IndisputableMonolith.Chemistry.CrystalGrowthFromPhiLadder
This module maps Recognition Science's phi-ladder to crystal growth parameters in chemistry. It defines CrystalHabit as rung-indexed habits, undercoolingThreshold, undercoolingRatio, and CrystalGrowthCert using the base time quantum from Constants. The module is purely definitional and supplies the interface for applying self-similar structures to crystallization. No theorems or proofs appear.
claimCrystalHabit : rung index to crystal habit; undercoolingThreshold = phi^{-1}; undercoolingRatio satisfies J(undercoolingRatio) = phi^{-3}; CrystalGrowthCert asserts valid growth configuration on the phi-ladder.
background
Recognition Science derives all structures from the J-functional equation and its phi fixed point, with the eight-tick octave setting periodic scales. The imported Constants module fixes the RS-native time quantum tau_0 = 1 tick as the base unit. This chemistry module extends that ladder to material growth by introducing CrystalHabit as the enumeration of discrete habits, crystalHabitCount as the cardinality of allowed habits, undercoolingThreshold as the initiation point, and CrystalGrowthCert as the certifying proposition.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The module supplies the chemistry-specific layer that applies the phi-ladder and Recognition Composition Law to crystal growth. It feeds the broader Recognition framework by providing CrystalGrowthCert for material certification, extending the T0-T8 chain into the chemistry domain. No downstream declarations are listed, marking it as a terminal definitions block.
scope and limits
- Does not derive lattice constants for specific substances.
- Does not include experimental matching or numerical simulation.
- Does not address non-crystalline phases or amorphous solids.
- Does not prove dynamical stability of the defined habits.