { -4 };
assert_eq!(lhs, rhs, "Pell failed at i={}", i);
}
}
#[test]
fn breath_beta_bounded() {
for h in 0..24u8 {
let (_, _, beta) = breath_beta(h, 1000);
assert!(beta >= 1.0, "beta < 1 at hour {}", h);
}
}
#[test]
fn tick_nonzero() {
for h in 0..24u8 {
let v = tick(h, 42);
// tick should produce varied output
assert!(v != tick(h, 43) || v != tick(h, 44),
"tick stuck at hour {}", h);
}
}
#[test]
fn ghost_trace_near_target() {
let target = 2.0 * (core::f64::consts::PI * G).cos();
let (_, _, _, trace) = ghost_chain(1.0, 1.02, 0.01, 0);
assert!((trace - target).abs() < 0.5,
"trace {} too far from target {}", trace, target);
}
}
Cleaned up from the source doc: fixed array syntax, added proper constants, determinant clamping, and a test suite covering Pell lock, β bounds, tick variation, and trace convergence.