What the result addresses

The physical question is how characteristic length, time and mass expressions emerge within the MQ count construction. The current manuscript develops their modern Planck-like forms from its adopted relations. It distinguishes that derivation from experimental determination of the numerical constants and from demonstrating a unique microscopic physical theory. [1]

MQ begins with discrete measure and treats physical references as realizations of logical count relations. The Internal Frame is the count-configuration domain; the System Frame is the realized relational encoding connected by the Frames mapping. The dimensional formulas below concern realized measures. They do not assign primitive kilograms or metres to the underlying configuration domain. [1] [9]

A measured value can select the coefficient corresponding to our universe without supplying every law’s functional form. Exact SI values can anchor numerical units without demonstrating the physical validity of a mapping. These distinctions preserve the framework’s intended architecture while leaving its particular derivations and empirical predictions open to source-specific assessment. [1] [3]

The dimensional starting relations

Let ${\mathrm{𝑙}}_{\mathrm{𝑓}}$, ${\mathrm{𝑚}}_{\mathrm{𝑓}}$ and ${\mathrm{𝑡}}_{\mathrm{𝑓}}$ be fundamental length, mass and time in m, kg and s. Let ${\mathrm{𝑝}}_{\mathrm{𝑠}\mathrm{𝑖}}$ be their momentum realization in kg m s⁻¹ and $\mathrm{𝑐}$ vacuum light speed in m s⁻¹. Equation (1a) states the fundamental relation and compatible light-speed relation used here. The momentum is a dimensional quantity, distinct from the invariant dimensionless coefficient even when adopted numerical coordinates coincide. [1] [7]

Let $\mathrm{G}$ denote the upright MQ upper-count gravitational quantity in m³ kg⁻¹ s⁻² and $\mathrm{ħ}$ the upright MQ upper-count action in J s. Equation (2b) supplies the gravitational and action assignments. Substituting the momentum from Equation (1a) into the action gives the final equality. These are all quantities from the same upper-count family. [1] [7]

Both sides of the fundamental relation have units kg m. The action expression has units kg m² s⁻¹. Replacing its momentum by a bare dimensionless coefficient would remove the required momentum dimensions. Figure 1 organizes the positive-root consequences of these compatible relations. [1]

Length, time and mass follow as positive roots

Multiplying the two expressions in Equation (2b) cancels fundamental mass and time. Dividing by light speed cubed leaves fundamental length squared. Equation (3c) gives that identity and its positive root. Positivity is an assumption about the physical measure, not an extra measurement selecting its scale. [1]

Dividing the positive length by light speed gives Equation (4d). The action–gravity product divided by light speed to the fifth power has units s². The positive time root therefore follows without a new scale input. [1]

The gravitational relation in Equation (2b) expresses mass in terms of time. Substituting Equation (4d) and taking the positive branch gives Equation (5e). Its radicand has units kg². These local labels correspond to the source’s length, time and mass roots in Eqs. (22), (24) and (27). [1]

Why the roots do not supply another independent equation

Starting with compatible positive reference measures, one can calculate action and gravitation from Equation (2b), then substitute them into Equations (3c)–(5e) and recover the starting measures. That round trip is a substantive algebra check. It does not provide independent numerical information that was absent from the starting relations. Counting each recovered root as a new determination would repeat the same dependencies. [1] [7]

The roots do establish the dimensional structure of the proposed framework under the stated premises. The stronger claim that nature implements those references requires a physical realization and empirical tests. Neither dimensional consistency nor choosing positive roots proves that the entire microscopic construction is unique. [1] [8]

The calibration chain and input roles

Table 1 identifies the inputs and choices used for the coherent numerical calculation in this Brief. The inverse fine-structure value selects the coefficient and count branch. The adopted momentum realization links its numerical coordinate to a quantity with momentum units. Exact SI light speed and Planck constant anchor the numerical reference system. Their roles should be stated individually rather than classified together as independent experimental confirmations. [1] [3] [4] [5]

The electron-mass–Bohr-radius product obeys the conventional identity equal to reduced Planck constant times inverse fine-structure constant divided by light speed. The exact SI reduced Planck input is already present through that identity. Recovery of that action at its associated demarcation is therefore a reconstruction of shared information, not an independent prediction of its numerical value. [1] [3] [4]

