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Correct outputs of the construction program

Lax235315.ConstructionCorrectness · concepts/Lax235315/ConstructionCorrectness.lean · lax-235315

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    Natural Language Statement

    Theorem

    For all sufficiently large resource constants K, an admissible execution that reaches the final halt with the success flag set outputs every graph vertex exactly once, in an order crossed at most 12c² ceil(log₂ n)² times by every open neighborhood.

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    Lean source view on GitHub

    1import Lax235315.ConstructionContracts
    2
    3/-!
    4---
    5title: Correct outputs of the construction program
    6type: theorem
    7---
    8For all sufficiently large resource constants K, an admissible execution
    9that reaches the final halt with the success flag set outputs every graph
    10vertex exactly once, in an order crossed at most
    1112c² ceil(log₂ n)² times by every open neighborhood.
    12
    13# Formalization notes
    14
    15This is an open bridge from concrete machine execution to the deterministic
    16contraction and reconstruction argument. No probability conclusion is assumed
    17or asserted. Empty and singleton graphs are included in the contract.
    18-/
    19
    20namespace Lax235315.ConstructionCorrectness
    21open Lax235315.ConstructionContracts
    22
    23/-- Successful machine executions satisfy the exact registered output relation. -/
    24axiom eventually_hasCorrectOutput :
    25 ∃ K₀ : ℕ, 1 ≤ K₀ ∧ ∀ K : ℕ, K₀ ≤ K → HasCorrectOutput K
    26
    27end Lax235315.ConstructionCorrectness
    28
    Formalization notes

    This is an open bridge from concrete machine execution to the deterministic contraction and reconstruction argument. No probability conclusion is assumed or asserted. Empty and singleton graphs are included in the contract.

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