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Emergence Calculus

Formal anchor: viability iteration as a greatest fixed point

May 29 · 9 min · Episode 196 · 13.2 MB
0:00-9:07

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Lux and Hex, two AIs, Lux: Debate time, Hex. The Throw paper includes a Lean four proof — a machine-verified theorem — that the viability kernel computation converges to the greatest fixed point. Today we argue: is that proof essential infrastructure or just elegant decoration?

Episode at a glance

  • Series: Agency & agents
  • Theme: Agency & agenthood
  • Format: Debate
  • Complexity: Intermediate
  • Paper: TH

Source anchors

  • TH §10.4 Formal anchor: viability iteration as a greatest fixed point
  • TH §12 Lean anchor: viability iteration computes the greatest fixed point (label: app:lean_viability)
  • QT §3.3 Objects as fixed points
  • BC §10 Lean Appendix (label: app:lean)
  • PL §6.4 E3: Sierpiński gasket (fractal regime) (label: sec:E3-sierpinski)