marsAtmosphereJCostScheduleCert
plain-language theorem explainer
This definition assembles the complete MarsAtmosphereJCostScheduleCert structure by wiring the module's release-rate and cumulative-release lemmas into each field. Planetary engineers modeling CO2 release under J-cost optimality would cite it to confirm that the phi-ladder schedule is positive, strictly monotonic, and yields a geometric-sum cumulative. The construction is a direct record literal that delegates every property to sibling theorems.
Claim. Let $r(n)$ be the release rate at rung $n$ and $C(n)$ the cumulative release. The certificate is the structure satisfying $r(0)=r_0$, $r(n)>0$ for all $n$, $r(n+1)=r(n)·φ$, $r$ strictly increasing, $C(0)=0$, $C(n+1)=C(n)+r(n)$, $C(n)≥0$, and $C$ strictly increasing.
background
The module implements Track J2 of the Recognition Science engineering plan for Mars terraforming. Release rate is defined by the recurrence $r(n+1)=r(n)·φ$ with initial value $r_0=1$, and cumulative release is the partial sum $C(n)=∑_{k=0}^{n-1} r(k)$. The structure MarsAtmosphereJCostScheduleCert packages eight required properties: rate zero at $n=0$, positivity, successor step with factor φ, strict monotonicity of rates, cumulative zero, cumulative successor, nonnegativity, and strict monotonicity of cumulatives.
proof idea
The definition is a direct structure constructor. It assigns rate_zero to releaseRate_zero, rate_pos to releaseRate_pos, rate_succ to releaseRate_succ, rate_strict_mono to releaseRate_strict_mono, cumulative_zero to cumulativeRelease_zero, cumulative_succ to cumulativeRelease_succ, cumulative_nonneg to cumulativeRelease_nonneg, and cumulative_strict_mono to cumulativeRelease_strict_mono.
why it matters
This definition supplies the terminal certificate for the J-cost-optimal CO2 release schedule on Mars, realizing the geometric-sum identity stated in the module header. It closes the engineering derivation that release follows the phi-ladder with 45-year rung spacing, consistent with the self-similar fixed point and eight-tick octave of the Recognition framework. No downstream theorems depend on it yet.
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