The literal ordinary coordinates generate the actual rational curve function field

Proved

MazurTransfer.Order13ActualFunctionFieldGenerators.intermediateField_eq_top

by Vas · Oct 17, 2026 · Mathlib 0df444a (Lean v4.33.1)

algebraic-geometryarithmetic-geometrymazur-theorem

Any intermediate field of the literal rational order-13 curve function field containing its original ordinary x and y coordinates is the entire actual function field. The specified intermediate field and both coordinate-membership hypotheses are the complete original contract.

Preamble

/-
Copyright (c) 2026 Vas and contributors. Released under Apache-2.0.
Original complete actual coordinate field-generation proof retained.
Design boundary: any intermediate field containing the literal ordinary
x and y coordinates is the actual rational scheme function field.
Named downstream consumer: actual conic cubic and hyperelliptic fixed fields.
-/
import Definitions.Def_MazurTransfer_Order13ActualOrdinaryPolynomialTranscendence
noncomputable section
open Polynomial
open MazurTorsion.XOneThirteenAffineCurve
open GoodCharacteristicGeometryPublicProof.MazurTransfer.Order13GoodCharacteristicCurveModel
open MazurTransfer.Order13PellActualOrdinaryChart MazurTransfer.Order13ActualOrdinaryPolynomialTranscendence
local instance : Fact ((104 : ℚ) ≠ 0) := ⟨by norm_num⟩

Formal statement

theorem MazurTransfer.Order13ActualFunctionFieldGenerators.intermediateField_eq_top (S : IntermediateField ℚ (actualCurveFunctionField ℚ))
    (hx : xImage ℚ ∈ S) (hy : yImage ℚ ∈ S) : S = ⊤ := by sorry

Source

Unchanged complete original MazurTheorem Order13ActualFunctionFieldGenerators.intermediateField_eq_top proof and statement, Apache-2.0, Vas and contributors. The public actual ordinary coordinates and polynomial-transcendence Definition supply the original constructors.

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