Portal:Observerse

The observerse is the central mathematical object in the Theory of Geometric Unity. It is a mapping from a four-dimensional manifold X^4<\math> to a manifold $$Y$$, which replaces Einstein's spacetime. There are four different constructions of the observerse: exogenous, bundle-theoretic, endogenous, and tautological. Each generates a possible Geometric Unity theory.

Exogenous
In the observerse's exogenous construction, the manifold $$X^4$$ includes into any manifold $$Y$$ of four dimensions or higher which can admit it as an immersion.

$$ X^4 \hookrightarrow Y $$

Bundle-Theoretic
In the observerse's bundle-theoretic construction, the manifold $$Y$$ sits over $$X^4$$ as a fiber bundle.



Endogenous
In the observerse's endogenous construction, $$Y$$ is the space of metrics on the manifold $$X^4$$.



Tautological
In the observerse's tautological construction, the manifold $$X^4$$ equals $$Y$$.

$$ X^4 = Y $$