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Orthogonal tensor (hypercube) assumes independent axes. Shear into parallelotope (hyper-rhomboid) models entangled dimensions. The shear angle encodes correlation strength; the Gram matrix of the shear IS the compression dictionary. 6 stack mappings: - PIST n-D: Cartesian → Bundle → Radial = hypercube → rhomboid → collapsed - Topological state machine: transition = shear on state tensor - N-D Gene Hypothesis: gene = n-D rhomboid, 3D structure = projection shadow - FAMM: preshaped delay = sheared time-domain rhomboid - OAC: latent cavity in sheared rhomboid space - Waveprobe: curvature = local shear angle of coordinate basis 3 compression interpretations + information gravity metric tensor
11 lines
718 B
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11 lines
718 B
Text
created: 20260507000000000
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modified: 20260507000000000
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tags: ResearchStack Lean Distributed Quine
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title: Networked Self Solving Space
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type: text/vnd.tiddlywiki
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! Networked Self Solving Space
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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.
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Durable Source: `0-Core-Formalism/lean/Semantics/Semantics/NetworkedSelfSolvingSpace.lean`
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