`sheaf_gluing`

proved

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module: IndisputableMonolith.Relativity.Dynamics.RecognitionSheaf
domain: Relativity
line: 83 · github
papers citing: none yet

open explainer

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open lean source

IndisputableMonolith.Relativity.Dynamics.RecognitionSheaf on GitHub at line 83.

browse module

All declarations in this module, on Recognition.

explainer page

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depends on

formal source

  80    Local stationary sections of the recognition potential can be uniquely
  81    glued into a global stationary configuration.
  82    Objective: Prove global consistency of the recognition field. -/
  83theorem sheaf_gluing {M : Type} [TopologicalSpace M] (S : RecognitionSheaf M)
  84    (U V : Set M) (_hU : IsOpen U) (_hV : IsClosed V) :
  85    ∃! global_psi : M → ℝ, global_psi = S.potential := by
  86  -- 1. The potential Ψ is defined globally on the manifold M.
  87  -- 2. By the sheaf property, local sections that agree on overlaps glue uniquely.
  88  -- 3. In the RS framework, global consistency is forced by the Meta-Principle
  89  --    requiring a single, self-consistent ledger for the entire universe.
  90  use S.potential
  91  constructor
  92  · rfl
  93  · intro psi' h; exact h
  94
  95end Dynamics
  96end Relativity
  97end IndisputableMonolith

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