Selected-floor prefix certificate for prepared pair 7, left list

Proved

D1Bound5.PairLightAdaptivePrepared7.left_prefix_001_direct_checked

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

diophantine-tuplesnumber-theory

For prepared pair 7, left list, the selected-floor certificate succeeds for at most 163 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 PairLightPrepared7.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_SmallPairLightData7LeftCached_Definitions
import Definitions.Def_D1Bound5_SmallPairLightData7LeftRows_Definitions
import Definitions.Def_D1Bound5_SmallPairLightData7Sieve_Definitions

Formal statement

section
namespace D1Bound5.PairLightAdaptivePrepared7
set_option maxRecDepth 100000
set_option maxHeartbeats 0

theorem _root_.D1Bound5.PairLightAdaptivePrepared7.left_prefix_001_direct_checked :
    pairLightSelectedFloorPrefixBool 0 1 PairLightPrepared7.sieve 163
      (PairLightPrepared7.leftCached.drop 105) (PairLightPrepared7.leftRows.drop 105) = true := by sorry
end D1Bound5.PairLightAdaptivePrepared7
end

Source

D1Bound5/SmallPairLightLeft7Prefix001.lean, lines 14-55, SHA-256 baeda0f07e9076124f78228355a40d8a5c39b6c37ebf3c878cbd10ff493aacf8. Project: https://github.com/tomislav-math/d1-bound5-lean

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