Foundation Economics

Foundation economics

Foundation economics in Recognition Science is the attempt to describe economic relationships using a single, universal measure of cost. The core idea is that the cost of a mismatch between two quantities depends only on their ratio, not on their absolute sizes. This means a 10% gap between a firm's assets and its liabilities carries the same cost whether the firm is a lemonade stand or a multinational bank.

The framework defines this cost using a function called cost, a measure of mismatch that is zero when the two quantities are equal and positive otherwise. For any two positive numbers m and e, the cost is written as J(m/e), where J is the universal cost function. The framework proves three basic facts about this cost: it is zero when m equals e, it is never negative for positive inputs, and a specific threshold value related to the golden ratio is positive. These are general mathematical facts about the cost function, not specific economic predictions.

The module also introduces a structure called FirmGrowth4Cert, which bundles these three facts into a single certificate. This certificate is a formal way of saying that the cost function behaves as expected. The framework proves that such a certificate exists, meaning the three facts are consistent with each other. This is a foundational step, not a finished economic theory.

In Recognition Science, the framework models economic growth as a process that follows a recognition-optimal trajectory. A research note in the module suggests that at this optimal trajectory, the growth rate relates to the golden ratio and a revenue growth of about 11.8% per year. This is a hypothesis, not a proved result. The module itself proves only the general facts about the cost function, not the specific economic application.

The key limitation is that the module does not define what m and e mean in economic terms. It proves facts about the cost function for any m and e, but it does not specify whether m is a firm's revenue, its assets, or something else. To make the module a theorem about economics, one would need to define m and e in economic terms. This is an open target for the framework.

def domainCost (m e : ℝ) : ℝ := Jcost (m / e)

theorem domainCost_at_eq (r : ℝ) (h : r ≠ 0) : domainCost r r = 0 := by
  unfold domainCost; rw [div_self h]; exact Jcost_unit0

theorem domainCost_nonneg (m e : ℝ) (hm : 0 < m) (he : 0 < e) : 0 ≤ domainCost m e := by
  unfold domainCost; exact Jcost_nonneg (div_pos hm he)

theorem canonicalThreshold_pos : 0 < canonicalThreshold := by
  unfold canonicalThreshold; linarith [phi_gt_onePointFive]

theorem cert_inhabited : Nonempty FirmGrowth4Cert := ⟨cert⟩

What this page does not claim

The module does not prove that firms grow at 11.8% per year; that is a research note, not a theorem. The module does not define m and e in economic terms, so it is not yet a theorem about any specific economic quantity. The three proved facts are general properties of the cost function, not specific economic predictions.

Verify this page

Every tagged claim above names its theorem. To check one yourself rather than trust this page, elaborate the source module with Lean 4 and audit its axiom basis:

$ lake env lean IndisputableMonolith/Foundation/Economics.lean
expected axiom basis: [propext, Classical.choice, Quot.sound] (the Lean kernel's standard three; no RS-specific axioms)

A page whose claims cannot be reproduced this way does not ship. In production, every anchor links to the exact declaration in the public source release, and this block carries the build receipt for the page itself.

Derived articles

This page is generated by a question-recursion engine: the questions its answers raise become the next pages. The current agenda, with open targets marked red: