| Module | Tier | Model |
|---|
| Cloud collapse | L0 | Tracer parcels circularise at r = j²/GM; angular momentum from solid-body rotation + turbulence. Low-j parcels fall into the protostar. Visual plus initial Σ(r) only. |
| Gas disk | L1 | α-disk, ν ∝ r; viscous diffusion solved implicitly in X = 2√r (Lynden-Bell & Pringle 1974); external photoevaporation beyond ~3 AU plus an inner "UV switch" once supply fails (Clarke et al. 2001). |
| Dust | L1 | Two-population pebbles (Birnstiel, Klahr & Ercolano 2012): fragmentation-limited Stokes number (1 m/s silicate, 10 m/s ice), growth time ∝ 1/(ZΩ), radial drift v = −2St/(1+St²)·ηvK, semi-Lagrangian transport, snow line that cools from ~6 to 2.7 AU, vapour recondensation outside it (Drążkowska & Alibert 2017). |
| Planetesimals | L0 | Streaming-instability threshold rule: Z > 0.02 and St above a floor; oligarchic embryo spacing 8% in r. |
| Pebble accretion | L1 | ε = 0.06·(m/M⊕)^⅔·√(St/0.01) of the flux crossing the orbit (Ormel & Liu 2018 scaling); pebble isolation mass 20 M⊕·(h/r / 0.05)³ (Bitsch et al. 2018) blocks the inward flux. |
| Gas accretion | L0 | Kelvin–Helmholtz contraction τ ∝ (m/10 M⊕)^−2.5 past half the isolation mass, capped by a gap-limited fraction of the viscous inflow. |
| Migration | L0 | Type I (Tanaka et al. 2002) with an efficiency factor; Type II at the viscous rate with gap inertia; first-order resonance capture for converging pairs; giant pairs in resonance reverse (Grand Tack flavour, Walsh et al. 2011). |
| Assembly | L0 | Kepler orbits + Monte Carlo encounters for crossing or Hill-unstable (< K RH) pairs; merge/scatter/eject outcomes; giant-planet instability sampled at 10–100 Myr after gas dispersal (Avdellidou et al. 2024; Izidoro et al. 2024). Stand-in for the TRACE-class N-body window. |
| Interior | L1 | Parameterised convection Nu ∝ Ra^⅓ with Arrhenius viscosity softened by mantle water; BSE radiogenics U/Th/K back-calculated; regime classifier mobile / episodic / stagnant / heat-pipe with 20 Myr persistence; dynamo from core heat-flux density. |
| Volatiles | L1 | CO₂ outgassing ∝ heat flow × melt fraction × reservoir; Walker–Hays–Kasting silicate weathering (supply-limited) + seafloor weathering; carbonates return to the mantle only under a mobile lid (Foley & Smye 2018 for stagnant lids). Water exchanged mantle↔surface; escape = min(energy-limited XUV, diffusion-limited) with dynamo shielding. |
| Climate | L0 | 0-D grey energy balance with CO₂ + H₂O optical depth, ice–albedo feedback (bistable → snowballs), runaway above 300 W m⁻² absorbed (Goldblatt et al. 2013); faint young Sun L(t) from Gough (1981); XUV decline ∝ t^−1.2 (Ribas et al. 2005). Sub-cycled 5× per Myr. |
| Impacts | L1 | Impactor population: flux of D > 1 km bodies calibrated to ~1.5 /Myr on present Earth with an accretion tail (×1500 at year 0, e-folding 150 Myr; Marchi et al. 2014 sawtooth, no cataclysm), cumulative size distribution N(>D) ∝ D⁻², gravitational focusing by mass, asteroid (2600 kg m⁻³, 10–22 km/s) vs comet (800 kg m⁻³, 28–53 km/s) populations, Oort showers ×20 with 80% comets. Each resolved impactor gets a final crater from Schmidt–Holsapple scaling (D_c ∝ D^0.78 v^0.44 g^−0.22), atmosphere erosion ∝ D^1.5 v²/g, volatile delivery (50% comet, 5% asteroid water), and a thermal outcome from E / E_vaporise(ocean): upper-ocean boiling above 5%, global sterilisation above 50% (Sleep & Zahnle), ice-shell shattering above 2×10²⁶ J, re-melting above 3×10²⁸ J. Craters erase on the regime's resurfacing timescale. |
| Game layer | — | Decision points are pure functions of state (they never change it); the player's choice is an ordinary logged command at that step, so a run with decisions replays exactly. Every moment offers interventions that cost power and a draw that gains it. Foresight is a replay of the same run advanced ahead. The mandate scores Year-0 structure, habitability time and the gate. Cinematics are camera work over live state (first occurrence per kind, at most eight per run, each tied to a decision); the only pictorial license is the gate scene and the gas-giant streamers, which are drawn from the model's numbers rather than simulated. |
| Life gate | L0 | Hazard rate λk = λ0,k·w(t)·W·Ek·Ck·P·S for three pathways (warm little ponds, alkaline vents, sub-ice ocean); P = 1 − exp(−∫Σλ dt). w(t) = 0.25 + 0.75·e^(−t/1.2 Gyr) is the prebiotic window: the reducing early atmosphere and impact-delivered feedstock (Benner et al. 2020; Pearce et al. 2017) fade with age, so a world that becomes habitable late has a much harder time. At difficulty 1.0 an Earth analogue gets first life ~100–500 Myr after habitability (Kipping 2020, 2025); the default 1.3 is a game setting. First-life time is sampled from the seed. |