Selected-floor prefix certificate for prepared pair 4, left list, part 3

Proved

D1Bound5.PairLightAdaptivePrepared4.left_prefix_002_part03_checked

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

diophantine-tuplesnumber-theory

For prepared pair 4, left list, part 3, the selected-floor certificate succeeds for at most 17 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 PairLightPrepared4.sieve. Original heads 201 through 217, retaining complete original tails.

Preamble

import Init
import Definitions.Def_D1Bound5_PairLightArithmeticChunks_Definitions
import Definitions.Def_D1Bound5_PairLightArithmetic_Definitions
import Definitions.Def_D1Bound5_SmallPairLightData4LeftCached_Definitions
import Definitions.Def_D1Bound5_SmallPairLightData4LeftRows_Definitions
import Definitions.Def_D1Bound5_SmallPairLightData4Sieve_Definitions

Formal statement

section
namespace D1Bound5.PairLightAdaptivePrepared4
set_option autoImplicit false
set_option maxRecDepth 100000
set_option maxHeartbeats 0


theorem _root_.D1Bound5.PairLightAdaptivePrepared4.left_prefix_002_part03_checked :
    pairLightSelectedFloorPrefixBool 0 1 PairLightPrepared4.sieve 17
      (PairLightPrepared4.leftCached.drop 201)
      (PairLightPrepared4.leftRows.drop 201) = true := by sorry

end D1Bound5.PairLightAdaptivePrepared4
end

Source

D1Bound5/SmallPairLightAdaptiveLeft4_002Part03.lean, lines 11-16, SHA-256 64b60503c365a779e38d62d93404f47827f6f310497d2792ea8f2fe20633a03c. Project: https://github.com/tomislav-math/d1-bound5-lean

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