Informativity Institute · Research brief · 26 October 2026

The gravitational measurement-mode target

How MQ obtains a +34.9284 ppm separation, what its denominator means and what remains to establish when transferring it to an apparatus.

Archive source/audit snapshot: September 27, 2026 · Brief prepared: October 26, 2026
Read the companion press release

The specific claim and its scope

The public MQ account proposes two regime-dependent evaluations of one gravitational coupling. The distinction concerns finite-count realization and its upper-count limit. It is not a claim that two separately established universal constants have replaced the conventional gravitational constant, or that all disagreement among historical experiments has this cause. [1] [10]

The Informativity differential is MQ’s proposed non-Lorentz length contraction associated with discrete count structure. The Internal Frame is the count-configuration domain; the System Frame is its observable relational realization, connected by the Frames mapping. In this application, a finite-count normalization enters the gravitational coupling. The normalization and the differential’s physical interpretation have related but distinct roles; the normalization factor is not itself a direct observation of contraction. [2] [10]

Exact count relations and the normalized target

Let 𝜃𝑠𝑖 denote the dimensionless MQ invariant coefficient and 𝑛𝐿 the positive-real electromagnetic-demarcation length-count parameter. The calibrated continuation of the count parameter is distinct from primitive integer cardinality. Equation (1a) uses the current central coefficient 3.26239030504. The lettered equation labels belong to this Brief. [2]

𝑛𝐿=276𝜃𝑠𝑖(1a)

Let 𝑄𝐿 be the dimensionless Diophantine realization residual. Equation (2b) defines it. For the numerical calculation, evaluating the reciprocal of the sum of the root and count gives the same result with better numerical stability than directly subtracting two nearly equal numbers. [2]

𝑄𝐿=1+𝑛𝐿2−𝑛𝐿(2b)

Upright G denotes the upper-count coupling, and italic 𝐺 the finite-count electromagnetic-demarcation evaluation. Both use units m³ kg⁻¹ s⁻². Their relationship is Equation (3c). The contrasting slant identifies the measurement regime; it does not identify two experimentally certified constants. [1] [10]

𝐺=2𝑄𝐿𝑛𝐿G(3c)

Dividing Equation (3c) by the finite coupling gives the exact dimensionless contrast in Equation (4d). Multiplication by one million expresses that contrast in parts per million. The denominator is the lower finite-count value. [1]

G𝐺−1=12𝑄𝐿𝑛𝐿−1(4d)

Table 1 reconstructs the target from the current central coefficient. No experimental mode difference is fitted in this computation. The absolute coupling scale cancels from the ratio, so uncertainty common to both absolute values cannot be treated as two independent errors on the target. The remaining dependency on the invariant coefficient and the model assumptions must still be retained. [1] [2] [10]

Table 1: Numerical reconstruction from the stated central count input
QuantityCalculated valueRole
Invariant coefficient3.26239030504Adopted current central input
Demarcation count84.600545671563Positive-real continuation in Equation (1a)
Realization residual0.005909920940206Stable evaluation of Equation (2b)
Finite-count normalization0.999965072834481Multiplier of the upper-count coupling
Upper / lower ratio1.000034928385469Dimensionless ratio
Lower-normalized separation34.9283855 ppmRounds to +34.9284 ppm

Absolute values and calibration versions

The current gravitational-constant preprint’s 2022-input summary gives the lower value 6.6738448317(10) × 10⁻¹¹ and upper value 6.6740779383(10) × 10⁻¹¹ m³ kg⁻¹ s⁻². Parentheses identify one standard uncertainty in the final displayed digits. Each written uncertainty is 0.0000000010 × 10⁻¹¹ in those units. These are input-propagated MQ results, conditional on the model; they do not include a general model-discrepancy allowance. [10]

Subtracting the displayed central values gives 2.331066 × 10⁻¹⁵ m³ kg⁻¹ s⁻². Forming their lower-normalized ratio gives 34.9283817 ppm, consistent with the count-derived 34.9283855 ppm at the reported four-decimal precision. The small difference reflects rounding of the printed absolute values. The extra arithmetic digits are reproducibility information, not independently established physical accuracy.

The public gravitational-constant explanation also retains the comparison pair 6.6738448362 and 6.6740779428, each multiplied by 10⁻¹¹ in the same units. Those belong to a different calibration presentation. Their displayed separation is also 2.331066 × 10⁻¹⁵. This Brief uses the current preprint pair above for absolute values and the explicit current count input for the ratio. It does not mix the versions into a new uncertainty estimate. [1] [10]

Why the ppm denominator matters

A separation in parts per million is incomplete without a reference value. Table 2 expresses the same count-derived contrast relative to the lower value, upper value and arithmetic mean. These are changes of normalization, not different physical predictions. In the proposed free/servo assignment, lower normalization becomes servo normalization. [1]

Table 2: The same theoretical separation under three explicit normalizations
Reference denominatorOperation in wordsSeparation (ppm)
Lower finite-count valueUpper divided by lower, minus one34.9283855
Upper-count valueOne minus lower divided by upper34.9271655
Arithmetic mean of bothDifference divided by their arithmetic mean34.9277755

The upper-normalized 34.9271655 ppm differs slightly from the lower-normalized 34.9283855 ppm. At today’s quoted experimental uncertainties that difference may be small, but the convention must be fixed before a high-precision comparison. Reversing the order of the two measurements would also reverse the sign and change the ratio denominator; it must not be done after seeing the outcome.

