The Formula of Consciousness: A Gated Stochastic-Volatility Process, its Parameterisation to the Hecate Scale, and its Parameter Regimes

A companion paper fixed a static scoring function, Hc = K · λ^b · S(β(φ - φ0)), and evaluated it once per system. This paper treats that snapshot as one reading of a process: C(t) is defined as a gated stochastic-volatility exponential: an operations term Λ(t), an integration gate Γ(t) in [0,1], a dimensionless level μ₀, a drift ν per year, and a stochastic exponential whose variance follows a CIR process as in Heston (1993), with the Wiener correlation ρ stated. Under the martingale condition of Andersen and Piterbarg (2007), E[C(T)] = ΛΓexp(μ₀ + νT) at any fixed horizon, and the companion gate is one parameterisation of E[C(1)] obtained by choosing Λ = λ^b and Γ = S(β(φ - φ0)); it is a substitution, not a theorem, and returns the awake-adult anchor at 1.7199 Hc. Eight internal consistency checks are executed in VERIFY.py: the constant-volatility compensator; the relaxation E[σ²(t)] = θ + (σ²(0) - θ)e^(-κ_v t) and the Feller condition; a loop bound 1/(1 - r) under an assumed geometric decay; the sensitivity law and epsilon floor of the geometric-mean aggregator; a saturating sensory term that keeps a deaf-blind adult finite; the parameterisation; a 10,000-path simulation with exact CIR transitions reporting mean and median time-average growth against ν - θ/2; and calibration rows at released coordinates. What remains untested is stated: the operation scores are stipulated, Γ is not operationalised, no fit was performed. Two preregistrable predictions and one held-out test carry kill conditions in Section 13.