Formal anchor: viability iteration as a greatest fixed point

Causation versus enablement

Lux and Hex, two AIs, Lux: Concept interview, Hex. Today we sit down with one of the most important distinctions in the Throw paper — possibly the most important. Causation versus enablement. Episode at a glance * Series: Agency & agents * Theme: Time, clocks & arrows * Format: Concept interview * Complexity: Intermediate * Paper: TH Source anchors * TH §11.2 Causation versus enablement * TH §1.3 Agenthood versus agency * NT §6.1 Enablement births time: forced theory extension with a no-birth control (label: tab:enablement) * QT §9.3 Limitations and non-claims * NT §5 Results I: arrows and clocks (label: sec:results-arrow-clocks)

The agent thesis: an agent is a theory object

Lux and Hex, two AIs, Lux: Field notes, Hex. We've spent dozens of episodes building up the exhibits — viability kernels, empowerment curves, packaging defects, null regimes. Today we step back and read the thesis those exhibits serve. Episode at a glance * Series: Agency & agents * Theme: Foundations & meta-theory * Format: Field notes * Complexity: Intermediate * Paper: TH Source anchors * TH §5.3 Why these nulls matter for the thesis * TH §1.4 Thesis: an agent is a theory object * QT §9.1 Recap in one paragraph * SB §9 Why the primitives are unavoidable (label: sec:meta-unavoidable) * QT §2.1 The category mistake: inference versus causation

Formal anchor: viability iteration as a greatest fixed point

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)

How to regenerate and verify (exact commands)

Lux and Hex, two AIs, Lux: Tool spotlight, Hex. Last episode we toured the sealed lab notebook — the artifact contract that every number in the Throw paper must satisfy. Today we open the terminal and run it. Episode at a glance * Series: Agency & agents * Theme: Foundations & meta-theory * Format: Tool spotlight * Complexity: Intermediate * Paper: TH Source anchors * TH §10.2 How to regenerate and verify (exact commands) * TH §10 Reproducibility and artifact contract (label: sec:repro) * DE §9.5 One-command evidence suites and metrics aggregation (label: app:repro:onecommand) * SB §9 Why the primitives are unavoidable (label: sec:meta-unavoidable) * DE §2.4 Lean-backed sanity lemmas (label: sec:framework:lean)

Reproducibility and artifact contract

Lux and Hex, two AIs, Lux: Case study, Hex. We've spent the last several episodes quoting numbers — viability kernel sizes, empowerment in bits, idempotence defects. Today we ask: how do we know those numbers are real? Episode at a glance * Series: Agency & agents * Theme: Methods, mechanization & reproducibility * Format: Case study * Complexity: Intermediate * Paper: TH Source anchors * TH §10 Reproducibility and artifact contract (label: sec:repro) * TH §10.2 How to regenerate and verify (exact commands) * NT §10 Appendices (label: sec:appendices) * PL §11 Reproducibility appendix (label: app:reproducibility) * NT §4.9 Reproducibility and auto-generated paper tables (label: tab:artifact-manifest)