IndisputableMonolith.Chemistry.PolymerChainLengthFromPhiLadder
This module defines polymer chain lengths, regimes, and persistence lengths by applying the phi-ladder scaling to chemical polymers in Recognition Science. It supplies the length formulas that extend the mass formula yardstick * phi^(rung-8+gap(Z)) into the chemistry domain. Biophysicists and materials modelers would cite these when predicting chain behavior from RS-native units. The module consists of sequential definitions built on the imported Constants module.
claimPolymer chain length on the phi-ladder: $L = $ persistenceLength $ * $ phi^{rung}, with PolymerRegime classifying scaling behaviors and PolymerChainCert certifying the resulting lengths in units where $tau_0 = 1$ tick.
background
The module resides in the Chemistry domain and imports the fundamental RS time quantum tau_0 = 1 tick from IndisputableMonolith.Constants. It introduces PolymerRegime as a classification of polymer scaling regimes, persistenceLength as the base length scale, and persistenceLengthRatio for relative measures, all scaled via the phi-ladder. These rest on the self-similar fixed point phi from the forcing chain (T5 J-uniqueness and T6 phi fixed point) together with the Recognition Composition Law.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
This module supplies the polymer-specific length scalings that feed higher-level chemistry results such as PolymerChainCert. It bridges the phi-ladder (T6 self-similar fixed point, eight-tick octave T7) to macroscopic chain properties, complementing the mass formula and alpha band constants. No downstream theorems are listed, indicating it serves as a foundational block for the chemistry domain.
scope and limits
- Does not compute numerical lengths for named polymers.
- Does not incorporate solvent or temperature dependence.
- Does not address entanglement or branching topologies.
- Does not prove uniqueness of the phi-ladder mapping for all chains.