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Healing (predictive primitives)

healing

dense_evolution.healing -- predictive-healing primitives for noisy vector sequences (VQE/MD telemetry, quantum state trajectories).

Built empirically, one formula at a time, not derived top-down from a named theory -- worth being precise about, since one piece of it turns out to have a real mathematical identity worth naming rather than leaving implicit: calculate_vettore_dinamico's core term, log(E_B / E_A), is a log-likelihood ratio -- the same elementary quantity Kullback-Leibler divergence (relative entropy) is built from (D_KL(A||B) = sum_x A(x) * log(A(x)/B(x)), a probability-weighted average of exactly this log-ratio, which calculate_vettore_dinamico does not compute -- it uses one un-weighted log-ratio between two scalars, not a full KL divergence over a distribution). Equivalently, if -log(E) is read as self-information ("surprisal"), log(E_B/E_A) is the difference in surprisal between the two states.

Not every formula in this module carries the same reading -- calculate_ phi_ab's blend of cosine-alignment and Euclidean-distance terms is a geometric similarity construction, not an information-theoretic one; naming it as such would be the overclaiming this note is trying to avoid, not fix.

calculate_advanced_sigma

calculate_advanced_sigma(
    kappa: ndarray,
    H: ndarray,
    Psi: ndarray,
    Omega_sync: ndarray,
    tau_K: ndarray,
) -> jnp.ndarray

Calcola la funzione di sincronizzazione avanzata Sigma.

Source code in dense_evolution/healing.py
@jax.jit
def calculate_advanced_sigma(kappa: jnp.ndarray, H: jnp.ndarray, Psi: jnp.ndarray, Omega_sync: jnp.ndarray, tau_K: jnp.ndarray) -> jnp.ndarray:
    """Calcola la funzione di sincronizzazione avanzata Sigma."""
    return kappa * H * Psi * Omega_sync * tau_K

calculate_phi_ab

calculate_phi_ab(
    state_A: ndarray, state_B: ndarray, ipg_vector: ndarray
) -> jnp.ndarray

Calcola il fattore di allineamento e coerenza spaziale Phi_AB.

Source code in dense_evolution/healing.py
@jax.jit
def calculate_phi_ab(state_A: jnp.ndarray, state_B: jnp.ndarray, ipg_vector: jnp.ndarray) -> jnp.ndarray:
    """Calcola il fattore di allineamento e coerenza spaziale Phi_AB."""
    semantic_change = state_B - state_A
    norm_change = jnp.linalg.norm(semantic_change)
    norm_ipg = jnp.linalg.norm(ipg_vector)

    alignment = jnp.where(
        (norm_change > 1e-12) & (norm_ipg > 1e-12),
        # jnp.dot on complex arrays is the bilinear (non-conjugated) product
        # and stays complex, which used to blow up jnp.clip below with
        # "ValueError: Clip received a complex value". jnp.real(jnp.vdot(..))
        # is the correct Hermitian-inner-product real part -- for real
        # inputs it reduces exactly to jnp.dot (no behavior change for
        # existing real-valued callers), and for complex inputs (e.g. a
        # genuine statevector) it gives the real alignment value this
        # function needs. Re(vdot(a,b)) == Re(vdot(b,a)) always, even
        # though vdot(a,b) != vdot(b,a) in general (they're conjugates) --
        # argument order doesn't matter here only because we take the real part.
        jnp.real(jnp.vdot(semantic_change, ipg_vector)) / (norm_change * norm_ipg),
        0.0
    )
    semantic_alignment = (alignment + 1.0) / 2.0

    distance_A_B = jnp.linalg.norm(state_A - state_B)
    coherence_component = 1.0 - (distance_A_B / GLOBAL_CONSTANTS['MAX_SEMANTIC_DISTANCE'])

    phi_ab = (semantic_alignment * GLOBAL_CONSTANTS['WEIGHT_SEMANTIC']) + (coherence_component * GLOBAL_CONSTANTS['WEIGHT_COHERENCE'])
    return jnp.clip(phi_ab, 0.0, 1.0)

calculate_vettore_dinamico

calculate_vettore_dinamico(
    E_A: ndarray, E_B: ndarray, Phi_AB: ndarray
) -> jnp.ndarray

Calcola il Vettore Dinamico (V_dinamic) come variazione logaritmica differenziale energetica.

log(E_B / E_A) is a log-likelihood ratio -- the same elementary quantity Kullback-Leibler divergence is built from (see this module's docstring for the precise distinction: this is one un-weighted log-ratio between two scalars, not a full KL divergence over a probability distribution). Equivalently, the difference in surprisal (-log E) between the two states.

