Amurlin mathematical model
> Documentation version 0.1. Amurlin’s creation is a scenario condition, not a forecast or a claim about a real political process.
Two distinct questions
The archive separates formation from development after formation. The working formulation for formation is P(M,T,G,U | E,D_t,θ): mechanism, timing, territory, stability, an explicit creation condition, information available at time (t), and transparent assumptions. It frames research questions; it does not yet estimate empirical probabilities.
Prototype 0.1 instead compares a specified territory under four formation pathways with a control path where no new state is formed. It does not calculate the probability of sovereignty or describe an existing country.
Prototype 0.1
- 17 regions in three territorial contours and seven external presets;
- annual time step, four age cohorts, and five productive sectors;
- capital, investment lags and depreciation; output constrained by energy and labour;
- budget, reserves and debt; public and private investment;
- external shocks, conditional energy imports and paired controls;
- medians, 10–90 intervals, reproducible seed, CSV and JSON export.
The archived 21 configurations × 150 paired runs test the core’s behaviour under illustrative coefficients. They are not a regional forecast and are not calibrated from daily monitoring records.
Core equations
P(t) = P(t−1) + births(t) − deaths(t) + net_migration(t)
Y_s(t) = A_s(t) × K_s(t)^α × L_s(t)^(1−α) × energy_multiplier(t)
energy_multiplier(t) = min(1, (supply(t) + imports(t)) / demand(t))
K_s(t+1) = (1−δ) × K_s(t) + investment_s(t−lag_s)
Δdebt(t) − Δreserve(t) = spending(t) − revenue(t)Scenarios, data, and next-version requirements
The four paths are treaty unification, gradual integration, a temporary buffer, and external patronage, plus a no-new-state control. They are modelling mechanisms rather than assessed political likelihoods. Data records require territory-version, period, unit, source, retrieval time, method and uncertainty. Current inputs still require harmonised boundaries, prices and sector classifications.
The next version must add: probability assessment for formation and recognition alongside competing explanations for observed signals; a political logit and explicit coalition game, with Blotto or Tullock variants only after players, resources and payoff functions are specified; a transport graph, interregional flows, food and water balances; and trade balance, currency regime, banks, default states, rights and political participation. Each module requires source data, identifiable parameters, alternative hypotheses, and held-out validation before it is presented as working. A Monte Carlo success share remains conditional on selected distributions, not a fact about the future.