IndisputableMonolith.Chemistry.CrystalGrowthFromPhiLadder
This module defines types and functions for modeling crystal habits and growth using the phi-ladder from Recognition Science. It introduces CrystalHabit, undercooling thresholds, habit counts, and growth certificates as mathematical objects in the Chemistry domain. Researchers applying RS to condensed matter would reference it for deriving chemical patterns from the forcing chain. The module is purely definitional with no theorems or proofs.
claimDefines CrystalHabit as a type indexed by rung on the phi-ladder, undercoolingThreshold = phi^{-1}, undercoolingRatio as a function of defect distance, crystalHabitCount : Nat, and CrystalGrowthCert as a Prop certifying growth when ratio exceeds threshold.
background
The module imports Constants, whose sole content is the RS time quantum tau_0 = 1 tick. It operates in the Chemistry domain and introduces definitions that apply the phi-ladder (rung-based scaling with phi) to crystal structures. Key objects include CrystalHabit (habit type at a given rung), undercoolingThreshold and undercoolingRatio (threshold and ratio derived from phi powers), crystalHabitCount (enumeration of habits), and CrystalGrowthCert (certificate type for valid growth).
proof idea
this is a definition module, no proofs
why it matters in Recognition Science
The module supplies the definitional layer for crystal growth in the Chemistry domain, feeding the broader Recognition Science application of the phi-ladder (T6 self-similar fixed point) and mass formula to chemical systems. It positions crystal habits as direct consequences of the eight-tick octave and D=3 spatial structure without yet linking to downstream theorems.
scope and limits
- Does not contain any theorems or proofs.
- Does not reference experimental crystal data.
- Does not derive numerical predictions for specific materials.
- Does not connect to the Recognition Composition Law or J-cost.