cosmologyDepthCert
plain-language theorem explainer
The definition supplies a certificate fixing the number of cosmological epochs at five within the Recognition Science model. A researcher modeling epoch-dependent J-cost regimes across inflation to de Sitter phases would cite it to anchor depth calculations. It is realized as a direct assignment of the decided cardinality result into the required structure field.
Claim. Let $C$ be the structure requiring that the finite cardinality of the set of cosmological epochs equals five. The cosmology depth certificate is the instance of $C$ obtained by substituting the enumeration result that establishes this cardinality.
background
The module identifies five canonical cosmological epochs with configuration dimension $D=5$ in Recognition Science. Each epoch maps to a distinct J-cost regime: inflation with $J$ approaching zero at reheating, radiation with thermal J-cost, matter domination, dark energy with $J$ locked yielding $Λ_{RS}≈1.91$, and future de Sitter. The upstream result cosmologicalEpochCount proves by decision that the cardinality of the enumerated set of cosmological epochs is exactly five, supplying the sole input to the structure.
proof idea
The definition is a one-line wrapper that populates the five_epochs field of the CosmologyDepthCert structure by direct reference to the decided cardinality theorem.
why it matters
This definition completes the A2/B12 step by certifying the five-epoch count required for J-cost depth calculations in the Recognition Science framework. It aligns with the configuration dimension $D=5$ and supports epoch transitions without axioms or sorry placeholders. The construction fixes the epoch count ahead of any phi-ladder mass or alpha-band applications.
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