The proposed observable

The test compares free deflection with electrostatic servo using the same gravitational source geometry. Its contrast is the free-mode result divided by the servo-mode result, minus one, multiplied by one million. Positive contrast means the free result is larger. All target and sensitivity ppm figures below use that servo normalization unless explicitly labeled otherwise. [1]

Free deflection infers gravitational torque through the suspended body’s mechanical response and calibration. Servo operation applies a balancing electrical torque to hold an angle near a reference. Both retain the gravitational source interaction. Figure 1 shows their functional distinction, not a built apparatus or a proof that the modes implement two MQ regimes. [3] [4]

Where the fixed numerical target comes from

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) uses the current central coefficient 3.26239030504. Brief equation labels are separate from source equation numbers. [1] [2]

Let ${\mathrm{𝑄}}_{\mathrm{𝐿}}$ denote the dimensionless Diophantine realization residual. Equation (2b) defines it. The calculation evaluates the algebraically equal reciprocal of the root plus the count to avoid subtractive cancellation. [2]

Upright $\mathrm{G}$ is the upper-count gravitational coupling; italic $\mathrm{𝐺}$ is the finite-count electromagnetic-demarcation coupling. Both have units m³ kg⁻¹ s⁻². Equation (3c) is their source relation. [1] [2]

The dimensionless separation in Eq. (4d), multiplied by one million, gives 34.9284 ppm after rounding. The count is 84.6005456716. No experimental contrast is fitted to obtain this target.

Applying this separation to an apparatus requires the additional assignment of free response and servo to the respective realization conditions. That transfer is not proved by the count equations or by the presence of electronics. The numerical construction and the later retrospective interpretation of the NIST modes have separate chronology. A prospective test must specify its assignment before the new data are inspected. [1] [9]

What the seven-ppm requirement means

Standard uncertainty is represented by an estimated standard deviation. For the conditional sensitivity calculation, assume an unbiased Gaussian contrast estimator with a fixed, valid total standard uncertainty and a true mean equal to the MQ target. Divide the target by that uncertainty to obtain its expected standardized distance from zero. Equivalently, divide the target by the chosen standardized distance to obtain the required uncertainty. [1] [6]

Table 1 reproduces the source’s approximately 11.6 ppm and 7 ppm goals. Figure 2 shows the same dependency. These are uncertainties on the normalized mode contrast, not specifications for each instrument channel separately. They must cover significant uncertainty contributions and the effects of relevant corrections, rather than just repeat-measurement scatter. [5] [6]

Expected separation is not guaranteed detection

At the exact five-standard-uncertainty goal, the assumed true mean lies at the positive five-standard-uncertainty threshold. In the ideal Gaussian model, half of repeated experiments would fluctuate above that threshold and half below. Thus expected five-standard-uncertainty separation corresponds to 50 percent power for that predeclared positive threshold, not certainty of reaching it. Median sensitivity and fluctuations have distinct roles. [10]

Table 2 illustrates this distinction with a fixed positive five-standard-uncertainty threshold and no fitted nuisance parameters. Calculate the target divided by the uncertainty, subtract five, and evaluate the standard-normal cumulative distribution to obtain the power. For a desired power, add the corresponding standard-normal quantile to five and divide the target by that sum. The resulting goals are idealized planning calculations, not measured error budgets.

The 90 percent and 95 percent power goals are 5.5605 and 5.2565 ppm, respectively. Unknown biases, non-Gaussian tails, uncertain variance estimates, selection effects or nuisance-parameter fitting can change these results. A small reported statistical error alone does not justify a Gaussian discovery interpretation.

