civilizationCert
plain-language theorem explainer
civilizationCert supplies the concrete instance of the CivilizationCert structure by wiring the five-tier cardinality together with the positivity and phi-squared ratio properties. Researchers modeling societal evolution via Z-rung complexity would cite it to instantiate the canonical five-tier archaeology model. The definition is assembled as a direct structure literal that delegates each field to the supporting tier theorems.
Claim. The civilization certificate is the structure satisfying: there are exactly five complexity tiers, every tier threshold is positive, and consecutive thresholds obey the ratio $threshold(k+1)/threshold(k)=phi^2$.
background
In the Archaeology module, civilizational complexity C is identified with the Z-rung of the societal recognition substrate. Five canonical tiers follow Bondarenko: band (Z-rung 0-2), tribe (3-5), chiefdom (6-8), state (9-11), empire (12+). The module states that adjacent tier thresholds stand in ratio phi squared, consistent with the RS prediction that complexity scales follow the golden ratio.
proof idea
The definition is a one-line structure constructor that supplies the five_tiers field from the tierCount theorem, the threshold_pos field from tierThreshold_pos, and the phi_sq_ratio field from tierThreshold_ratio.
why it matters
This definition closes the CivilizationComplexityFromZRung module by furnishing the concrete certificate that realizes the five-tier model with phi-squared scaling. It directly encodes the RS claim that complexity thresholds follow phi^2, aligning with configDim D=5 and the eight-tick octave. No downstream uses are recorded, indicating it functions as a terminal interface for higher-level archaeology statements.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.