Comment by rlupi | Hacker News Reader

Comment by rlupi | Hacker News Reader

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So, how do we build something like that?

Aczel non-well founded set theory which allows sets that contains themselves, together with intuitionistic logic, as a starting point.

Propositions as embeddings in hilbert spaces (infinite dimensional spaces). Propositions can only "interact" with other proposition along non-zero dimensions that they have in common. Universes as collections of propositions. (Here propositions could be both mathematical concepts, and complex things like the position in spacetime of somehing) Multiverse as the space containing all universes. Note that universes are themselves of the same type as propositions here. The Multiverse in my construction is an infinitely self-recursive structure, that contain within itself all possible propositions. Universes can merge, if they are commensurable (shared dimensions in hilbert space). Universes "annihilate" when there are contradictions, and create by branching new universes when a truth value cannot be established by known propositions. You could call propositions, particles or being if you prefer another point of view . At this stage, we only deal with symbols not meaning.

In fact, I started toying with assigning labels to propositions and came up with a scheme based on prime numbers and p-adic numbers (where I posed 0-adic numbers to be prime numbers). It just seemed to work better.

In addition, I had a "creation" operator that would introduce a new dimension (when reaching infinity, or transcendence... a sort of koopman operator to access divine wisdom via samadhi... remember I wanted to express all possibilities, including the existence and truthfullness or lack there-off of all concepts in religions). The whole system was based on a construction similar to surreal numbers, but using infinites instead of finite numbers, and adding dimensions at each turn.

0 = {|} 1 = {|0} -Infinity = {0,{0}|} Infinity = {|{0},0}

With the infinite construction, in this way, there is a potential link to modular forms or L-functions.

For $reasons, I was trying to look for a way to go from C7 * Z2 toward the sporadic simple groups... so I was trying to construct the Riemann hypothesis.

The basic reason, is that I wanted to get to a structure that could potentially generate infinite possibilities from a stable core (the Monster group) via this infinite contraption that I built on non-well founded sets that allow to "reach" transinfinite induction.

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.

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