Which experimental record controls

The primary source is Schlamminger and collaborators’ Redetermination of the gravitational constant with the BIPM torsion balance at NIST, Metrologia 63, 025012, DOI 10.1088/1681-7575/ae570f. The paper prints publication on April 16, 2026. It reports a combined estimate of 6.67387 ± 0.00038, multiplied by 10⁻¹¹ m³ kg⁻¹ s⁻², with relative standard uncertainty about 57 ppm. [1]

The NIST publication-metadata abstract displays a different numerical result. The paper itself, including its results tables and consensus treatment, governs this Brief. The combined estimate is not a mode gap or an independent fifth configuration. Its uncertainty reflects the consensus procedure rather than a simple reading of one primary mode budget. [1] [2]

What the two operating modes do

A torsion balance detects the torque generated by source masses acting on suspended test masses. In the free-deflection or Cavendish method, the pendulum moves and its angular response supplies the mechanical signal. In electrostatic-servo operation, feedback applies a balancing electrical torque to keep the angle fixed. Figure 1 shows these functions, rather than an engineering drawing of the actual apparatus. [3]

Both methods retain the gravitational interaction and their own calibration chain. Free operation is not devoid of electrical metrology, and servo operation does not replace gravity with an electromagnetic force between the source and test masses. The proposed MQ association concerns how the measured torque is realized and read out; it is an additional interpretation. [3] [4]

The four values and the covariance

Table 1 transcribes the mode central values from the paper’s Table 16 and the more detailed combined relative standard uncertainties from Tables 17–18. The uncertainty values include the stated primary contributions, rather than Type A statistical uncertainty alone. The common unit multiplier applies to each central value. [1]

The modes share input quantities, so their errors are correlated. Table 2 reproduces the six off-diagonal correlation coefficients from the paper’s Table 18 and supplies the unit diagonal appropriate to a correlation matrix. In the source table the diagonal instead prints relative standard uncertainties; those values are kept separately in Table 1 here. [1]

Copper provides a more precise contrast than sapphire. The paper’s uncertainty budget gives sapphire-free autocollimator nonlinearity as 85.7 ppm, compared with 14.2 ppm in copper-free operation. Its pressure-correction contribution is 21.5 ppm in both sapphire modes and 1.6 ppm in copper. These differences motivate examining the copper configuration without discarding the sapphire results. [1]

How the printed values give the mode contrast

The normalized contrast is the free-deflection central value divided by the servo central value, minus one, multiplied by one million. Thus the denominator is the servo value. Normalizing instead to free deflection or to a combined constant would define a different statistic. Parts per million, abbreviated ppm, means a dimensionless ratio scaled by one million.

First-order propagation uses the derivatives of this ratio with respect to both inputs. In ppm units, multiply the free-to-servo ratio by the square root of the sum of the squared relative standard uncertainties minus twice their correlation times their product. The negative cross term retains cancellation of shared uncertainty in the difference. This is correlated-input propagation, not addition of independent error bars. [1] [10]

For copper the ratio uses 6.674021 divided by 6.673642. The relative uncertainties are 30.3 and 23.2 ppm, with correlation 0.42. The calculation gives a contrast of 56.7906 ppm and standard uncertainty 29.4269 ppm, rounding to 56.79 ± 29.43 ppm. Ignoring the correlation would give 38.16 ppm uncertainty instead.

For sapphire the corresponding ratio uses 6.673636 divided by 6.672637, relative uncertainties 93.9 and 37.5 ppm and correlation 0.25. The result rounds to 149.72 ± 92.01 ppm. Small differences in extra decimal places from earlier MQ summaries reflect use of printed rounded inputs, not a different experimental dataset. The reproduced values here are rounded calculations from those explicit inputs.

The fixed MQ target in current notation

Let ${\mathrm{𝜃}}_{\mathrm{𝑠}\mathrm{𝑖}}$ be the dimensionless MQ invariant coefficient and ${\mathrm{𝑛}}_{\mathrm{𝐿}}$ the positive-real electromagnetic-demarcation length-count parameter. This calibrated continuation is distinct from primitive integer cardinality. Equation (1a) is the count constraint used for the current target. The central coefficient used in this illustration is 3.26239030504. [4] [7]

Let ${\mathrm{𝑄}}_{\mathrm{𝐿}}$ denote the dimensionless Diophantine realization residual. Equation (2b) defines it for the positive count. The numerical evaluation uses the algebraically equal reciprocal of the sum of the root and the count to avoid subtractive cancellation. [7]

Here upright $\mathrm{G}$ denotes the upper-count gravitational coupling, while italic $\mathrm{𝐺}$ denotes the finite-count electromagnetic-demarcation coupling. Both have units m³ kg⁻¹ s⁻². The source relation is Equation (3c); typography distinguishes the realization regimes. [4] [7]

Dividing Equation (3c) gives the exact fractional separation in Equation (4d). Multiplying that dimensionless expression by one million produces the ppm target. Brief labels are separate from the source’s equation numbers.

