Metaphysical Coherentist approach to mutually-grounding emergent reality
I have recently been working on a philosophical framework centered around mutually grounded entities that relies on a modern take on Hegelian dialectics, particularly the logic surrounding determinacy and negation. I know this is a rather odd place to be asking a largely philosophical question, but I believe that my framework has enough logical merit that it is time to see about getting it to work with relativity.
The core of the idea is to use mutually grounded entities such that they effectively overlap with one another in an abstract topological space. By overlapping, they have a similarity measure about them, and effectively encapsulate a "component" or "aspect" of the other entity within their own reality. When I say that an entity has its own reality, I am simply referring to the invariant nature of identity and that anything that matters to some entity (whereas an entity could be a particle, brane, string, etc.) is already encoded within the nature of that entity.
This overlap, I argue, creates a structure remniscent of an inner product if you attach a simple scalar metric to deal with similarity, because you must multiply once by this similarity to see how similar some entity A is to the shared region, and multiply again to see how similar this region is to entity B, thus telling us that the accumulated similarity measure between A and B is proportional to k^2 - or rather, the component's proportional contribution to A times its proportional contribution to B.
To avoid a viciously circular grounding, which would contradict the very premise of considering the possibility of two determinate, overlapping entities, there must be a helical overlap instead that leads to the geometric series (1 + k^2 + k^4...) which interestingly evaluates to the Lorentz factor squared if one takes k to mean v/c, which seems like a bold jump until you consider the plausibility of this corresponding with the River Model given the idea of an inner product and potential correspondence with the metric tensor.
I have attached both the abstract and the draft of my framework. Anyhow, what are y'all's thoughts on how to formalize these ideas?
Main doc (read highlighted):
Abstract: https://docs.google.com/document/d/1H9l24L0Xs1TUC5YbNnn_T2p02JW0LEuQ3gAIxwEafAI/edit?usp=sharing