Count dependence is a model property

For positive count, the residual is positive, and the finite-count normalization remains below unity. As the count increases, the finite coupling approaches the upper-count evaluation and the normalized separation tends to zero. Table 3 and Figure 1 evaluate Equations (2b)–(4d) at illustrative counts. The electromagnetic-demarcation entry is fixed by Equation (1a); the other rows are mathematical sensitivity examples. [2]

Table 3: Exact count-response evaluations; no apparatus count scan implied
Illustrative caseCount parameterLower-normalized separation (ppm)
Illustrative count 2020.00000000624.6098625
Illustrative count 4040.00000000156.2255936
Electromagnetic demarcation84.6005456734.9283855
Illustrative count 100100.0000000024.9993750
Illustrative count 200200.000000006.2499609

The curve does not mean a laboratory source-to-test-body distance can simply be set to a chosen value of this count parameter. Translating an apparatus configuration into an MQ realization condition requires a physical measurement model. Numerical continuity of the count expression does not supply that transfer model.

Figure 1. Finite-count separation decreases toward the upper-count limitExact theoretical lower-normalized contrast is plotted for positive-real counts from 40 to 200. The electromagnetic-demarcation point at 84.60054567 has a gap of 34.9284 ppm. The graph is a mathematical evaluation, not an observed distance scan or a measured confidence band.A finite-count target with a vanishing upper-count limitExact model relation · illustrative positive-real counts · no apparatus-distance identification 40 80 120 160 200 0 40 80 120 160 Demarcation target: 34.9284 ppmPositive-real length-count parameterLower-normalized separation (ppm)
Figure 1. Calculated from Equations (2b)–(4d), using the same normalization as Table 3. The marked point follows from the fixed central input in Table 1. The curve is not experimental evidence for a count-dependent gravitational response.

The additional apparatus-to-regime assignment

Free-deflection operation infers gravitational torque from the pendulum’s angular response and mechanical calibration. Electrostatic-servo operation holds a reference angle by applying a balancing electrical torque. Both retain the gravitational interaction between source and test bodies. Their distinction is an inference and calibration route, not gravity being present in only one mode. [3] [4]

MQ’s proposed apparatus assignment identifies free response with the upper-count evaluation and servo with the lower electromagnetic-demarcation evaluation. That identification is additional to Equations (1a)–(4d). The algebra does not prove that an electrical torque calibration realizes the demarcation, or that a mechanically read angle realizes the limiting regime. Figure 2 makes the extra hypothesis visible. [1] [9]

Figure 2. The mode assignment is an additional physical hypothesisFree deflection measures mechanical angular response and is proposed to correspond to the upper-count coupling. Servo holds angle through balancing electrical torque and is proposed to correspond to the finite electromagnetic-demarcation coupling. Both modes measure gravitational torque. Their correspondence to the MQ quantities is unverified.Both modes measure gravitational torque Free deflectionMeasure angular responseApply mechanical calibrationProposed MQ assignment: upper-count Electrostatic servoHold the reference angleInfer balancing electrical torqueProposed MQ assignment: finite-count Mode definitions are experimental; MQ assignments require a separate test.
Figure 2. Functional diagram based on the experimental procedures in [3] and [4], with the proposed MQ assignments explicitly labeled. This is neither an engineering drawing nor a demonstrated causal mechanism.

Chronology, covariance and a decisive comparison

MQ’s broad distinction between electromagnetic and macroscopic approaches predates the April 16, 2026 NIST/BIPM publication. The specific pairing of free deflection and servo with the two realization evaluations was made retrospectively. A numerical target established within a theory and a later apparatus-specific interpretation are different milestones. The available comparison is not a preregistered discovery test. [1] [3] [9]

Shared apparatus can cancel some geometry and calibration effects, but the two estimators also have mode-dependent response, electrical transfer and drift. A normalized contrast must propagate the covariance of the actual mode results. Its uncertainty cannot be inferred by adding two independently treated absolute uncertainties when important inputs are shared. The required correlations must come from the measurement model and supporting data. [4] [5]

Under an ideal unbiased Gaussian contrast model, dividing 34.9284 ppm by the desired expected standardized separation gives total differential standard uncertainty goals of 11.6428 ppm for three and 6.9857 ppm for five. These are planning requirements, not achieved precision, per-channel uncertainties or guaranteed detection thresholds. At an expected mean exactly on a positive five-standard-uncertainty threshold, an ideal Gaussian experiment has only a 50-percent chance of exceeding that threshold. [1] [6]

