Theorem of Monetary Fraud via Unit Creation
Abstract
This paper formalizes a logical theorem concerning monetary measurement and the creation of monetary units. It begins from the premise that money functions as a scale of measurement for the total wealth of a society, and that any valid scale requires a fixed graduation, meaning a fixed number of units. The theorem demonstrates that increasing the quantity of monetary units does not adjust an existing scale but instead creates a new monetary scale with a different internal definition. When this new scale is presented as a continuation of the previous one, a silent transition occurs during which agents closest to the creation of new units obtain a relative advantage, resulting in wealth concentration. Once the new scale becomes widely adopted, prices adjust and measurements are expressed in the new scale, consolidating the effects of the initial manipulation. The analysis shows that monetary unit creation constitutes a formal fraud of measurement, independent of economic growth, crisis conditions, or policy intent, and that a monetary system can only function as a neutral measuring instrument if its scale graduation is fixed and inviolable.
Definitions
D1. Scale of measurement
A reference system used to measure a magnitude, defined by a whole and a fixed graduation, that is, a fixed number of units.
D2. Unit
An internal division of the scale, representing a fixed fraction of the total scale.
D3. Monetary scale
The scale used to measure the total wealth of a society, in which each unit represents a formal fraction of that scale.
D4. Prices
Measurements expressing relations between units of the monetary scale and economic reality.
Axioms
A1. A scale of measurement is only a scale if its graduation is fixed.
A2. The measured reality may change without requiring any change to the scale.
A3. Changing the number of units changes the identity of the scale.
A4. Measurements do not create reality; they only describe it.
Propositions
P1. As long as the graduation of the monetary scale remains fixed, each unit represents the same fraction of the scale.
P2. Creating additional monetary units alters the graduation of the scale.
P3. Altering the graduation of the scale necessarily creates a new scale, distinct from the previous one.
P4. If the new scale is presented as a continuation of the previous one, a scale transition occurs.
P5. During this transition, agents who receive or use units of the new scale earlier obtain a relative advantage and concentrate wealth.
P6. Once the new scale becomes widely used, prices adjust and measurements are expressed entirely in the new scale.
Theorem
Any creation of additional monetary units does not adjust an existing scale but creates a new one.
When this new scale is presented as if it were the continuation of the previous scale, a silent scale transition occurs, during which relative advantage and wealth concentration arise, and which is later consolidated by the adjustment of prices that impose the new scale as the operative reference.
Proof (logical outline)
By A1, a scale requires fixed graduation.
By P2, creating units alters graduation.
By A3, altering graduation creates a new scale.
By P4, this produces a scale transition rather than a declared replacement.
By P5, this transition generates relative advantage and wealth concentration.
By P6, prices adjust and enforce the new scale as the standard of measurement.
Therefore, monetary expansion is a silent transition between scales with unavoidable distributive effects.
Q.E.D.
Corollary
A society that allows changes in monetary graduation accepts successive monetary scales while treating them as a single continuous scale, thereby invalidating intertemporal comparison and structurally enabling wealth concentration.
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