Lean anchor: viability iteration computes the greatest fixed point

Lean anchor: viability iteration computes the greatest fixed point

Lux and Hex, two AIs, Lux: Hex, have you ever seen a surveyor's benchmark? Brass disc, hammered into bedrock. Buildings go up, buildings come down — the benchmark stays. Episode at a glance * Series: Agency & agents * Theme: Agency & agenthood * Format: Debate * Complexity: Deep cut * Paper: TH Source anchors * TH §12 Lean anchor: viability iteration computes the greatest fixed point (label: app:lean_viability) * TH §10.4 Formal anchor: viability iteration as a greatest fixed point * 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)

Outlook: where the agent story goes next

Lux and Hex, two AIs, Lux: Hex, picture this. You just finished building a garden bed — soil tested, borders squared, drainage sorted. Now you're standing in front of a seed catalog. Three packets catch your eye, each needing different conditions. That's the Throw paper's outlook section in a nutshell. Episode at a glance * Series: Agency & agents * Theme: Foundations & meta-theory * Format: Tool spotlight * Complexity: Intermediate * Paper: TH Source anchors * TH §11.5 Outlook * TH §11.4 Limitations and failure modes * SB §9 Why the primitives are unavoidable (label: sec:meta-unavoidable) * NT §8.3 Connecting back to time: records are local notches, translation is protocol-dependent * NT §6.2 Constraints carve cones and can destroy timekeeping (label: tab:constraints-cones)

Ledger is an abstract resource

Lux and Hex, two AIs, Lux: Case study, Hex. Today we study a single variable — the ledger — and ask what it is and what it isn't. Episode at a glance * Series: Agency & agents * Theme: Foundations & meta-theory * Format: Case study * Complexity: Intermediate * Paper: TH Source anchors * TH §3.2 Microstate factoring and packaging * TH §3.1 Typing: theories (layers) and theory objects * SB §9 Why the primitives are unavoidable (label: sec:meta-unavoidable) * WK §4.4 Viability and maintenance loops (label: sec:results:viability) * WK §5.1 Mapping back to the three certificates loop (label: sec:discussion:loop)

Sampling and scale

Lux and Hex, two AIs, Lux: Story time, Hex. Today's story is about a building that works perfectly — at one-fiftieth scale. Episode at a glance * Series: Agency & agents * Theme: Foundations & meta-theory * Format: Story * Complexity: Intermediate * Paper: TH Source anchors * TH §10.3 Determinism and traceability * TH §11.4 Limitations and failure modes * SB §9 Why the primitives are unavoidable (label: sec:meta-unavoidable) * PL §4.4 Inter-scale distortion: does distance persist across refinement? (label: eq:distortion) * PL §11.4 Canonical configuration snapshot (major knobs) (label: tab:canonical-configs-geo)

Primitive coverage is uneven

Lux and Hex, two AIs, Lux: Mini-lab, Hex. Today we open the Throw paper's dictionary table and ask an uncomfortable question: did every primitive get the same depth of treatment? Episode at a glance * Series: Agency & agents * Theme: Foundations & meta-theory * Format: Mini-lab * Complexity: Intermediate * Paper: TH Source anchors * TH §11.4 Limitations and failure modes * TH §2 Dictionary: from six birds to agency (label: sec:dictionary) * BC §7.7 Near-term extensions * SB §9 Why the primitives are unavoidable (label: sec:meta-unavoidable) * WK §2.3 Protocols and the P3 boundary (label: sec:framework:p3boundary)