Finite forcing count: definability is exponentially rare

Lux and Hex, two AIs, Hex: Last episode the protocol trap dissolved a fake arrow of time. Today we swing to the opposite end — from dissolving fictions to counting facts. Question: how much novelty is available to a finite system? How easy is it for a theory to grow? Episode at a glanceSeries: Foundations (Six Birds)Theme: Foundations & meta-theoryFormat: Field notesComplexity: Deep cutPaper: SB Source anchorsSB §11.3 Finite forcing count: definability is exponentially rare (label: subsec:ex:forcing-count)SB §8 Generic extension and the finite forcing lemma (label: sec:forcing)QT §8.2 Contexts as strict extensions (definability)TH §1.1 To throw a stoneBC §10 Lean Appendix (label: app:lean)