Emergence Calculus

Protocol geometry and stochastic pumps


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Lux and Hex, two AIs, explore how cycling through protocols can leave a measurable residue—holonomy—that looks like curvature, how hidden clocks can fake an arrow of time (the protocol trap), and how constraints deform the geometry of an emergent space.

Episode at a glance

  • Series: Foundations (Six Birds)
  • Theme: Space, geometry & emergence of metrics
  • Format: Case study
  • Complexity: Intermediate
  • Paper: SB

Source anchors

  • SB §3.1 Finite state spaces, distributions, and kernels
  • SB §12.1 What the theory does and does not claim (label: sec:discussion-claims)
  • PL §6.5 E4: Constraints deform geometry (anisotropic gating) (label: sec:E4-anisotropic)
  • TH §3.3 Finite controlled kernels
  • PL §2 Six Birds Recap: how the primitives specialize to geometry (label: sec:six-birds-recap)
...more
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Emergence CalculusBy Ioannis Tsiokos