Covariance and the two-mode uncertainty budget

For first-order propagation, multiply the free-to-servo ratio by the square root of the sum of squared relative mode uncertainties minus twice the correlation times their product. This retains cancellation of shared calibration contributions in a difference. A full evaluation starts from the actual estimators and their common inputs, rather than choosing a correlation because it produces a favorable uncertainty. [5]

Table 3 is an illustrative inversion of that propagation formula. Assume both mode results have equal relative standard uncertainty, the free-to-servo ratio equals one plus the target divided by one million, and the desired contrast uncertainty is 7 ppm. Divide seven by that ratio and by the square root of twice one minus the stipulated correlation to obtain the per-mode uncertainty shown. These are algebraic examples, not proposed budgets certified for a particular apparatus.

Positive correlation can cancel a shared contribution, but it does not remove an unmodeled mode-specific offset. The NIST paper’s additional unidentified configuration effects and its primary budgets are distinct parts of the analysis. A new experiment cannot assume those missing effects disappear because it uses one apparatus. [3]

Keep the ppm denominator explicit

A 7 ppm servo-normalized uncertainty is about 20.04 percent of a 34.9284 ppm signal. An engineering specification expressed instead in parts per million of the gap uses a much smaller reference quantity. For example, 5 ppm of the gap corresponds to only 0.0001746 servo-normalized ppm. These are numerical conversions, not achieved specifications. A torque-domain design must identify its own estimator and reference torque before transferring a fractional target to it. [1] [7]

Similarly, taking a proposed fractional gap and multiplying it by a modeled source torque produces a conditional benchmark. It does not prove that an apparatus implements the MQ mapping, that the mechanical/electrical estimator transfers that gap unchanged, or that the resulting torque can be resolved experimentally. This Brief does not adopt a version-specific torque model as established performance. [7]

What must remain the same, and what must be checked

Same apparatus is valuable because it can reduce changes in source geometry and provide controlled interleaving. It does not mean the two modes have identical responses, identical calibrations or independent errors. Table 4 identifies the principal comparisons that make the proposed difference interpretable. [3] [4]

A protocol should specify the positive sign, servo denominator, measurement window, exclusions, correction procedure, mode assignment and comparisons with both zero and the MQ target before unblinding. A blinding plan should preserve calibration diagnostics while protecting the final contrast from discretionary tuning. Changes and failed qualifications remain part of the record; they are not grounds to discard an unfavorable final contrast after looking at it.

The larger historical gap is an uncertain estimate

The public synthesis quotes a historical common gap of 60.994 ± 26.930 ppm. Treating 60.994 as an exact competing hypothesis would put it 5.213 standard uncertainties from the fixed MQ target for an ideal future 5 ppm measurement. That comparison concerns two stipulated fixed values, not the uncertainty of the historical estimate. [1] [8]

If a future result centered on the MQ target had 5 ppm standard uncertainty and were independent of that historical estimate, the comparison uncertainty would be the square root of 26.930 squared plus five squared, or 27.3902 ppm. The difference would then be only 0.952 comparison standard uncertainties. Shared inputs or campaign correlations would need their own covariance treatment. This distinction prevents a precision goal from being misreported as an achieved high-significance disagreement with past data.

Outcomes, current status and reporting scope

A sufficiently precise result near zero would challenge the proposed apparatus-to-realization assignment under its stated assumptions. A stable positive gap excluding the fixed target would also require revision. A value compatible with the target would strengthen that specific comparison, while independent controls and alternative mechanisms would still matter for causation. The protocol must permit all three outcomes. [1] [9]

The current public project page describes a research proposal seeking an experimental host and identifies outstanding qualification work. It is not a completed, independently qualified measurement. Its version-specific hardware and torque assumptions should be assessed separately from the generic sensitivity requirement in this Brief. No host, grant, schedule or completed apparatus is announced here. [7]

September 27, 2026 is the release’s recorded source-audit snapshot. This Brief was prepared October 26, 2026. The exact target and conditional sensitivity arithmetic were reproduced, but no physical experiment, complete systematic budget or engineering qualification was performed. Journalists should request the preregistered protocol, full uncertainty model, calibration data and criteria for rejecting the hypothesis before describing a proposed precision as demonstrated capability.