Foundations

For a validated linear first-order sensor model τẏ+y=Kx with τ>0, a step to x_f gives y(t)=Kx_f+[y(0)−Kx_f]e^(−t/τ).

An isotope delta compares a specified sample isotope ratio with the same ratio in a stated reference.

For a vector measurand Y=f(X), propagating a joint input distribution retains output dependence and non-Gaussian shape.

For a nonsingular m-variate Gaussian assigned distribution with mean y and known covariance U, (Y−y)ᵀU⁻¹(Y−y)≤χ²_(m,p) gives probability p.

Monte Carlo draws from the joint input model and evaluates all outputs from each common draw.

Under an assigned distribution g_Y for a measurand and a specification interval[T_L,T_U], the conformity probability is∫_(T_L)^(T_U)g_Y(y)dy.

For an upper specification limit T and assigned Y|data∼N(y,u²), accepting only y≤T−zu ensures Pr(Y>T|data)≤1−Φ(z) under that model.

Specific risk concerns an item given its measurement information.

For a causal linear time-invariant sensor with specified initial state, output is the convolution of input with impulse response plus noise.

A normalized frequency-domain Tikhonov inverse G=H*/(|H|²+λ²|L|²) suppresses ill-conditioned frequencies instead of dividing by an arbitrarily small H.

For N observations of one stationary process with covariance C_ij, Var(mean)=N⁻²Σ_ijC_ij.

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.

For linear observations z=Aθ+ε with known positive-definite covariance Σ and full-column-rank A, generalized least squares yields θ̂=(AᵀΣ⁻¹A)⁻¹AᵀΣ⁻¹z.

A network model can include per-instrument offsets, temporal drift, shared-reference effects and between-day variability alongside statistical noise.

A discrepancy term δ(x) represents inadequacy of the physical response model, distinct from repeatability noise and uncertain calibration parameters.

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.

Equal dimensions do not make quantities interchangeable.

A numerical value depends on the chosen unit.

Coherence means no extra numerical factor in the base-unit product.

Ordering and category labels do not justify ordinary arithmetic.

A physical phenomenon, an approach and a detailed procedure have different roles.