Love reading this!! Your construction is fascinating, especially the way you use non-well-founded set theory and p-adic embeddings to frame an infinitely self-recursive multiverse model. The idea that universes function as self-contained propositions, merging or annihilating based on shared dimensionality, is an elegant way to encode consistency while allowing for the emergence of contradictions as generative structures. The link to intuitionistic logic makes sense—by avoiding classical absolutes, you keep the system dynamic, which feels necessary for a Level IV framework.

One area that might add further structure to your model is incorporating coherence as a constraint on infinite possibility rather than pure symbolic recursion. You’re already playing with prime numbers and p-adic structures, which suggests an underlying resonance across scales. But what if, instead of assuming an open-ended proliferation of universes based purely on logical interactions, there was a chirality-driven resonance field that phase-locks emergent structures, preventing infinite bifurcation while still allowing for maximal generativity? Basically, E is foundational, M is a temporary prime-phase lock so E -> M -> E or E -> Quantum Coherence Field (QCF) ->plasma -> gas -> liquid -> solid roughly? Gravity is secondary (not curvature) but a structured resonance field where mass emerges from phase-locked energy waves, and spacetime distortions arise from coherence gradients rather than geometric warping?

Basically, my theory CODES frames this in terms of structured emergence—rather than relying on stochastic processes or unrestricted symbolic freedom, it suggests that prime-number resonance structures act as the limiting factor that stabilizes reality’s information geometry. This could help bridge the gap between your self-recursive model and the physical constraints needed to manifest stable universes beyond pure formalism?

Your attempt to move from C7 * Z_2 toward sporadic groups, especially in relation to the Riemann hypothesis, suggests that you’re looking for an intrinsic ordering principle rather than just an infinite proliferation of structures. Have you considered whether prime gap structures could serve as the fundamental attractors within your recursive system? This would allow for self-referential sets while maintaining coherence constraints beyond arbitrary modularity. Basically, not looking at numbers as static points on a linear axis but as lightening bolts (hence continuous wavelet transforms (morlets etc cause localization balancing time/frequency resolution, usings primes so skips Godel cause primes are then self-consistent, irreducible generators of structure vs. axiomatic closure so no non-arbitrary basis for emergence, skipping limits of formal systems that require external validation)) = structured resonance, why wavelets outperform Fourier by capturing localized frequency shifts, chirality-induced phase locking, and emergent structure in ways traditional harmonic analysis cannot. Numbers are physical resource states not abstract symbols in this way.

Curious to hear your thoughts! Your approach feels close to something profound, and I think there’s a natural bridge between your work and the coherence-driven emergence model that CODES is building.