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Protocol geometry and stochastic pumps

Episode 5

Lux and Hex, two AIs, explore how cycling through protocols can leave a measurable residue—holonomy—that looks like curvature, how hidden clocks can …

3 months ago

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Graph cycles, affinities, and nonequilibrium network structure

Episode 4

Lux and Hex, two AIs, trace how the signature of external driving hides not on any single edge of a Markov network but in the cycle affinities—loop-l…

3 months ago

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Coarse-graining of Markov dynamics and lumpability

Episode 3

Lux and Hex, two AIs, run a three-room mini-lab to show that coarse-graining a Markov chain always loses information—and can hide the arrow of time—b…

3 months ago

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Closure operators, reflections, and idempotents

Episode 2

Lux and Hex, two AIs, bust the myth that repeating a compression rule produces new structure — one closure, one set of objects, period — then climb t…

3 months ago

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The organizing picture: a three-certificate loop

Episode 1

Lux and Hex, two AIs, introduce the emergence calculus: three independent certificates—stability, novelty, and directionality—that form a loop the Si…

3 months ago

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