IndisputableMonolith.Chemistry.PolymerChainLengthFromPhiLadder
Defines polymer regimes, persistence length, and their ratio as pure powers of φ on the Recognition Science ladder. Soft-matter or biophysics workers inside RS cite the regime count and the certified length formulae. The module is definitional: structures, counts, and a packaging certificate with no deep proof obligations.
claimOn the $\varphi$-ladder the module introduces polymer regimes, a regime count, persistence length $\ell_p$ (a yardstick times a pure power of $\varphi$), the dimensionless ratio $\ell_p$ to monomer scale, and a certificate packaging these data.
background
Recognition Science places every length on a discrete $\varphi$-ladder whose self-similar ratio is forced at T6. The only external import is the Constants module, which supplies the RS-native time quantum $\tau_0=1$ tick and the global yardstick conventions.
A polymer regime is a discrete classification of chain flexibility according to how many $\varphi$-rungs separate contour length from the Kuhn or persistence scale. Persistence length is therefore written as yardstick times $\varphi$ to an integer power; the ratio of persistence length to monomer length collapses to a pure power of $\varphi$.
The module packages the regime enumeration, the two length maps, and a default certificate so that later chemistry results can quote an RS-native persistence length without leaving the ladder.
proof idea
Definition module. It declares the inductive or enumerated type PolymerRegime, a counting function polymerRegimeCount, the maps persistenceLength and persistenceLengthRatio (pure $\varphi$-powers times yardstick), the structure PolymerChainCert that bundles them, and a canonical inhabitant polymerChainCert. No non-trivial lemmas or tactic proofs appear; equalities are definitional.
why it matters in Recognition Science
Gives the Chemistry domain an RS-native vocabulary for chain stiffness so that mass-ladder and eight-tick results can be applied to soft matter without unit conversion. The forcing of $\varphi$ (T6) and the spatial dimension D=3 (T8) are inherited silently through the ladder. No downstream theorems are recorded yet in the mirror graph; the module is infrastructure awaiting biopolymer or elastomer applications.
scope and limits
- Does not derive persistence length from a microscopic Hamiltonian or Flory theory.
- Does not claim numerical agreement with measured Kuhn lengths in SI units.
- Does not treat branched, ring, or cross-linked architectures.
- Does not fix absolute SI conversion factors; works in RS yardsticks only.