What the correspondence record establishes

The reviewed author-held record is a forwarded message containing an embedded original-message header dated Sunday, September 26, 2021. Its original portion communicates a general distinction between electromagnetic and macroscopic approaches to determinations of the gravitational constant and associates the distinction with MQ count-related contraction. Later forwarding commentary must be distinguished from that original portion. [1]

The embedded date is the basis for this archive entry. A secondary manuscript gave September 21; the preserved header supports September 26. Correcting that date does not authenticate delivery or prove that recipients accepted the analysis. The copy is not a public institutional email archive, a mail-server delivery log or a published response from NIST. [1]

No private recipient addresses, message quotations or attachments are reproduced in this Brief. A shareable redacted export should preserve the original date, original text and relevant source versions, while distinguishing later forwarding additions. Request it through the media contact if the chronology is material to a story. [1]

Three claim levels that must remain separate

The record identifies Geiger as a theoretical proponent and correspondent, rather than a designer, operator or analyst of the experimental campaign. That is the stated nonparticipation claim. It is compatible with prior contact and must not be recast as evidence that no contact occurred or that no influence was possible. [1] [3]

Conversely, contact alone is not evidence that it affected the work. The reviewed account does not establish whether the communication influenced the experiment. The absence of such evidence is not proof either of influence or of its absence. This Brief does not report an institutional reply or speak on behalf of the collaboration. [1]

Chronology and the meaning of each date

Figure 1 highlights three dated milestones. Publication dates cannot be substituted for the dates of experimental design, data acquisition, unblinding or first inspection. A message preceding a 2026 publication is not thereby shown to precede every relevant observation or design decision. The dual-mode apparatus has its own earlier experimental history. [2] [3]

What the two torsion-balance modes do

The International Bureau of Weights and Measures (BIPM) torsion balance was designed to determine the gravitational interaction between source and test-mass assemblies through different operating methods. In the free-deflection or Cavendish method, the pendulum is allowed to move and its torsional response is measured. In electrostatic-servo operation, a feedback system supplies a balancing electrostatic torque to maintain the pendulum angle. [2]

These are two measurement procedures for the same gravitational-constant question. Free deflection does not eliminate electromagnetic or optical metrology from the apparatus, and servo operation does not remove the gravitational interaction. Their estimator equations, calibrations, geometry, alignment and control behavior must be examined before a new physical interpretation is assigned. [2] [3]

Figure 2 illustrates the functional distinction only. It is an explanatory redraw, not a photograph, engineering drawing or claim about a previously undisclosed apparatus modification.

Current MQ technical context, not a reconstruction of the 2021 attachment

The current MQ account associates free deflection with a count-resolved gravitational realization and electrostatic servo with a finite-count electromagnetic realization. It expressly identifies that apparatus-specific assignment as retrospective. A general statement about measurement regimes and an exact physical map of every estimator component are different claims. [4]

For context, let ${\mathrm{𝜃}}_{\mathrm{𝑠}\mathrm{𝑖}}$ denote the dimensionless invariant MQ coefficient, ${\mathrm{𝑛}}_{\mathrm{𝐿}}$ the positive realized separation count at the electromagnetic demarcation and ${\mathrm{𝑄}}_{\mathrm{𝐿}}$ the dimensionless Diophantine realization residual. Equations (1a)–(3c) state the count relation and two exact forms of the same residual. These are Brief labels, and the current calibration digits below are not assigned to the 2021 message. [5]

In Equation (4d), italic $\mathrm{𝐺}$ is the gravitational coupling evaluated at the electromagnetic demarcation and upright $\mathrm{G}$ its upper-count-limit realization. Both have units m³ kg⁻¹ s⁻². The distinction is a source-defined realization regime, rather than two newly observed universal constants. The current finite-count relation is [4] [5]

Dividing Equation (4d) gives the exact relative separation in Equation (5e). Its denominator convention is the finite-count electromagnetic value. Changing that denominator would produce a slightly different ppm number, so the convention must be declared.

For a present explanatory calculation, use the rounded coefficient 3.26239030504. The stable residual form in Equation (3c) avoids subtraction of nearly equal values. Table 3 evaluates the current count geometry and converts the dimensionless separation to parts per million by multiplying by one million. These are conditional model calculations, not a new NIST measurement or proof of what the 2021 attachment contained. [4] [5]

The result rounds to 34.9284 ppm. Its mathematical existence does not assign an apparatus mode to either realization. Such an assignment requires a physical account of the actual torque estimators and their measured quantities. The current MQ discussion cautions against applying one universal extra rescaling to every apparatus length or double-counting effects already present in laboratory-realized electrical measurements. [4]

The Internal Frame denotes the discrete configuration description and the System Frame its observable relational realization under the Frames mapping. The regime comparison above belongs to that realized physical description. Neither the 2021 email nor the current arithmetic independently establishes the framework’s ontology or its application to the instrument. [4] [5]

What would establish a stronger prospective test

A prospective test would fix the apparatus-to-realization map, numerical contrast, estimator treatment, material/configuration choices, uncertainty model and analysis rule before inspection of the relevant results. It would retain correlations between operating modes and investigate conventional sources of mode dependence. A dated general email supplies only part of that evidentiary chain. [4] [6]

For a retrospective comparison, report the choices and their timing explicitly. Numerical compatibility is distinct from establishing a physical mechanism, ruling out apparatus systematics or proving the exact target value. Publication of the experimental work is not evidence that the collaboration adopted the later theoretical interpretation. [3] [4]

This Brief does not reanalyze copper or sapphire data, quote a combined experimental result or construct a significance. Those numerical comparisons belong to the separate technical treatment linked below. Their conclusions cannot be inferred from the correspondence date. [8]

Reporting and source access

Request the earliest shareable record, its attachments or immutable cited versions, and a separation of original and later forwarding text. Ask what was fixed at each date. A sent-date header is evidence within the preserved copy; delivery, receipt, reply, influence and institutional endorsement require additional evidence. Any institutional perspective should be obtained through public NIST channels. [1]

The publication history and current interpretation remain distinguishable. The 2018 paper supplies historical theoretical context, the 2021 record supplies a dated general communication, the experimental papers supply the collaboration’s methods and results, and the later MQ account supplies the retrospective mode assignment. This Brief was prepared October 26, 2026. [1] [2] [3] [4] [7]