Invariant Structural Value: Fundamental Constants and Formulas as Invariant Relations

In the paper's words

A measured physical quantity is a number that survives all arbitrary choices. The unit system, the coordinate system, the gauge choice, the Hilbert-space basis, and the energy scale are all choices; what is invariant under them is what is physical. This essay develops the structuralist reading that follows: fundamental constants and formulas encode invariant relations — the logical architecture of physical law — rather than magnitudes in human units.

The abstract, verbatim, and its opening sentence is the claim. Every line below is quoted from the text.

Numbers it reports

No sentence of this paper reports a figure with a unit or a quantity word, so none is shown.

How it is done

1. C3 is claimed constructively, not by pattern-matching.

   from Formal derivation (constructive, pre-registered)

What would falsify it

1. These are quantized invariants of a mathematical structure, not continuously tunable decimals. [TERRITORY — the claim that measurable content is invariants of a mathematical structure is falsifiable: a gauge-dependent observable that is nonetheless measured would disconfirm it.]

   from S-matrix and topological invariants

2. The fixed point of that loop is $e$. [TERRITORY — disconfirmation: if e can be exhibited as requiring an additional primitive beyond self-application of a mark-and-distinction (a resource not derivable from the calculus of indications), the claim is false.]

   from e as the invariant of self-application

3. Thus $\pi$ is the invariant that makes self-adjoint differentiation on a compact domain consistent. [TERRITORY — disconfirmation: if a self-referential equation is exhibited whose fixed point is a constant other than $e$ or $\pi$ with no structural characterization, the fixed-point reading is incomplete.]

   from pi as the invariant of self-closure

Where the claim stops

1. Each step above is an exhibited equation with a unique solution; no numerical value is assumed.

   from Formal derivation (constructive, pre-registered)

2. The Standard Model's measured parameters and the underdetermination arguments against structural realism are audited with identical rigor, not assumed superior.

   from Symmetric audit

Where to read

1. Introduction164 words · 1 min
2. Measured Quantities as Invariants251 words · 1 min
3. Quantum Mechanics as Invariant Structure162 words · 1 min
4. The Non-Measurable Mathematical Scaffolding183 words · 1 min
5. Self-Adjointness and Self-Reference: e and pi from Mark and Distinction810 words · 4 min
6. Falsifiability and Symmetric Audit152 words · 1 min
7. Conclusion85 words · 1 min
8. Declarations46 words · 1 min