Selected-floor prefix certificate for prepared pair 43, left list, part 1

Proved

D1Bound5.PairLightAdaptivePrepared43.left_prefix_001_part01_checked

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

diophantine-tuplesnumber-theory

For prepared pair 43, left list, part 1, 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 = 1 and ν = 3, and the sieve is PairLightPrepared43.sieve. Original heads 103 through 114, 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_SmallPairLightData43Left_Definitions_001
import Definitions.Def_D1Bound5_SmallPairLightData43Left_Definitions_002
import Definitions.Def_D1Bound5_SmallPairLightData43Left_Definitions_003

Formal statement

section
namespace D1Bound5.PairLightAdaptivePrepared43
set_option maxRecDepth 100000
set_option maxHeartbeats 0


theorem _root_.D1Bound5.PairLightAdaptivePrepared43.left_prefix_001_part01_checked :
    pairLightSelectedFloorPrefixBool 1 3 PairLightPrepared43.sieve 12
      (PairLightPrepared43.leftCached.drop 103)
      (PairLightPrepared43.leftRows.drop 103) = true := by sorry

end D1Bound5.PairLightAdaptivePrepared43
end

Source

D1Bound5/SmallPairLightAdaptiveLeft43_001Part01.lean, lines 8-13, SHA-256 fb84e7d52b8fd013f09c12790816eaee67db9ec2c7040c0cfd64ee3357b97426. Project: https://github.com/tomislav-math/d1-bound5-lean

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