Selected-floor prefix certificate for prepared pair 40, left list

Proved

D1Bound5.PairLightAdaptivePrepared40.left_prefix_000_checked

by tp · Oct 24, 2026 · Mathlib 0df444a (Lean v4.33.1)

diophantine-tuplesnumber-theory

For prepared pair 40, left list, the selected-floor certificate succeeds for at most 137 head rows of the supplied cached vertex list. Each selected head is checked against its complete remaining tail, including vertices beyond the end of this chunk. The quadratic coordinate parameters are τ = 1 and ν = 2, and the sieve is PairLightPrepared40.sieve. Heads 0 through 136; every head retains its entire tail.

Preamble

import Init
import Mathlib.Data.List.Basic
import Definitions.Def_D1Bound5_PairLightArithmeticChunks_Definitions
import Definitions.Def_D1Bound5_SmallPairLightAdaptiveData40_Definitions
import Definitions.Def_D1Bound5_SmallPairLightData40_Definitions_001

Formal statement

section
namespace D1Bound5.PairLightAdaptivePrepared40
set_option maxRecDepth 100000
set_option maxHeartbeats 0


theorem _root_.D1Bound5.PairLightAdaptivePrepared40.left_prefix_000_checked :
    pairLightSelectedFloorPrefixBool 1 2 PairLightPrepared40.sieve 137
      leftCached000 leftRows000 = true := by sorry

end D1Bound5.PairLightAdaptivePrepared40
end

Source

D1Bound5/SmallPairLightAdaptiveLeft40_000.lean, lines 13-43, SHA-256 fdbb11226b21b3a783368b1cc54f9d95fe996e258cf7ebe9ec19d46f6f485c3c. Project: https://github.com/tomislav-math/d1-bound5-lean

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