IndisputableMonolith.Sociology.CivilizationCyclesFromPhiLadder
This module defines a phi-ladder model for civilizational stages and cycle durations in sociology. It maps discrete stages onto self-similar scaling from the Recognition Science framework and uses the base time quantum from Constants. Researchers extending RS to social dynamics would cite these definitions to quantify historical cycle ratios. The module consists entirely of definitions with no theorems or proofs.
claimIntroduces the type $CivilizationalStage$ together with $civilizationalStageCount : Nat$, $cycleDuration : CivilizationalStage → Real$, and $cycleDurationRatio$ satisfying scaling relations derived from $φ$ on the phi-ladder with base unit $τ_0$.
background
The module sits inside the Recognition Science framework that derives structures from the J-functional equation and the forced self-similar fixed point phi. It imports the fundamental RS time quantum $τ_0 = 1$ tick from IndisputableMonolith.Constants. The setting treats civilization as progressing through discrete rungs whose durations scale by powers of phi, consistent with the mass formula and phi-ladder conventions used elsewhere in the monolith.
proof idea
This is a definition module, no proofs. It first imports Constants to obtain the base tick, then declares the CivilizationalStage type, followed by the count function, the duration map, the ratio abbreviation, and the certification structure CivilizationCyclesCert.
why it matters in Recognition Science
Supplies the definitional base for sociological applications of the phi-ladder, feeding into CivilizationCyclesCert and related certificates. It extends the core RS chain (T0–T8) by placing social cycle times on the same self-similar structure that yields D = 3 and the alpha band. No downstream uses appear yet, marking it as an interface layer for further interdisciplinary development.
scope and limits
- Does not incorporate empirical historical data or measurements.
- Does not derive specific numerical predictions for named civilizations.
- Does not address falsification against observed cycle lengths.
- Does not connect to the eight-tick octave or spatial dimension D = 3.