recognition › ask › explain-the-lean-theorem-forced-of-factorization-in-module-i-4ce95b26

Explain the Lean theorem `forced_of_factorization` in module `IndisputableMonolith.Cost.Ndim.Uniqueness`. Write for an educated reader who knows science and programming but may not know Lean. Cover: (1) what the declaration says in plain English, (2) why it matters in Recognition Science, (3) how to read the formal statement, (4) visible dependencies or certificates in the supplied source, and (5) what this declaration does not prove. Cite only declarations present in the supplied Recognition source.

permalink: https://pith.science/recognition/ask/explain-the-lean-theorem-forced-of-factorization-in-module-i-4ce95b26 · first asked 2026-05-10 · browse all asks

confidence: low outside recognition cached

The supplied Lean source slice does not contain the module IndisputableMonolith.Cost.Ndim.Uniqueness or the theorem forced_of_factorization.

While the Recognition Science framework establishes the uniqueness of the reciprocal-symmetric cost function (as THEOREM t5_holds / washburn_uniqueness_aczel from the broader canon, detailed in the primer), the specific mathematical and formal details of the multidimensional factorization theorem you asked about are absent from this slice. Therefore, I cannot give a step-by-step breakdown of its formal statement, dependencies, or limitations based solely on the provided source code.

outside recognition

Aspects Recognition does not yet address:

The module IndisputableMonolith.Cost.Ndim.Uniqueness is not in the supplied source.
The Lean declaration forced_of_factorization is not in the supplied source.

recognition modules consulted

The Recognition library is at github.com/jonwashburn/shape-of-logic. The model is restricted to the supplied Lean source and instructed not to invent theorem names. Treat output as a starting point, not a verified proof.