Editing Openai/6961e230-053c-8013-9840-af60b05b3856 (section)

==== Pseudo-code: QEF-stabiele integratiestap (1 tijdstap) ====

<syntaxhighlight lang="text">Given state at time n:
  Hydro fields: ρ_g, v, P, T, ...
  Coherence state: Ψ
  AGN sources: {AGN_i} with injection schedules
  Grid scales: Δx, Δt_CFL
  Parameters: η_min, η_max, χ_min, χ_max, κ_Cas, p, q, r, ...

STEP 0 — Precompute baseline timestep
  dt0 = dt_CFL

STEP 1 — Update / predict coherence state Ψ (predictor)
  Ψ* = CoherencePredictor(Ψ, hydro_fields, AGN_sources)

STEP 2 — Compute coherence invariant η
  num  = |∫_V Ψ*(x) dV|^2
  denom= ∫_V |Ψ*(x)|^2 dV
  η    = clamp(num / denom, 0, 1)

STEP 3 — Compute AC/DC energy partition and ratio χ
  E_DC = EnergySlow(hydro_fields, gravity_potential, smoothed_terms)
  E_AC = EnergyFast(shocks, AGN_injection_rate, wave_terms, residuals)
  χ    = ||E_AC|| / max(||E_DC||, ε)

STEP 4 — Stiffness-aware timestep control (dt_η and dt_χ)
  dt_η = dt0 * ((1 - η) / (1 - η0))^q          // smaller dt when η → 1
  dt_χ = dt0 * (χ_max / max(χ, ε))^r           // smaller dt when χ is large
  dt   = clamp(min(dt0, dt_η, dt_χ), dt_min, dt_max)

STEP 5 — Compute Casimir regularization term (local, scale-aware)
  ℓ     = max(Δx, mfp_proxy(hydro_fields))
  fℓ    = (ℓ / ℓ0)^(-4)
  H_Cas = - κ_Cas '' fℓ '' η^p

  // Guard: Casimir must not dominate bulk hydro energy
  H_Cas = clamp(H_Cas, -0.05''H_hydro_local, +0.05''H_hydro_local)

STEP 6 — Apply governance loop: coherence damping / anti-smoothing
  if η > η_max or DetectRunawayEnergySpike(hydro_fields, E_spike):
       Ψ''   = Ψ'' * (1 - g_η)                   // mild coherence damping
       ApplySpectralFilter(E_AC, strength=g_η) // tame stiff oscillations
  if χ < χ_min:
       ReduceDamping(strength=g_χ)             // protect tSZ-relevant structure

STEP 7 — Main update: hydro + AGN + QEF terms (corrector)
  hydro_fields^{n+1} =
       HydroSolverStep(hydro_fields^n, dt,
                       source_terms = {gravity, AGN_injection(dt), H_Cas, QEF_coh(Ψ*)})

STEP 8 — Coherence corrector (synchronize Ψ with updated hydro fields)
  Ψ^{n+1} = CoherenceCorrector(Ψ*, hydro_fields^{n+1}, dt)

STEP 9 — Diagnostics & acceptance criteria
  Recompute η^{n+1}, χ^{n+1}
  if η^{n+1} < η_min:
       Flag: "Decoherence drop" (increase resolution or adjust AGN cadence)
  if χ^{n+1} > χ_max and persists N steps:
       Flag: "AC runaway risk" (tighten dt or κ_Cas slightly)
  Log: dt, η, χ, max|H_Cas|/H_hydro, tSZ_proxy(Compton-y)

Return state at n+1

</syntaxhighlight>