The Conceptual and Philosophical Foundations

1. Entropy is physical.

From thermodynamics, entropy is not just a bookkeeping device; it has measurable, physical consequences.

2. Entropy creates information.

Changes in entropy structure the space of possible states and their distinguishability—i.e., they generate information.

3. Information has geometry.

Information geometry (Fisher–Rao, Fubini–Study, etc.) shows that distinguishability between states defines a metric and hence a geometry.

4. Geometry is a field.

In Einstein’s view, geometry is not a static backdrop but a dynamical field (the metric field).

5. Therefore, entropy must define a field with its own geometry.

If entropy generates information, and information induces geometry, and geometry is a field, then entropy itself must be representable as a field with an associated geometry—the Entropic Field.

6. A physical field with geometry must admit an action principle.

Every fundamental field in modern physics (electromagnetic, Yang–Mills, metric, scalar fields) is governed by an action.

So, the Entropic Field must have an action and field equations.

7. Therefore, the Obidi Action is not optional—it is logically and physically required.

Thus, the Obidi Action becomes a mathematical necessity for physics. It is the unique kind of object that can encode: