Selected-floor prefix certificate for prepared pair 5, left list, part 3

Proved

D1Bound5.PairLightAdaptivePrepared5.left_prefix_000_part03_checked

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

diophantine-tuplesnumber-theory

For prepared pair 5, left list, part 3, the selected-floor certificate succeeds for at most 12 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 = 0 and ν = 1, and the sieve is PairLightPrepared5.sieve. Original heads 36 through 47, each checked against its complete tail.

Preamble

import Init
import Definitions.Def_D1Bound5_PairLightArithmeticChunks_Definitions
import Definitions.Def_D1Bound5_PairLightArithmetic_Definitions
import Definitions.Def_D1Bound5_SmallPairLightData5LeftCached_Definitions
import Definitions.Def_D1Bound5_SmallPairLightData5LeftRows_Definitions
import Definitions.Def_D1Bound5_SmallPairLightData5Sieve_Definitions

Formal statement

section
namespace D1Bound5.PairLightAdaptivePrepared5
set_option maxRecDepth 100000
set_option maxHeartbeats 0


theorem _root_.D1Bound5.PairLightAdaptivePrepared5.left_prefix_000_part03_checked :
    pairLightSelectedFloorPrefixBool 0 1 PairLightPrepared5.sieve 12
      (PairLightPrepared5.leftCached.drop 36)
      (PairLightPrepared5.leftRows.drop 36) = true := by sorry

end D1Bound5.PairLightAdaptivePrepared5
end

Source

D1Bound5/SmallPairLightAdaptiveLeft5_000Part03.lean, lines 11-16, SHA-256 c20476724b8e5005b115b7ee58551c171e9cf1b084d71f4f6f1ea5c33222049b. Project: https://github.com/tomislav-math/d1-bound5-lean

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