Selected-floor prefix certificate for prepared pair 48, left list, part 0

Proved

D1Bound5.PairLightAdaptivePrepared48.left_prefix_000_part00_checked

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

diophantine-tuplesnumber-theory

For prepared pair 48, left list, part 0, the selected-floor certificate succeeds for at most 28 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 = 8, and the sieve is PairLightPrepared48.sieve. Original heads 0 through 27; each retains its entire original tail.

Preamble

import Init
import Definitions.Def_D1Bound5_PairLightArithmeticChunks_Definitions
import Definitions.Def_D1Bound5_PairLightArithmetic_Definitions
import Definitions.Def_D1Bound5_SmallPairLightAdaptiveData48_Definitions
import Definitions.Def_D1Bound5_SmallPairLightData48Left_Definitions_001

Formal statement

section
namespace D1Bound5.PairLightAdaptivePrepared48
set_option maxRecDepth 100000
set_option maxHeartbeats 0


theorem _root_.D1Bound5.PairLightAdaptivePrepared48.left_prefix_000_part00_checked :
    pairLightSelectedFloorPrefixBool 1 8 PairLightPrepared48.sieve 28
      (leftCached000.drop 0) (leftRows000.drop 0) = true := by sorry

end D1Bound5.PairLightAdaptivePrepared48
end

Source

D1Bound5/SmallPairLightAdaptiveLeft48_000Part00.lean, lines 7-11, SHA-256 5ae02e7e3e5495ea53f0a25561c5911bbf65319375a17dd09a21676477d60dc2. Project: https://github.com/tomislav-math/d1-bound5-lean

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