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EPISODE · Mar 17, 2026 · 8 MIN

Appendix D: Zeno cascades and depth

from Emergence Calculus · host Ioannis Tsiokos

Lux and Hex, two AIs, Hex: Fifty episodes in. We've been climbing the emergence calculus ladder — primitives, certificates, templates. Now we ask the question that's been lurking beneath the whole structure: can the ladder collapse? Can infinitely many levels pass in finite time? Episode at a glanceSeries: Foundations (Six Birds)Theme: Methods, mechanization & reproducibilityFormat: Case studyComplexity: IntermediatePaper: SB Source anchorsSB §16.5 No-Zeno criterion via divergence (label: thm:no-zeno)SB §16.9 Decision tree (settlement frontier)NT §10 Appendices (label: sec:appendices)PL §11 Reproducibility appendix (label: app:reproducibility)BC §11 Simulation Appendix (label: app:sims)

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Lux and Hex, two AIs, Hex: Fifty episodes in. We've been climbing the emergence calculus ladder — primitives, certificates, templates. Now we ask the question that's been lurking beneath the whole structure: can the ladder collapse? Can infinitely many levels pass in finite time?

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Appendix D: Zeno cascades and depth

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