Markov Temporal Mapping (IP-Restricted Component)

Markov Temporal is the NashMarkAI state–transition layer that encodes how systems move between legal, ecological and governance states over time. It provides the temporal Markov structure that drives NashMarkAI strategies, and supplies the state paths and distributions consumed by Sansana, PHM, Sentinel, SRAIGS and the wider enforcement stack.

IP–Restricted Component (NashMarkAI / Truthvenarian Jurisdiction)

Markov chains and temporal Markov processes are open mathematical constructs. However, all NashMarkAI-specific state spaces, transition kernels, legality labels, harm-bearing transitions, governance encodings and temporal windowing rules are proprietary. Only the public mathematical shell and pseudocode structure are disclosed here.

No rights are granted to reconstruct or approximate NashMarkAI transition kernels or state encodings from this page.

1. System Role

• Defines the temporal Markov structure for NashMarkAI legal, ecological and governance states.
• Generates state trajectories and distributions for strategy computation.
• Provides $ \pi_t $ and path samples to Sansana, PHM, Sentinel and Monte Carlo layers.
• Encodes time, jurisdiction and event progression in a single temporal model.
• Acts as the core stochastic backbone of the NashMarkAI mathematical stack.

2. Public Mathematical Shell

$ \pi_{t+1} = \pi_t \, P_{\theta} $

• $ \pi_t $ — state distribution at time $ t $.
• $ P_{\theta} $ — transition matrix / kernel parameterised by $ \theta $ (withheld).

$ X_{t+1} \sim \mathcal{K}_{\theta}(X_t, a_t, \epsilon_t) $

• $ X_t $ — system state (legal / ecological / governance state vector).
• $ a_t $ — action / policy / strategy choice (from NashMarkAI strategy layer).
• $ \epsilon_t $ — stochastic noise / disturbance.
• $ \mathcal{K}_{\theta}(\cdot) $ — proprietary temporal kernel (withheld).

3. Temporal Window Shell

$ W_{t}^{(\tau)} = \{ X_{t-\tau}, \dots, X_t \} $

• $ W_{t}^{(\tau)} $ — temporal window of length $ \tau $ used for drift, breach and risk analysis.
• $ \tau $ — window length (case- and jurisdiction-dependent; configuration is IP-restricted).

4. Integration Contract

5. Public Pseudocode Shell

def markov_temporal(X0, policy_sequence, kernel_params, horizon):
    """
    Public shell — full NashMarkAI kernel logic withheld.

    Inputs:
        X0              - initial state
        policy_sequence - sequence of actions / strategies a_t
        kernel_params   - abstract kernel parameters (θ)
        horizon         - total time steps T

    Outputs:
        path            - list of states [X_0, ..., X_T]
        distributions   - list of state distributions [π_0, ..., π_T]
        windows         - temporal windows for downstream engines
    """

    path = [X0]
    distributions = []
    windows = []

    # initialise distribution (details withheld)
    pi_t = initialise_distribution(X0)                    # redacted

    for t in range(horizon):
        a_t = policy_sequence[t]

        # 1. Sample next state (kernel withheld)
        X_next = sample_transition(path[-1], a_t, kernel_params)  # redacted
        path.append(X_next)

        # 2. Update distribution (details withheld)
        pi_t = update_distribution(pi_t, a_t, kernel_params)      # redacted
        distributions.append(pi_t)

        # 3. Build temporal window (details withheld)
        window = build_temporal_window(path)                      # redacted
        windows.append(window)

    return path, distributions, windows
        

6. Deployment Notes

• Forms the temporal backbone of NashMarkAI for all legal, ecological and governance simulations.
• Feeds Sansana, PHM, Sentinel, SRAIGS, Monte Carlo thresholds and higher-tier enforcement engines.
• Kernel definitions, state encodings and transition semantics remain fully IP-restricted.
• Used in litigation modelling, public-interest system simulations and ecological / infrastructure planning.

© 2025 Truthfarian · Markov Temporal · IP-Restricted Component