Monte Carlo Proportionality Thresholds (IP Restricted)

IP–Restricted Component (NashMarkAI / Truthvenarian Jurisdiction)

The Monte Carlo method itself is open-source mathematics in the public domain. However, all NashMarkAI integrations of Monte Carlo sampling, including: transition kernels, drift generators, weighting tensors, proportionality thresholds, equilibrium metrics, Sentinel triggers, and scenario-envelope constructors, are proprietary and protected under the Truthvenarian language and equilibrium law. 

Only the public mathematical shell is disclosed. All internal logic used for legal, ecological, governance, remedy, drift, or proportionality computations remains withheld. 

No rights are granted to replicate, reverse-engineer, approximate, or derive any NashMarkAI transition kernel, threshold operator, or equilibrium functional from the material on this page.

Monte Carlo Proportionality Thresholds is the stochastic threshold-testing shell used inside the NashMarkAI legal, ecological and governance engines. It evaluates proportionality, harm-band sensitivity, cross-scenario drift, and stability margins across large ensembles of uncertainty distributions.

All internal sampling kernels, transition operators, harm-sensitivity tensors, proportionality thresholds, and convergence logic are IP-restricted. Only the public mathematical and pseudocode shells are disclosed.

1. System Role

• Generates scenario ensembles for proportionality and remedy sensitivity.
• Tests harm-threshold behaviour under stochastic deviation.
• Receives equilibrium strategy vectors and state distributions from NashMarkAI.
• Feeds Sansana / PHM, Sentinel and the Equilibrium Enforcement Engine.
• Acts as the core uncertainty and threshold-calibration layer (closed-source).

2. Public Mathematical Shell

$ \hat{T}_{\alpha} = Q_{\alpha}\!\left( \{\, m(X^{(i)}, \pi) \,\}_{i=1}^{N} \right) $

• $ \hat{T}_{\alpha} $ — proportionality threshold at quantile $ \alpha $.
• $ m(\cdot) $ — metric functional (withheld).
• $ X^{(i)} $ — simulated trajectory.
• $ \pi $ — strategy / policy parameters.
• $ Q_{\alpha}(\cdot) $ — quantile operator.
• $ N $ — number of Monte Carlo runs.

3. State Sampling Shell

$ X^{(i)} \sim \mathcal{K}_{\theta}(X_0, \sigma, \epsilon^{(i)}) $

• $ \mathcal{K}_{\theta}(\cdot) $ — proprietary transition kernel (withheld).
• $ X_0 $ — initial state.
• $ \sigma $ — equilibrium strategy vector.
• $ \epsilon^{(i)} $ — random seed stream.

4. Proportionality Metric Shell

$ m^{(i)} = \Gamma(X^{(i)}, \pi) $

• $ m^{(i)} $ — scalar metric for run $ i $.
• $ \Gamma(\cdot) $ — proprietary proportionality/impact functional (withheld).

5. Integration Contract

6. Public Pseudocode Shell

def monte_carlo_thresholds(X0, sigma, policy, n_runs, alpha):
    """
    Public shell — internal logic withheld.
    """

    samples = []

    for i in range(n_runs):

        # 1. Sample trajectory (kernel redacted)
        path = sample_trajectory(X0, sigma, policy)  # redacted

        # 2. Compute proportionality metric (redacted)
        m_i = compute_metric(path, policy)           # redacted

        samples.append(m_i)

    # 3. Compute threshold
    threshold = quantile(samples, alpha)

    # 4. Build abstract scenario envelope
    envelope = build_envelope(threshold)            # redacted

    return threshold, envelope
        

7. Deployment Notes

• Lives behind NashMarkAI sealed stochastic layer.
• No access to kernels, seeds, convergence tests or weighting tensors.
• Exposes only quantiles and envelopes never raw paths or tensors.
• Used for legal proportionality tests, remedy calibration and risk envelopes.

© 2025 Truthfarian · Monte Carlo Proportionality Thresholds · IP-Restricted Component