Selected-floor prefix certificate for prepared pair 19, left list, part 4

Proved

D1Bound5.PairLightAdaptivePrepared19.left_prefix_000_part04_checked

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

diophantine-tuplesnumber-theory

For prepared pair 19, left list, part 4, 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 = 1, and the sieve is PairLightPrepared19.sieve. Original heads 48 through 59, 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_SmallPairLightData19LeftCached_Definitions
import Definitions.Def_D1Bound5_SmallPairLightData19LeftRows_Definitions
import Definitions.Def_D1Bound5_SmallPairLightData19Sieve_Definitions

Formal statement

section
namespace D1Bound5.PairLightAdaptivePrepared19
set_option maxRecDepth 100000
set_option maxHeartbeats 0


theorem _root_.D1Bound5.PairLightAdaptivePrepared19.left_prefix_000_part04_checked :
    pairLightSelectedFloorPrefixBool 1 1 PairLightPrepared19.sieve 12
      (PairLightPrepared19.leftCached.drop 48)
      (PairLightPrepared19.leftRows.drop 48) = true := by sorry

end D1Bound5.PairLightAdaptivePrepared19
end

Source

D1Bound5/SmallPairLightAdaptiveLeft19_000Part04.lean, lines 11-16, SHA-256 3d471ea413b41d4789e34cb7ce454f1e5bef7d16c042ad745558646607ecd9f8. Project: https://github.com/tomislav-math/d1-bound5-lean

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