Report-backed operational evidence with uncertainty

Adopt the laboratory region with its inertial chart and fixed-time reading of Laboratory geometry: a restricted inertial chart, its spatial slices and fixed-time fields, the electric and magnetic fields of The electric and magnetic fields as fixed-time spatial vector fields, the charge parameter, frame charge and current densities and charge integrals of Charge parameter, frame charge and current densities, volume charge and flux, and the four-current, and the SI units and constants of Framework-local SI units, the vacuum constants and the exact/measured status of their values. This definition fixes the framework's report-record vocabulary; it selects no experiment, records no value, evaluates no indicator and asserts no measurement.

(a) [Primary source] A primary source is a declared bibliographic identification of a report (author, title, date, publication, and the identification of the passages actually inspected) together with the declared limits of the reading: which parts of the report were read, which were not, and any carrier defects (for instance corrupted optical-character-recognition text of formulae or tables).

(b) [Comparison quantity and measurand] Let $d\ge 1$ be an integer. A comparison quantity of dimension $d$ is a declared map from a declared condition set to ${\mathbb{R}}^d$, with declared units, whose components are finite expressions in specified framework quantities. These may include the values of $E,B,\rho ,J$ at declared events, the charge parameter $q$, and the declared charge or current integrals of Charge parameter, frame charge and current densities, volume charge and flux, and the four-current; declared field circulations and surface fluxes on the admitted fixed geometries of Fixed volume and patch test geometries, outward normals and induced orientations; and declared finite-time or period averages of specified derived field quantities, including $u$ and $S$ of Vacuum electromagnetic energy density and energy flux (the Poynting vector). An integral or average is admitted only with its domain, orientation where needed, integration convention and actual well-definedness hypotheses declared. For example, a component $Q(t)$ continuous on a declared compact interval $[a,b]$ inside the laboratory time domain, with $a<b$, has the finite Riemann average $(b-a{)}^{-1}{\int }_a^{b}Q(t)dt$ by A continuous function on $[a,b]$ is Riemann integrable, by Heine-Cantor and Riemann's criterion; a period average additionally declares the period and interval. Field fluxes inherit the regularity, compactness, boundary presentation and measure/choice conventions of their fixed-test supplier. A declared detector-response integral may be used only when its declared model and integral suppliers establish a finite real value. An extended nonnegative integral with value $+\mathrm{\infty }$ is not a component of this real-valued comparison map or a recorded finite rate. No existence or finiteness of an arbitrary field integral, distributional product or detector response is asserted. A measurand is a comparison quantity together with a declared condition description under which it is to be read. All quantities carry the SI conventions of Framework-local SI units, the vacuum constants and the exact/measured status of their values.

(c) [Apparatus and preparation description] An apparatus-and-preparation description is a declared finite record of the apparatus, the preparation, the controls and the environment in the report's own terms, with the identification of the passage of the primary source of (a) from which each item of the description is taken. The definition asserts only that the description is declared and finite; it asserts nothing about its correctness or completeness.

(d) [Recorded data and reported observations] For an integer $d\ge 1$, a recorded datum is a vector $z_k\in {\mathbb{R}}^d$ with declared units together with a condition annotation $a_k$, a declared finite text identifying the declared run condition of the datum and, when the datum is taken from a report, its locator in the primary source. A reported observation is a declared finite text recording a qualitative observation of the report. A record is a finite tuple of recorded data and reported observations together with the declared condition annotations. The record contains no probability space, random variable, distribution, sampling law, independence assumption, likelihood or coverage statement.

(e) [Calibration model] A calibration model is a tuple $(Z,c,\delta )$ in which $Z$ is a declared nonempty set of apparatus-output values, $c:Z\to {\mathbb{R}}^d$ is a declared calibration map and $\delta \in [0,\mathrm{\infty })$ is a declared calibration-error bound: it declares that for every output $o\in Z$ obtained under the declared conditions, the value of the comparison quantity of (b) lies in the closed box ${\prod }_{j=1}^d[c_j(o)-\delta ,c_j(o)+\delta ]$ in the declared units. A calibration model is a declaration; the definition asserts no accuracy beyond the bound $\delta$ and no statistical property of $c$ or $\delta$. A declared missing calibration is recorded as missing, and no value or bound is then available from this clause.

(f) [Uncertainty record] An uncertainty record is a finite tuple of declared bounds, each carrying a declared source label from the finite list $\{calibration,resolution,systematic,sampling-variability,rounding,other\}$ and a declared value in the declared units; each entry is a declared constraint of the form of (e), and the record may state that a bound is unavailable. No entry is a standard-deviation convention, a coverage probability, a confidence level, a $p$-value, a posterior or a probability law.

(g) [Analysis assumptions] An analysis-assumption list is a finite tuple of declared assumptions used to obtain the recorded data or to compare them with a model (binning, background model, selection rules, corrections, fitting or estimation procedure, independence or dependence of entries, and the treatment of the sources of uncertainty); declared omissions are recorded as omissions and are not filled in by the definition.

(h) [Interpretation] An interpretation is a declared statement that identifies a specified model prediction and declares the result of comparing the record with it (support, constraint, failure to distinguish, or no conclusion), conditional on (a)-(g). The interpretation is part of the report account and not of the data; it asserts no probability, no significance level and no truth of any framework, and it records a comparison of a specified model, not of a whole theory.

(i) [Well-definedness and scope] All components of (a)-(h) are finite tuples, real numbers, declared maps on declared sets and finite text labels; forming this finite vocabulary uses no choice principle. Evaluating a comparison quantity inherits every hypothesis and axiom of its actual suppliers, including countable choice when the selected fixed-test surface or Lebesgue-measure interface requires it; no measurability, integrability, completeness or differentiability is inferred merely from the record. A comparison quantity is evaluated only where the cited items supply its ingredients and a finite value. Missing source detail stays missing: no universal sampling law, precision, independence, coverage or calibration correctness is part of the definition, and none may be inferred from it. The definition is the framework-local vocabulary for the reports of this page; it does not assert that any laboratory realises a measurand or that any reported observation is correct.

The vocabulary above formalises the record fields of the three primary reports recorded on this page: a declared primary source with its reading limits, an apparatus-and-preparation description, finite recorded data or reported qualitative observations with condition annotations, a calibration model that may be declared missing, an uncertainty record of declared bounds with source labels, an analysis-assumption list with recorded omissions, and an interpretation separated from the data. The GUM clauses cited in the frontmatter supply the metrological vocabulary of measurand, measurement model, error correction and uncertainty source; the definition keeps every declared bound distinct from any coverage, confidence or probability statement, and it performs no numerical evaluation. No measurement, apparatus behaviour, sampling law, precision or calibration correctness is asserted, and no experiment is selected.