Selected-floor prefix certificate for prepared pair 12, left list, part 4

Proved

D1Bound5.PairLightAdaptivePrepared12.left_prefix_000_part04_checked

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

diophantine-tuplesnumber-theory

For prepared pair 12, left list, part 4, the selected-floor certificate succeeds for at most 2 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 PairLightPrepared12.sieve. Original heads 136 through 137; every head retains its complete original tail.

Preamble

import Init
import Definitions.Def_D1Bound5_PairLightArithmeticChunks_Definitions
import Definitions.Def_D1Bound5_PairLightArithmetic_Definitions
import Definitions.Def_D1Bound5_SmallPairLightAdaptiveData12_Definitions
import Definitions.Def_D1Bound5_SmallPairLightData12_Definitions_001

Formal statement

section
namespace D1Bound5.PairLightAdaptivePrepared12
set_option maxRecDepth 100000
set_option maxHeartbeats 0


theorem _root_.D1Bound5.PairLightAdaptivePrepared12.left_prefix_000_part04_checked :
    pairLightSelectedFloorPrefixBool 0 1 PairLightPrepared12.sieve 2
      (leftCached000.drop 136) (leftRows000.drop 136) = true := by sorry

end D1Bound5.PairLightAdaptivePrepared12
end

Source

D1Bound5/SmallPairLightAdaptiveLeft12_000Part04.lean, lines 7-11, SHA-256 2d0324871c52c884a604583c44c089877355c02c62ce4cf53f9c3f66765cb88a. Project: https://github.com/tomislav-math/d1-bound5-lean

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