created: 20260507000000000
modified: 20260507000000000
tags: ResearchStack Lean Distributed Quine
title: Networked Self Solving Space
type: text/vnd.tiddlywiki

! Networked Self Solving Space

Networked Self Solving Space (`0-Core-Formalism/lean/Semantics/Semantics/NetworkedSelfSolvingSpace.lean`) formalizes a distributed quine where the PIST manifold transitions across a 5D torus using Menger sponge fractal addressing. Key equations: distributed quine axiom, networked Lyapunov with communication cost, and Gossip(Prune(Expand(S_t))) master equation. The [[GlobalConsistency]] theorem proves invariance under torus hops.

Durable Source: `0-Core-Formalism/lean/Semantics/Semantics/NetworkedSelfSolvingSpace.lean`