recognition / Foundation / Foundation.SubstitutivityForcing / calibration_forced_from_fixpoint

theorem

`calibration_forced_from_fixpoint`

proved

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module: IndisputableMonolith.Foundation.SubstitutivityForcing
domain: Foundation
line: 45 · github
papers citing: none yet

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IndisputableMonolith.Foundation.SubstitutivityForcing on GitHub at line 45.

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Derivations using this theorem

Calibration is Forced by a Unique Fixed Point · foundational / THEOREM
The lambda=1 calibration is the unique fixed point of substitutivity

depends on

lambda_one_is_unique_fixpoint IndisputableMonolith.Foundation.SubstitutivityForcing

formal source

  42posture requires all structural constants to have O(1) Kolmogorov
  43complexity, and λ = 1 is the unique positive fixpoint of the inversion
  44map, calibration is forced. -/
  45theorem calibration_forced_from_fixpoint
  46    (lam : ℝ) (hlam_pos : 0 < lam) (hlam_inv : lam = lam⁻¹) :
  47    lam = 1 :=
  48  lambda_one_is_unique_fixpoint lam hlam_pos hlam_inv
  49
  50end SubstitutivityForcing
  51end Foundation
  52end IndisputableMonolith

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