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REVIEW 2 major objections 1 minor 10 references

The structure of the new SI

T0 review · 2 major / 1 minor · reviewed 2026-07-01 · grok-4.3

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Pith's one-line read Interpreting the new SI constants strictly as conversion factors produces a single geometric table that organizes all units and exposes hidden geometry in physics.

desk verdict This paper reframes the new SI constants as conversion factors to produce a geometric unit table, but the result is a restatement of the definitions with no new physics or testable claims. read the letter →

arxiv 2606.30679 v1 pith:CWSRVB2B submitted 2026-06-26 physics.class-ph

B. C. Regan This is my paper · ORCID
classification physics.class-ph
keywords SIunitsconversionfactorsgeometricframeworkfundamentalconstantsunitsystemsnewphysicaldimensionlessnumbers
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper claims that the constants fixed by the 2019 SI redefinition, including the speed of light and the Planck constant, serve only as conversion factors between units. When viewed this way, the units arrange themselves into rows and columns of one conversion table, or else appear as dimensionless numbers. This arrangement separates constants whose values are chosen by people from those fixed by nature. It also brings out geometric relations inside physical theories that a surplus of units normally conceals. A reader would care because the view promises a simpler, more unified picture of measurement without introducing new physical content.

What carries the argument

The unifying geometric framework: a single conversion table whose rows and columns capture all unit relations among the SI-defining constants.

What would settle it

A required physical unit relation that cannot be expressed either as a row or column entry or as a dimensionless number in the proposed single table without producing an inconsistency.

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Extended reading notes

Core claim

The new SI is defined by a set of constants. Interpreting these constants purely as conversion factors organizes the units they relate into a unifying geometric framework. In this framework units appear, perhaps raised to some power, either as rows or columns in a single conversion table or as entries in a list of dimensionless numbers. The organization distinguishes constants whose values are set by people from those set by nature and reveals geometry in physical theories that is normally hidden by extra units.

Load-bearing premise

That the SI-defining constants can be treated purely as conversion factors, without any extra physical content, and still produce one consistent geometric table covering all unit relations.

Editorial extensions

If this is right

  • All units connected by the SI constants fit into one table rather than separate systems.
  • Constants with values fixed by human choice are exactly those chosen to define the SI.
  • Physical theories contain geometric structures that become visible once surplus units are removed.
  • Dimensionless numbers arise naturally as the entries that remain once units are aligned in the table.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The same table approach could be applied to older unit systems to check whether they also hide geometric relations.
  • Teaching the SI might become simpler if students learn the table structure before memorizing individual definitions.
  • The framework suggests that some apparent complexity in fundamental constants may be an artifact of unit choice rather than nature.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

2 major / 1 minor

Summary. The paper claims that interpreting the constants defining the new SI (such as the speed of light, Planck constant, Boltzmann constant, and elementary charge) as conversion factors organizes the related units into a single unifying geometric framework. In this framework, units appear as rows or columns in a conversion table or as entries in a list of dimensionless numbers. This is said to clarify the distinction between constants whose values are set by convention (like those in the SI) versus those set by nature, and to reveal geometry in physical theories that is normally obscured by excess units.

Significance. If the interpretive reorganization genuinely exposes relations or structures beyond those already visible in standard dimensional analysis, the result could offer a useful conceptual tool for thinking about metrology and the role of fixed constants. The manuscript receives credit for attempting a parameter-free reorganization grounded directly in the 2019 SI definitions. However, because the construction begins from those same definitions, the significance remains primarily interpretive rather than predictive or falsifiable.