For numerical consistency here, the matched orbital identity is used throughout, with the same inverse fine-structure calibration and fixed rounding branch. A 90-digit recalculation obtains coefficient 3.2623903050381235 and the corresponding fundamental measures. The source’s separately stated positive-real count continuation and realization assumptions remain attached to that calibration; a numerical solution does not by itself prove integer physical admissibility. [1] [3]

Reproduced values and distinct quantity assignments

The resulting MQ upper-count gravity is about 6.67407793828 × 10⁻¹¹ m³ kg⁻¹ s⁻², and upper-count action about 1.05453498444 × 10⁻³⁴ J s. The latter is distinct from conventional reduced Planck constant, 1.054571817646… × 10⁻³⁴ J s, fixed exactly by the SI Planck constant and the circle constant. Using the conventional action while silently retaining an MQ upper-count gravitational value would mix the two assignments. [1] [3] [4]

Table 2 compares the coherent MQ roots with conventional Planck units evaluated from recommended conventional gravity and exact conventional action and light speed. The familiar root forms are the same algebraic functions; their inputs and uncertainty meanings differ. Parentheses give standard uncertainty in the final displayed digits. MQ uncertainties are conditional propagated input uncertainties, not independent observations of the reference measures. [1] [3] [4]

The current Planck manuscript’s printed-input profile gives length 1.61619991147(12) × 10⁻³⁵ m, time 5.39106261127(41) × 10⁻⁴⁴ s and mass 2.17643254057(16) × 10⁻⁸ kg. It multiplies printed electron mass and Bohr radius and quotes a slightly different coefficient. Table 2 instead uses the coherent matched-identity evaluation of the current constants manuscript. These last-digit differences are numerical-profile and rounding differences, not physical variation or new observations. [1] [3]

Uncertainty and covariance stay attached to the inputs

The common inverse fine-structure input was shifted by its stated standard uncertainty and the entire MQ chain recalculated. Its reference measures have relative conditional standard uncertainties of about 7.66 × 10⁻¹¹. The much larger conventional relative uncertainty is about 1.12 × 10⁻⁵, inherited from half the relative gravitational uncertainty in the square-root propagation. Figure 2 compares these specified budgets without treating them as equivalent empirical claims. [3] [4] [6]

The MQ gravitational and action outputs are not independent uncertain inputs when they have been calculated from the same underlying calibration. Propagating each root from their printed uncertainties as if they were unrelated would lose their covariance. Likewise, length and time share their exact light-speed relation; listing both does not supply an additional independent measurement. [3] [6]

Under the conventional input chain, a higher gravitational value raises the length and time roots and lowers the mass root. In the MQ chain, all variations must be propagated through its specified coefficient and mapping relations instead. A smaller propagated interval cannot account for unquantified physical-model error simply by being printed with more digits. [3] [6]

What has been checked, and what still requires evidence

Table 3 separates the checked results from additional physical claims. The present calculation verifies all three positive roots against the reference measures that generated their upper-count inputs. It also evaluates the conventional roots with their own inputs. Neither operation supplies direct access to microscopic length or clock intervals. [1] [8]

A prospective test must identify an observable whose comparison adds information beyond the numerical selectors and reference identities already used. It should specify the applicable count regime, source assumptions, measurement protocol and joint uncertainty. The manuscript’s equality-case use of uncertainty bounds and the associated count identifications also retain their own assumptions; a statistical uncertainty inequality alone does not establish discrete reference units. [1] [8]

Chronology and source requests

October 13, 2026 identifies the source-version milestone in this retrospective archive. It is not established here as an original discovery, announcement or journal publication date. This Brief was prepared November 2, 2026. Journal publication of the cited current Planck-unit and constants manuscript versions is not established. [1] [3]

For an interview, request the exact numerical profile and ask which quantities are conventional inputs, MQ upper-count outputs or finite-count realizations. Ask which argument derives a form and which specifies its numerical scale. Request the correlated uncertainty calculation before interpreting a long string of digits as independent physical precision.