Table 4 sets out the records needed to transfer this numerical target into a discriminating test. The public proposed-experiment page supplies a research design rather than evidence that a fully qualified apparatus has achieved these requirements. [7]

Table 4: Records needed for a prospective measurement-mode test
RecordWhat must be specifiedWhy it matters
Physical assignmentWhy each instrument mode realizes the proposed regimeSeparates a physical model from a post hoc label
Contrast conventionFree minus servo, relative to servo, with a fixed signKeeps target and result comparable
Calibration and correctionsMechanical response, electrical torque, drift and reversal controlsTests instrumental alternatives to a mode gap
Uncertainty modelShared-input covariance and mode-specific uncertaintyPrevents an understated differential error
Protocol and outcomesPredeclared selection, blinding and target-rejection criteriaPermits failure as well as agreement

A validated result near zero with uncertainty small enough to exclude the target would challenge this apparatus assignment. A stable gap far from the target would likewise require revision. Agreement would strengthen the specific comparison while leaving alternative mechanisms and systematic controls to be assessed. A positive offset alone does not identify the Informativity differential as its cause. [9]

The published NIST experiment and other paired determinations provide experimental context. Their combined-gap analysis is a separate MQ statistical synthesis with its own covariance and heterogeneity assumptions. Its fitted center is not substituted for the fixed count-derived target here. This Brief does not claim a new measurement, a unique mechanism, an institutional endorsement or a change in recommended constants. [3] [8]

September 27, 2026 is the release’s recorded source/audit snapshot. This Brief was prepared October 26, 2026 using the current public sources. The count ratio, denominator conversions, displayed-value difference and illustrative sensitivity arithmetic were reproduced. No original discovery date is inferred, and no independent apparatus qualification or physical validation was performed.

Research sources and further reading

  1. Informativity Institute, Gravitational Constant: MQ Derivation and Experimental Test. Public source of the +34.9284 ppm servo-normalized hypothesis and approximately 11.6 ppm and 7 ppm differential-uncertainty goals. These are conditional sensitivity calculations, not achieved apparatus performance. Open source →
  2. J. A. Geiger, Distance Corresponding to the Length Contraction Associated with a Measure of Charge Couplings. Current public preprint. Supplies the count constraint and residual used for the present numerical target. Journal publication of this version is not established. Open source →
  3. S. Schlamminger and collaborators, Redetermination of the gravitational constant with the BIPM torsion balance at NIST. Metrologia 63, 025012 (2026), DOI 10.1088/1681-7575/ae570f. Published April 16, 2026. Published paper PDF; Tables 16–18 and the consensus analysis give the measurement and uncertainty context. This is an existing experiment, distinct from the proposed test. Open source →
  4. S. Schlamminger, L. Chao, V. Lee, D. B. Newell and C. C. Speake, Design of electrostatic feedback for an experiment to measure G. Public author preprint arXiv:2206.04173, submitted June 8, 2022; journal DOI 10.1109/OJIM.2022.3182391. Explains the free-deflection and electrostatic-servo procedures. Open source →
  5. Joint Committee for Guides in Metrology, JCGM 100:2008, Evaluation of measurement data — Guide to the expression of uncertainty in measurement. Section 5.2 treats correlated inputs. General metrology guidance, not an assessment or endorsement of MQ. Open source →
  6. NIST, Basic definitions of uncertainty. Measurement models include significant uncertainty contributions; standard uncertainty is expressed as an estimated standard deviation. Type A and Type B identify evaluation methods. Open source →
  7. Informativity Institute, planned measurement-mode experiment. Current public research proposal, including qualification requirements and the search for an experimental host. The precision requirements in this Brief are not certification of that design or its achieved performance. Open source →
  8. Informativity Institute, Gravity Mode-Gap Evidence and Its Limits. Related release with access to the four-pair technical synthesis. The quoted historical center and its uncertainty are an estimate, not an alternative exact theoretical prediction. Open source →
  9. Informativity Institute, Predictions of Measurement Quantization. Public target, dependency and testing qualifications. Historical numerical constructions and retrospective apparatus assignments have different evidentiary roles. Open source →
  10. J. A. Geiger, Gravitational Constant Derived from First Principles. Current public preprint. Its 2022-input summary gives upper-count 6.6740779383(10) and electromagnetic-demarcation 6.6738448317(10), each multiplied by 10⁻¹¹ m³ kg⁻¹ s⁻². These are conditional MQ calculations, not CODATA recommendations. Older numerical versions are distinguished in the source. Journal publication of this version is not established. Open source →

Prepared October 26, 2026. Numerical target and normalization arithmetic were checked. The equations are conditional MQ constructions; the particular apparatus-to-regime assignment remains a separate empirical hypothesis.

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