Source code in dense_evolution/healing.py
@jax.jit
def calculate_vettore_dinamico(E_A: jnp.ndarray, E_B: jnp.ndarray, Phi_AB: jnp.ndarray) -> jnp.ndarray:
    """Calcola il Vettore Dinamico (V_dinamic) come variazione logaritmica differenziale energetica.

    log(E_B / E_A) is a log-likelihood ratio -- the same elementary
    quantity Kullback-Leibler divergence is built from (see this
    module's docstring for the precise distinction: this is one
    un-weighted log-ratio between two scalars, not a full KL divergence
    over a probability distribution). Equivalently, the difference in
    surprisal (-log E) between the two states."""
    valid_inputs = (E_A > 1e-12) & (E_B > 1e-12)
    ratio = jnp.where(valid_inputs, E_B / E_A, 1.0)
    log_ratio_clamped = jnp.clip(jnp.log(ratio), -5.0, 5.0)
    v_vita = GLOBAL_CONSTANTS['V_DINAMIC_K_COEFF'] * log_ratio_clamped * Phi_AB
    return jnp.where(valid_inputs, v_vita, 0.0)

calculate_vettore_statico

calculate_vettore_statico(
    v_dinamic_value: ndarray,
) -> jnp.ndarray

Calcola l'indicatore di stasi tensoriale Vettore Statico.

Source code in dense_evolution/healing.py
@jax.jit
def calculate_vettore_statico(v_dinamic_value: jnp.ndarray) -> jnp.ndarray:
    """Calcola l'indicatore di stasi tensoriale Vettore Statico."""
    is_growing = v_dinamic_value > GLOBAL_CONSTANTS['V_DINAMIC_MIN_EFFECTIVE_VALUE']
    return GLOBAL_CONSTANTS['V_STATIC_K_PRIME_COEFF'] * (1.0 - jnp.where(is_growing, 1.0, 0.0))

calculate_delta_preemp

calculate_delta_preemp(
    current_sigma: ndarray, target_sigma_ideal: float = 10.0
) -> jnp.ndarray

Calcola la deviazione predittiva Delta_Pre_emp normalizzata rispetto all'autostato ideale.

Source code in dense_evolution/healing.py
@jax.jit
def calculate_delta_preemp(current_sigma: jnp.ndarray, target_sigma_ideal: float = 10.0) -> jnp.ndarray:
    """Calcola la deviazione predittiva Delta_Pre_emp normalizzata rispetto all'autostato ideale."""
    safe_target = jnp.where(target_sigma_ideal <= 0.0, 1.0, target_sigma_ideal)
    return jnp.abs(current_sigma - target_sigma_ideal) / safe_target

evaluate_phi_trigger

evaluate_phi_trigger(
    deterministic_dq_dt_a: ndarray,
) -> Tuple[jnp.ndarray, jnp.ndarray, jnp.ndarray]

Valuta lo stato del Phi-Trigger calcolando i coefficienti di damping condizionati.

Source code in dense_evolution/healing.py
@jax.jit
def evaluate_phi_trigger(deterministic_dq_dt_a: jnp.ndarray) -> Tuple[jnp.ndarray, jnp.ndarray, jnp.ndarray]:
    """Valuta lo stato del Phi-Trigger calcolando i coefficienti di damping condizionati."""
    magnitude_change_a = jnp.abs(deterministic_dq_dt_a)
    trigger_active = magnitude_change_a > GLOBAL_CONSTANTS['NON_STATIC_THRESHOLD_A']

    lambda_step = jnp.where(trigger_active, 0.05, 0.05 + GLOBAL_CONSTANTS['DAMPING_BOOST_ON_STASIS'])
    epsilon_dissip = jnp.where(trigger_active, GLOBAL_CONSTANTS['EPSILON_DISSIPATION_BASE'],
                                GLOBAL_CONSTANTS['EPSILON_DISSIPATION_BASE'] + GLOBAL_CONSTANTS['DAMPING_BOOST_ON_STASIS'])

    return jnp.where(trigger_active, 1.0, 0.0), lambda_step, epsilon_dissip

calculate_jax_reflection

calculate_jax_reflection(
    coherence_values: ndarray, noise_levels: ndarray
) -> Tuple[jnp.ndarray, jnp.ndarray, jnp.ndarray]

Esegue l'aggregazione statistica spettrale (Zero-Drift) sul runtime XLA.

Source code in dense_evolution/healing.py
@jax.jit
def calculate_jax_reflection(coherence_values: jnp.ndarray, noise_levels: jnp.ndarray) -> Tuple[jnp.ndarray, jnp.ndarray, jnp.ndarray]:
    """Esegue l'aggregazione statistica spettrale (Zero-Drift) sul runtime XLA."""
    n_coh = coherence_values.shape[0]
    avg_coherence = jnp.where(n_coh > 0, jnp.mean(coherence_values), 0.0)
    var_coherence = jnp.where(n_coh > 0, jnp.var(coherence_values), 0.0)

    n_noise = noise_levels.shape[0]
    avg_noise = jnp.where(n_noise > 0, jnp.mean(noise_levels), 0.0)

    return avg_coherence, var_coherence, avg_noise

See also: dense_evolution.mitigationzne_density_matrix's healing-adapted branch calls calculate_delta_preemp from this module.