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Success probability of the construction program

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

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    Natural Language Statement

    Theorem

    For all sufficiently large resource constants K, at least two thirds of the equally likely finite random tapes cause an admissible construction run to reach the final halt with the success flag set.

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    1import Lax235315.ConstructionContracts
    2
    3/-!
    4---
    5title: Success probability of the construction program
    6type: theorem
    7---
    8For all sufficiently large resource constants K, at least two thirds of the
    9equally likely finite random tapes cause an admissible construction run to
    10reach the final halt with the success flag set.
    11
    12# Formalization notes
    13
    14This is an open probability obligation for the explicit program, not for an
    15ideal uniform-sampling oracle. Its proof must account for collisions of the
    16finite random keys, conditional sampling at every adaptive round, and the
    17available tape length. Output quality is proved separately.
    18-/
    19
    20namespace Lax235315.ConstructionProbability
    21open Lax235315.ConstructionContracts
    22
    23/-- At least two thirds of the finite tapes lead to successful termination. -/
    24axiom eventually_hasSuccessProbability :
    25 ∃ K₀ : ℕ, 1 ≤ K₀ ∧ ∀ K : ℕ, K₀ ≤ K → HasSuccessProbability K
    26
    27end Lax235315.ConstructionProbability
    28
    Formalization notes

    This is an open probability obligation for the explicit program, not for an ideal uniform-sampling oracle. Its proof must account for collisions of the finite random keys, conditional sampling at every adaptive round, and the available tape length. Output quality is proved separately.

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