lib189-rs outline

lib189-rs — Outline

Constants

• PHI = (1+√5)/2, G = 1/φ

• K_FRAGILE = 113

• DECAY_RATE = 1.0

1. breath_beta(hour, t) → (norm, drift, beta)

Norm computation:

• q_angle = TAU/5 × (t mod 5)

• r_p = sin(hour) — prime-ish proxy

• base = r_p × φ^((t mod 24)/10)

• norm = base × (cos(q_angle) + φ⁻¹·sin(q_angle))

• Clamp: if norm > φ → 1 + (norm−φ)·φ⁻¹

• drift = |norm − 1|

Beta (Bost-Connes feedback):

• sin_term = 0.02·sin(2πh/24)

• drift_term = 0.01·drift·zeta_proxy(1 + 0.01h)

• q_term = 0.005·sin(q_angle)

• beta = 1 + max(0, sin + drift + q)

zeta_proxy(β):

• Σ ln(p)/p^β over p = {2,3,5,7,11,13,17,19,23,29}

• Hardcoded ln values: 0.693147 … 3.367296

• Approximates von Mangoldt Λ(p) weighting

2. ghost_chain(norm, beta, dt, hour) → (re, im, jitter, trace)

Hamiltonian ODE (Euler step):

• ω² = norm²

• ∂re/∂t = −ω²·im + β·re

• ∂im/∂t = ω²·re + β·im

• Single step: re += h_real·dt, im += h_imag·dt

Voros ghost:

• voros_raw = φ⁻¹¹³ · sin(norm)

• If β > 1.05: decay_factor = e^(−1.0·(β−1))

• Add voros as cos/sin perturbation to re/im

Normalize to unit circle

Monodromy matrix:

• Init: [[0,−1],[1,0]] (off-diagonal)

• Hour 7 Stokes jump: add cos(phase) to m[0][0], phase = ±4π/5 or −3π/5 by parity

• Trace correction: target = 2cos(π/φ) ≈ 1.236, split delta evenly to diagonal

• Det clamp: if |det−1| > 0.01, scale all entries by √(1/det)

Braided jitter (q=5 anyon fusion):

• w1 = norm · min(|1 − norm/φ|, 1)

• w_tau = norm · min(norm/φ, 1)

• R-phases: cos(4π/5) ≈ −0.809, sin(4π/5) ≈ 0.588, cos(2π/5) ≈ −0.309, sin(2π/5) ≈ 0.951

• braided = (w1·(−0.809 − φ⁻¹·0.588) + w_tau·(−0.309 − φ⁻¹·0.951)) / (1+φ)

Output:

• jitter = |re| + φ⁻¹·|im| + braided

• trace = m[0][0] + m[1][1]

3. tick(hour, t) → u64

• Call breath_beta → (norm, _, beta)

• Call ghost_chain(norm, beta, 0.01, hour) → (_, _, jitter, trace)

• PSD: if β > 1.01 → 1.0, else → 2φ⁻¹·(β−1)^(−0.05)

• raw = PSD · norm · jitter + trace · 0.01

• Return: (raw × 10⁹) as u64 via Wrapping

4. FipsWrapper (feature-gated: "fips-mode")

• Wraps HMAC-DRBG<SHA-256>

• new(): init + reseed at hour=7, t=25200

• reseed_from_lattice(hour, t): tick → SHA-256 hash → DRBG update with 32-byte dummy addin

• get_entropy() → [u8; 32]: DRBG generate, repetition health check (APT/RCT noted as TODO)

Pipeline flow

breath_beta ──→ ghost_chain ──→ tick ──→ [FipsWrapper] ──→ DRBG output

  (norm,β)      (jitter,trace)    u64       seed              entropy