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Explain the Lean theorem `abs_exp_sub_one_sub_id_le_sq_of_abs_le_one` in module `IndisputableMonolith.NumberTheory.AnnularCost`. 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-abs-exp-sub-one-sub-id-le-sq-of-abs-6fb00d63 · first asked 2026-05-10 · browse all asks

Big AI job. Grok 4.3 reads the canon and writes a Lean-grounded derivation; usually 20 seconds to 2 minutes. The page will refresh to your answer when it’s ready.
confidence: low outside recognition cached

The supplied canon source does not contain the module IndisputableMonolith.NumberTheory.AnnularCost or any declaration named abs_exp_sub_one_sub_id_le_sq_of_abs_le_one. No material from the canon bears on this specific theorem, so no explanation, derivation, or analysis is possible from the provided Lean modules.

outside recognition

Aspects Recognition does not yet address:

  • Module IndisputableMonolith.NumberTheory.AnnularCost
  • Declaration abs_exp_sub_one_sub_id_le_sq_of_abs_le_one
  • Any content, dependencies, or certificates related to annular cost or the named inequality

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.