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"1. quantising General Relativity

2. quantising a different classical theory, while still having general relativity emerge as a low- energy (large-distance) limit.

3. having general relativity emerge as a low-energy limit of a quantum theory that is not a quantization of a classical theory

4. having both general relativity and quantum theory emerge from a theory very different from both"

Can anyone give an example of the fourth road, this part about having both general relativity and quantum theory emerge from a theory very different from both? Is there really such? How many theories along this line? How viable?