The current calculation gives count 84.6005456716 and target 34.9284 ppm after displayed rounding. Associating free deflection with the upper-count regime and servo with the finite electromagnetic regime makes this a servo-normalized target. That apparatus assignment is additional physical interpretation; it is not proved by the count equations or by the presence of active electronics alone. [4]

These current digits describe the present calibrated construction. They do not show that the exact digits or the apparatus-specific assignment were preregistered before the experiment. The numerical realization history and the later apparatus identification must retain separate evidentiary roles. [4] [9]

Compatibility and departure from zero are different questions

Table 3 uses the current target as a fixed reference. A target pull is the contrast minus the target, divided by the contrast standard uncertainty. A zero pull divides the same contrast by its standard uncertainty. Only the primary experimental contrast budget is used; uncertainty in the physical validity of MQ’s mapping is not quantified by either pull.

Copper is 0.743 standard uncertainties above the fixed target and 1.930 above zero. Sapphire is 1.248 from the target and 1.627 from zero. Both central contrasts are positive, but neither excludes zero at two standard uncertainties under this budget. These statements are not posterior probabilities of competing physical causes.

Figure 2 shows one-standard-uncertainty intervals with the same normalization and values as Table 3. Such intervals must not be relabeled as 95% intervals. The two contrasts also remain correlated because their underlying measurements share entries in Table 2.

What the primary contrast budget leaves out

The paper does not conclusively explain the mode offset. Its final consensus model allows unidentified configuration-specific biases in addition to the primary measurement uncertainties. The authors call these additional components dark uncertainty; the term concerns unexplained measurement variation and is unrelated to dark matter. Their combined estimate cannot be reconstructed by treating the primary contrasts as the whole uncertainty model. [1]

The 0.74-standard-uncertainty copper compatibility therefore has a defined scope. It includes the published primary systematic contributions and covariance, but not the additional bias terms used for the consensus. Using Type A uncertainty alone would be narrower still and would omit stated contributions. Neither procedure licenses an assumption that all unknown mode bias has been bounded.

The source authors regard instrumental systematics as more plausible than new physics in explaining the broader scatter of gravitational-constant measurements. The residual offset in this apparatus remains unresolved. The MQ account also warns against applying one extra universal rescaling to every laboratory length or to already realized electrical measurements. A valid physical explanation must follow the actual estimators without double-counting a calibration. [1] [4]

Chronology, authorship and a prospective test

The paper’s experimental data and primary analysis belong to Schlamminger and collaborators. Geiger’s subsequent calculation compares them with MQ. His reported nonparticipation in designing, conducting or analyzing the experimental campaign must not be confused with the absence of any earlier communication. The correspondence record separately distinguishes a broad earlier measurement-regime statement from a later apparatus-specific assignment. [4] [9]

A prospective test would fix the mode assignment, target, normalization and uncertainty procedure before inspecting new results. It would compare both zero separation and the specified MQ value, while controlling thermal, pressure, optical, electrical and mechanical effects. Better precision alone does not separate physics from an unrecognized mode-dependent bias; independent diagnostics and reversals are needed. [4] [8]

The covariance in Table 2 prevents treating copper and sapphire as independent discoveries. No new joint likelihood with historical BIPM campaigns is constructed here. A positive gap can remain compatible with several mechanisms, and compatibility with the target is not evidence that NIST endorsed MQ or that the proposed cause was isolated.

Source dates and reproducibility requests

April 16, 2026 is the experimental publication date. September 27, 2026 is the companion release’s recorded source-review snapshot. This Brief was prepared October 26, 2026. The current source notation and calibration digits are not assigned as historical apparatus predictions on those earlier dates.

For a reproducibility request, specify the four primary values, their relative budgets, all six correlations, denominator convention, rounding and the treatment of configuration-specific effects. For an experimental interpretation, request the torque and calibration diagnostics and the consensus-model assumptions. The calculations here reproduce the printed-input contrasts and current MQ target; they do not repeat the experiment, reprocess raw torque data or refit the full Bayesian consensus.