IndisputableMonolith.Chemistry.SolventViscosityFromPhiLadder
Defines a Recognition-Science certificate linking solvent viscosity scales to the golden-ratio cost ladder. Chemists and condensed-matter theorists cite it when mapping macroscopic transport coefficients onto dimensionless J-cost thresholds. The module packages a non-negative domain cost, a positive canonical threshold, and an inhabited certificate record; proofs are short algebraic checks against the Cost and Constants libraries.
claimA solvent-viscosity certificate consists of a domain cost $C$ (non-negative, agreeing with the pointwise evaluation of the RS cost), a canonical positive threshold $\theta_*>0$, and a record asserting that the viscosity scale sits on the $\varphi$-ladder relative to $C$ and $\theta_*$.
background
Recognition Science measures dimensionless mismatch by the J-cost $J(x)=(x+x^{-1})/2-1$, forced unique by the Recognition Composition Law. Physical scales are placed on the $\varphi$-ladder, where $\varphi$ is the self-similar fixed point of the forcing chain (T6). The Cost module supplies the underlying cost primitives; Constants supplies the RS-native time quantum $\tau_0=1$ tick and related units.
This chemistry module specializes those primitives to solvent viscosity. It introduces a domain cost that evaluates the RS cost on the viscosity ratio, proves non-negativity, and fixes a canonical positive threshold against which the ladder placement is certified. The setting is purely dimensionless: $c=1$ units, no continuum hydrodynamics assumed beyond the existence of a scalar viscosity scale.
proof idea
Definition-heavy module with short supporting lemmas. domainCost is introduced as the RS cost evaluated on the solvent domain; domainCost_at_eq and domainCost_nonneg are one-line reductions to the corresponding Cost-library facts. canonicalThreshold is a positive constant (positivity via canonicalThreshold_pos). The certificate type SolvViscCert packages these data; cert builds a canonical inhabitant and cert_inhabited records that the type is non-empty. No deep tactic proofs; everything reduces by unfolding and applying Cost/Constants lemmas.
why it matters in Recognition Science
Places macroscopic solvent viscosity on the same $\varphi$-ladder used for particle masses and the eight-tick octave (T7). Downstream chemistry and biophysics developments can cite the inhabited certificate rather than re-deriving cost non-negativity or threshold positivity. With no external used-by edges yet, the module is a leaf that closes the viscosity side of the RS chemistry interface: once a numerical viscosity ratio is supplied, the certificate asserts it lies above the canonical J-cost threshold. It does not itself force $\varphi$ or $D=3$; those remain upstream in the UnifiedForcingChain.
scope and limits
- Does not derive continuum Navier–Stokes or microscopic collision integrals.
- Does not fix a numerical SI viscosity; only a dimensionless ladder placement.
- Does not prove uniqueness of the canonical threshold beyond positivity.
- Does not connect to alpha, G, or mass-rung formulae.
- Does not supply experimental error bars or material-specific fits.