IndisputableMonolith.Physics.QuantumDot_Charging
Quantum-dot charging costs and thresholds in Recognition Science units. Defines a domain cost from the J-functional, a canonical charging threshold, and a certificate asserting nonnegativity and positivity. Anyone matching Coulomb-blockade or single-electron data to RS scales would cite the cert package. Structure is definitional, with short nonnegativity and positivity lemmas.
claimThe module defines a domain charging cost $C$ built from the Recognition cost $J$, a canonical threshold $\theta>0$, and a certificate package asserting $C\ge 0$ together with positivity of $\theta$, all in RS-native units.
background
Recognition Science measures configuration cost with the unique functional $J(x)=(x+x^{-1})/2-1$ (equivalently $\cosh(\log x)-1$), forced at T5 of the unified chain. The Cost import exposes that functional; Constants supplies the RS time quantum $\tau_0=1$ tick and the native unit conventions $c=1$, $\hbar=\phi^{-5}$.
This module specializes those primitives to quantum-dot charging: the energy scale for adding an electron to a confined island (Coulomb blockade / SET setting). Domain cost is the J-based cost of a charging configuration; the canonical threshold is the positive scale at which charging becomes favorable under RS units.
Sibling definitions record nonnegativity of the cost and positivity of the threshold, then bundle them into an inhabited certificate type for downstream physics checks.
proof idea
Definition module with short algebraic lemmas, not a forcing-chain argument. Domain cost wraps the imported $J$-cost on a domain parameter; equality-at-a-point and nonnegativity are immediate from Cost facts. The canonical threshold is a positive RS scale; its positivity lemma is a one-line arithmetic check. QDChargingCert packages those facts; cert and cert_inhabited witness that the package is inhabited.
why it matters in Recognition Science
Places quantum-dot charging on the RS cost ladder so Coulomb-blockade and single-electron-transistor observables can be compared to phi-ladder predictions and the native constants ($c=1$, $\hbar=\phi^{-5}$, $G=\phi^5/\pi$). Downstream used_by is currently empty: this is a leaf packaging layer rather than a link inside T0-T8. It closes a local physics interface (nonnegative cost, positive threshold) ready for numerical or experimental comparison, without claiming a full microscopic derivation of blockade spectra.
scope and limits
- Does not derive Coulomb-blockade spectra from first principles.
- Does not fix gate capacitance or charging energy in SI units.
- Does not connect to eight-tick octave or D=3 forcing steps.
- Does not prove uniqueness of the threshold beyond positivity.
- Does not model multi-electron or spin-blockade regimes.