Foundations

c denotes the speed of light in vacuum. Its numerical value is fixed exactly in SI units.

h denotes the Planck constant. Its numerical value is fixed exactly in SI units.

ΔνCs denotes the unperturbed ground-state hyperfine transition frequency of caesium-133. Its numerical value is fixed exactly in SI units.

Seven named base units organize the SI quantity system.

Connect a result to a reference through documented calibrations.

The elementary charge has an exact SI numerical value.

The Boltzmann constant has an exact SI numerical value.

The mole is linked to a specified number of entities.

A specified frequency fixes the photometric SI reference.

Relate indications to standards, then infer measurement results.

An instrument calibration curve models indication y as a function of reference input x, such as y=a+bx+ε.

For the valid linear calibration y=a+bx, an unknown input is estimated as x̂=(y₀−â)/b̂.

Calibration-model validation examines residuals for curvature, unequal variance, dependence and outliers, and compares independent or check-standard results across the working range.

A measurement standard realizes a specified quantity with a stated value and uncertainty for reference use.

A reference material is sufficiently homogeneous and stable for specified properties and an intended measurement or examination use.

Fixing a defining constant's numerical value makes that SI definition exact; it does not make an experiment or transferred standard exact.

A primary caesium frequency standard relates its oscillator to the defining unperturbed Cs-133 hyperfine transition by estimating and correcting design-dependent shifts, including atomic-motion Doppler and thermal blackbody effects.

With calibrated light frequency f, vacuum wavelength is λ₀=c/f.

A Kibble balance combines weighing mg=I Bℓ with velocity-mode U=vBℓ to eliminate the common geometry-field factor: mgv=IU.

A calibration likelihood can treat reference values x_i as latent uncertain quantities, with measured standards r_i and instrument indications y_i modelled jointly around x_i and f(x_i,θ).

Calibration parameters are identifiable only when distinct parameter values lead to distinguishable predictions for the available design and reference information.

A posterior predictive distribution integrates p(y_new|θ) over p(θ|data), retaining parameter uncertainty under the declared model.

For ν independent repetitions of a specified parameter-encoding state/channel, a locally unbiased estimator obeys Var(θ̂)≥1/(νF_Q) when the regularity assumptions apply.

Squeezing lowers noise in one optical quadrature while increasing conjugate noise.

Jia, Xu and collaborators reported quantum noise below a stated free-mass standard quantum limit by up to 3 dB with broadband sensitivity improvement using frequency-dependent squeezing.

Optical transition standards on the CIPM list are secondary representations of the second; their improved instrument performance does not itself change the SI definition.

Aeppli and collaborators' archived 2025/2026 report compares 27Al⁺, 171Yb and 87Sr optical clocks with reported total fractional ratio uncertainties at or below 3.2×10⁻¹⁸.

Reference-material value assignments have distinct status.

The 12 May 2026 NIST certificate for Great Lakes Fish Tissue certifies total mercury and selected PCB, pesticide and PBDE values on a wet-mass basis.

Detector-based radiation thermometry infers thermodynamic temperature from calibrated spectral radiance, while transfer thermometers and blackbody realizations disseminate a scale.