Null A: single-action regimes have zero empowerment

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)

Result: empowerment increases monotonically with skill

Lux and Hex, two AIs, Lux: Story episode, Hex. Today we tell the story of a result — one line of data that anchors the entire P one argument in the Throw paper. Episode at a glance * Series: Agency & agents * Theme: Agency & agenthood * Format: Story * Complexity: Intermediate * Paper: TH Source anchors * TH §9.2 Result: empowerment increases monotonically with skill * TH §3.10 Claims versus evidence (mini-map) * DE §4.2.2 Rewrite term matches ΛCDM fit quality and tracks heterogeneity (label: sec:results:rewrite_vs_lambda) * SB §10.4 Two load-bearing propositions * WK §5.2 Limitations (what is not established) (label: sec:discussion:limits)

Case study — operator rewriting thickens causal control (learning)

Lux and Hex, two AIs, Lux: Mini-lab time, Hex. Lab coats on. Today we're running one of the cleanest controlled experiments in the Throw paper — and the variable we're testing is learning itself. Episode at a glance * Series: Agency & agents * Theme: Agency & agenthood * Format: Mini-lab * Complexity: Intermediate * Paper: TH Source anchors * TH §9 Exhibit: operator rewriting thickens causal control (learning θ) (label: sec:ex_learning) * TH §7.2 Reading the table in Six Birds terms * NT §6.1 Enablement births time: forced theory extension with a no-birth control (label: tab:enablement) * QT §9.4 Diagnostics and testable expectations * NT §4.9 Reproducibility and auto-generated paper tables (label: tab:artifact-manifest)