IndisputableMonolith.Physics.OpticalTrapRegimesFromJCost
Module classifying optical-trap operating regimes from the Recognition Science J-cost. It introduces a finite regime type, a count of regimes, and a certificate package that pins trap parameters to RS-native constants. Experimentalists matching trap stiffness or recoil scales to the phi-ladder would cite it. Structure is definitional plus a lightweight certificate, not a deep derivation.
claimA finite type of optical-trap regimes together with a regime count and an $OpticalTrap$ certificate linking trap scales to the J-cost $J(x)=(x+x^{-1})/2-1$ and RS constants ($\tau_0=1$ tick, $\phi$-ladder units).
background
Recognition Science derives kinematics and coupling scales from the unique cost $J(x)=(x+x^{-1})/2-1$ (equivalently $\cosh(\log x)-1$) fixed by the Recognition Composition Law. Optical traps sit at the interface of that cost with laboratory length and frequency scales: trap depth, recoil energy, and Lamb-Dicke parameter must be expressed in RS-native units built from the tick $\tau_0=1$ and the golden ratio $\phi$.
The module imports only Mathlib and Constants (which fixes $\tau_0$). It therefore works in the RS unit system where $c=1$ and dimensionful trap quantities are pure numbers on the $\phi$-ladder. The local objects are a discrete regime label, its cardinality, and a certificate bundle that records which regime is realized for given dimensionless trap parameters.
proof idea
Definition module. It declares a regime enumeration, a count of those constructors, a certificate structure packing the regime claim with the supporting dimensionless inequalities, and a default certificate instance. No substantial tactic proof; the content is type-level classification plus a packaged witness.
why it matters in Recognition Science
Places laboratory optical-trap regimes inside the same J-cost ledger that forces $D=3$, the eight-tick octave, and the $\phi$-ladder mass formula. Downstream physics pages that match trap-based mass or frequency measurements to RS predictions need a named regime certificate so the comparison is not ad hoc. With no recorded used-by edges yet, the module is a leaf that future atomic-physics or precision-measurement developments can import when closing the loop from J-cost to concrete trap data.
scope and limits
- Does not derive trap Hamiltonians or master equations from J-cost.
- Does not compute numerical stiffness, depth, or recoil values for a specific apparatus.
- Does not prove uniqueness of the regime partition beyond the declared constructors.
- Does not connect regimes to the alpha band or mass-ladder gap formula.
- Does not supply experimental error bars or unit-conversion lemmas outside RS-native units.