major comments (2)
  1. [Abstract] Abstract: the claim that the organization 'reveals geometry permeating our theories of physics that is normally hidden by a surplus of units' is load-bearing for the central thesis, yet the provided text presents the table as following directly from re-expressing the SI definitions as conversion factors. This makes the geometric structure consistent by construction without demonstrating a specific new relation or prediction not already obtainable from dimensional analysis.
  2. [Abstract] Abstract: no error analysis, external validation, or explicit comparison to existing dimensional-analysis tables is mentioned, leaving unclear whether the single conversion table captures all unit relations rigorously or simply asserts the input definitions in a new format.
minor comments (1)
  1. [Abstract] The abstract contains a LaTeX artifact (Syst`eme) that should be rendered correctly in the final version.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive comments on our manuscript. We provide point-by-point responses to the major comments below.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the claim that the organization 'reveals geometry permeating our theories of physics that is normally hidden by a surplus of units' is load-bearing for the central thesis, yet the provided text presents the table as following directly from re-expressing the SI definitions as conversion factors. This makes the geometric structure consistent by construction without demonstrating a specific new relation or prediction not already obtainable from dimensional analysis.

    Authors: The manuscript presents an interpretive framework rather than a predictive theory. The geometric table is constructed from the SI definitions, but this allows the relations among units to be visualized in a single structure, thereby revealing the geometric interconnections that are obscured when units are treated separately. This distinction between conventional constants and natural ones emerges clearly from the table format, offering a conceptual tool beyond standard dimensional analysis, even without new predictions. revision: no

  2. Referee: [Abstract] Abstract: no error analysis, external validation, or explicit comparison to existing dimensional-analysis tables is mentioned, leaving unclear whether the single conversion table captures all unit relations rigorously or simply asserts the input definitions in a new format.

    Authors: Given the conceptual nature of the work, there are no numerical results requiring error analysis or external validation. The table captures the unit relations exactly as defined by the SI. We will add an explicit comparison to traditional dimensional analysis in the revised manuscript to clarify the differences and rigor of the approach. revision: partial

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity

full rationale

The paper offers an interpretive reorganization of the SI-defining constants, treating them as conversion factors to produce a table of unit relations. This construction is explicitly derived from the chosen fixed constants in the 2019 SI revision, but the text presents no derivation chain, first-principles prediction, or uniqueness theorem that reduces by construction to its own inputs. No self-citations, fitted parameters renamed as predictions, or ansatzes smuggled via prior work are referenced in the abstract or reader's summary. The resulting geometric table is definitionally consistent with the SI by design, yet the paper does not claim it yields new falsifiable content beyond the reorganization itself; the framework is therefore self-contained as a descriptive perspective rather than a circular derivation.

Assumptions & free parameters 0 free parameters · 1 assumptions · 0 invented entities

Review performed on abstract only; no explicit free parameters, axioms, or invented entities are stated in the provided text. The central interpretive move (constants as conversion factors) functions as an unstated domain assumption.

assumptions (1)
  • domain assumption The SI-defining constants can be treated purely as conversion factors without loss of physical content.
    This premise is required for the claimed geometric table to organize all units; it is invoked implicitly when the abstract states that interpreting the constants as conversion factors produces the framework.

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Cite this review

Pith. "Pith review of The structure of the new SI." pith.science (2026). https://pith.science/paper/CWSRVB2B

@misc{pith2026260630679,
  author       = {Pith},
  title        = {Pith review of: The structure of the new SI},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/CWSRVB2B}},
  note         = {Machine review of arXiv:2606.30679}
}
read the original abstract

The "new" Syst\`eme international d'unit\'es (SI), which became effective May 20, 2019, defines and is defined by a set of constants. These include the speed of light, the Planck constant, the Boltzmann constant, and the constant relating the elementary electric charge to the coulomb. Interpreting such constants as conversion factors organizes the units they relate into a unifying geometric framework. In this framework, units appear (perhaps raised to some power) either as rows/columns in a single conversion table or as entries in a list of dimensionless numbers. This organization clarifies the distinction between "fundamental" physical constants with values that are set by people, like those defined in the SI, and those with values that are set by nature. It also reveals geometry permeating our theories of physics that is normally hidden by a surplus of units.

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

10 extracted references · 10 canonical work pages

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