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| The '''observerse''' is the central mathematical object in the [[Theory of Geometric Unity]]. It is a mapping from a four-dimensional manifold <math>X^4</math> to a manifold <math>Y</math>, 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.
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| == Exogenous ==
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| In the observerse's exogenous construction, the manifold <math>X^4</math> includes into any manifold <math>Y</math> of four dimensions or higher which can admit it as an immersion.
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| <math> X^4 \hookrightarrow Y </math>
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| == Bundle-Theoretic ==
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| In the observerse's bundle-theoretic construction, the manifold <math>Y</math> sits over <math>X^4</math> as a fiber bundle.
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| [[File:Observerse-Bundle-Theoretic.jpg]]
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| == Endogenous ==
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| In the observerse's endogenous construction, <math>Y</math> is the space of metrics on the manifold <math>X^4</math>.
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| [[File:Observerse-Endogenous.jpg]] | |
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| == Tautological ==
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| In the observerse's tautological construction, the manifold <math>X^4</math> equals <math>Y</math>.
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| <math> X^4 = Y </math>
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| [[Category:Geometric Unity]] | | [[Category:Geometric Unity]] |
| [[Category:Ericisms]]
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