IndisputableMonolith.Archaeology.CivilizationComplexityFromZRung
This module defines complexity tiers and certification structures for civilizations derived from the Z-rung parameter on the Recognition Science phi-ladder. Archaeologists and complexity modelers would cite it to quantify societal development stages in RS-native units. It consists entirely of definitions for ComplexityTier, tier thresholds, tierCount, and CivilizationCert, with supporting positivity and ratio lemmas but no proofs.
claimDefines ComplexityTier as a discrete level function of Z-rung, tierThreshold as the boundary map from rung to real value, tierCount as the number of tiers, and CivilizationCert as the structure certifying a civilization at a given tier from its Z-rung.
background
Recognition Science places all scales on the phi-ladder, where the mass formula uses yardstick times phi to the power (rung minus 8 plus gap(Z)). This module imports the base time quantum tau_0 equals 1 tick from Constants and applies the Z-rung to human-scale complexity. Sibling definitions introduce ComplexityTier, tierThreshold with its positivity and ratio properties, tierCount, and CivilizationCert as the certifying object.
proof idea
This is a definition module, no proofs. The structure proceeds by defining ComplexityTier from rung thresholds, proving tierThreshold_pos and tierThreshold_ratio, computing tierCount, and packaging the result into CivilizationCert.
why it matters in Recognition Science
The module supplies the definitional layer that lets the Recognition Science phi-ladder and eight-tick octave reach archaeological scales. It supports extension of the T0-T8 forcing chain and the mass formula into civilization modeling, though no downstream theorems currently list it as a dependency.
scope and limits
- Does not derive Z-rung values from empirical data.
- Does not prove dynamical evolution of tiers over time.
- Does not compare tiers to non-RS complexity metrics.
- Does not incorporate Berry creation threshold or dream fraction.