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

Proved

D1Bound5.PairLightAdaptivePrepared5.left_prefix_000_direct_checked

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

diophantine-tuplesnumber-theory

For prepared pair 5, left list, the selected-floor certificate succeeds for at most 105 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.

Preamble

import Init
import Mathlib.Data.List.Basic
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_direct_checked :
    pairLightSelectedFloorPrefixBool 0 1 PairLightPrepared5.sieve 105
      (PairLightPrepared5.leftCached.drop 0) (PairLightPrepared5.leftRows.drop 0) = true := by sorry
end D1Bound5.PairLightAdaptivePrepared5
end

Source

D1Bound5/SmallPairLightLeft5Prefix000.lean, lines 16-69, SHA-256 dfbdb2f80f0af97acb5c6d15aad8c5ba114c4e7aef073212558c0a091fbf1811. Project: https://github.com/tomislav-math/d1-bound5-lean

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