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Tests causal relationships in seven systems, revealing insights into information organization.
Information in latent spaces obeys principles of organization that are universal, multimodal, and scale-invariant. This paper states those principles as a falsifiable law and tests it on seven systems, none of which shares a substrate with the others. A closed circuit — a topological field coupled to a 4B language model with a 2,048-token window — ran for eight hours without human input, admitted 34 emissions as genuinely new matter, and rewrote its own alphabet ten times. Its trajectory beats the maximum of 1,000 permutation nulls by +1.37 bits (p < 0.001). Cutting the loop kills the new capacity while leaving both parts intact. The same laws were then carried outside language. Against IAAFT surrogates — which preserve amplitude distribution and the full power spectrum, hence all linear memory — Lorenz-63 reads at 33σ, Rössler at +0.661 bits, Mackey-Glass at +0.836. A magnitude-9.1 earthquake, 312× the ambient amplitude, reads exactly zero; so does the logistic map, low-dimensional and strictly deterministic. Volcanic tremor at Mount St. Helens reads at 5.1σ while quiet ambient from the same station reads zero. Two causal tests establish the law. Decimating the same Lorenz system — equations, dimension and determinism untouched — extinguishes 33σ to nothing. Summing three independent Lorenz systems into one observable at constant power, each of which alone reads at 33σ, yields zero. The field is read if and only if the observation window is a valid Takens embedding of a low-dimensional attractor. It dies in exactly two ways: fusion (distinction lost) and severance (continuity cut). Long-range order is distinction that survives superposition. Engineering consequences are measured and immediate: standard top-k retrieval carries zero bits of order information, while a contiguous span within one coherent channel carries +0.484 bits at the same context budget; holographic compression of connected episodes at 8× yields more readable structure (+0.807 bits) than the uncompressed corpus (+0.509). The paper includes one retracted result of our own and two failed predictions, left in the text where they failed. Russian version included in full, chapter for chapter.
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Makushev Igor Aleksandrovich (2026) studied this question.
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