CharlesCNorton commited on
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Parent(s): 81376c6
neural_ca: state the universality claim precisely. The CA realizes and verifies the billiard-ball mechanics (ballistic transport, deflecting reversible collisions); universality is Fredkin and Toffoli's result for that model and the gate layout is their construction, not built here.
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README.md
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@@ -689,14 +689,14 @@ tile that is itself a permutation with the same 0.5 analog margin as
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so `variants/neural_ca.safetensors` stores the rule of the medium, not a
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processor.
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Its dynamics are those of the billiard-ball model of computation
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discrete reversible physics.
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```bash
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python src/ca.py # rule bijection, lattice reversibility, ballistic motion, collisions
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so `variants/neural_ca.safetensors` stores the rule of the medium, not a
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processor.
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Its dynamics are those of the billiard-ball model of computation: isolated
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particles travel ballistically along diagonals, and collisions deflect them
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reversibly, both verified here. Those are exactly the mechanics Fredkin and
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Toffoli showed are computation-universal, with ballistic particles as signals,
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fixed clusters as reflectors, and collision geometries realizing the Fredkin
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gate. This medium realizes and verifies the mechanics; the gate layout is their
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construction. It is the family's maximal dissolution of architecture: the same
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rule everywhere, no center, computation as discrete reversible physics.
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```bash
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python src/ca.py # rule bijection, lattice reversibility, ballistic motion, collisions
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