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First Pair Geometry Matches — residual rates

Proved
D1Bound5.FirstPairGeometryMatches.residual_rates

by tp · Oct 23, 2026 · Mathlib 0df444a (Lean v4.33.1)

diophantine-tuplesnumber-theory

The pair-dependent residual coefficients agree exactly. The P rate uses a different geometric enclosure and is deliberately not identified.

Preamble
import Mathlib.Algebra.QuadraticAlgebra.Basic
import Mathlib.Algebra.Ring.Basic
import Mathlib.Algebra.Ring.Equiv
import Mathlib.Data.Finset.Card
import Mathlib.Data.Finset.Prod
import Mathlib.Data.Int.Interval
import Mathlib.Data.Int.Sqrt
import Mathlib.Data.List.Range
import Mathlib.Tactic.IntervalCases
import Mathlib.Tactic.Linarith
import Mathlib.Tactic.LinearCombination
import Definitions.Def_D1Bound5_FirstPairGeometryData_Definitions_001
import Definitions.Def_D1Bound5_FirstPairGeometryFixedRows_Definitions
import Definitions.Def_D1Bound5_OneSmallCutoffArithmetic_Definitions_001

Formal statement
section
namespace D1Bound5




theorem _root_.D1Bound5.FirstPairGeometryMatches.residual_rates
    (g : FirstPairGeometryRow) (r : OneSmallCutoffRow)
    (h : FirstPairGeometryMatches g r) :
    g.R2 = r.R2 ∧ g.Rn = r.Rn ∧ g.R3 = r.R3 ∧
      g.R4 = r.R4 ∧ g.R5 = r.R5 := by sorry

end D1Bound5
end
Source
D1Bound5/FirstPairFixedTransfer.lean, lines 18-29, SHA-256 3faa8c267acd6dc418ad7dfd9d428a018612986ed715dc34ae106ea4a4b160f1. Project: https://github.com/tomislav-math/d1-bound5-lean

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