feat(SUSY/N1): add chiral scalar configuration space and coordinate CLMs

Physlib.lean

@@ -368,6 +368,7 @@ public import Physlib.Relativity.Tensors.RealTensor.Velocity.Basic
 public import Physlib.Relativity.Tensors.TensorSpecies.Basic
 public import Physlib.Relativity.Tensors.Tensorial
 public import Physlib.Relativity.Tensors.UnitTensor
+public import Physlib.SUSY.N1.Basic
 public import Physlib.SpaceAndTime.Space.Basic
 public import Physlib.SpaceAndTime.Space.ConstantSliceDist
 public import Physlib.SpaceAndTime.Space.CrossProduct

Physlib/SUSY/N1/Basic.lean

@@ -0,0 +1,88 @@
+/-
+Copyright (c) 2026 Andrea Pari. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Andrea Pari
+-/
+module
+
+public import Mathlib.Data.Fintype.Defs
+public import Mathlib.Analysis.Complex.Basic
+public import Mathlib.Logic.Equiv.Basic
+
+/-!
+
+# SUSY N=1 chiral sector — basic indexing data
+
+## i. Overview
+
+The minimal label and configuration data for the N=1 chiral sector.
+
+A `Model` packages two finite index types — `ChiralIndexingType` (written `C`
+below) indexing the chiral scalars and `AntiChiralIndexingType` (written `A`)
+the anti-chiral (barred) slots — with an equivalence `equiv : C ≃ A`, kept
+distinct so the two slots of a contraction `g_{IJ̄}` cannot be confused. The
+physical configuration is `ChiralScalarConfiguration C = C → ℂ`, carrying
+`2 · Fintype.card C` real degrees of freedom — the only field data; the
+anti-chiral scalars are its complex conjugates, never an independent
+configuration.
+
+Doubling — adding an independent `A → ℂ` configuration — is the wrong choice:
+the physical identities would then hold only where anti-chiral is the conjugate
+of chiral, so every theorem carries that subspace as a hypothesis (e.g. the
+Kähler potential is real only there, making hermiticity of `g_{IJ̄}`
+conditional). Building the conjugate in keeps them unconditional — `K` is real
+by construction — and leaves `A` an index type only.
+
+This file carries only the index/configuration data; the chiral and anti-chiral
+derivatives `∂_I` / `∂_J̄` (the `Model` methods `M.dChiralScalar` /
+`M.dAntiChiralScalar`) are built on top of it in `Derivative.lean`.
+
+The files of this `SUSY/N1/` folder:
+
+* `Basic.lean` (this file) — the `Model` indexing data and the chiral
+  configuration type.
+* `Derivative.lean` — the chiral / anti-chiral derivative wrappers
+  `M.dChiralScalar` / `M.dAntiChiralScalar` over the Wirtinger calculus.
+* `SuperPotential.lean` — the abstract holomorphic superpotential `W` and its
+  conjugate `W̄`.
+* `KahlerPotential.lean` — the abstract Kähler potential `K`.
+* `KahlerMetric.lean` — the Kähler metric `g_{IJ̄} = ∂_I ∂_J̄ K` and its
+  hermiticity.
+* `LogKahlerHn.lean` — worked example: the `Hⁿ` log Kähler potential (the
+  reusable upper-half-plane calculus lives in
+  `Mathematics/Calculus/Wirtinger/UpperHalfPlane.lean`).
+
+## ii. Key results
+
+- `SUSY.N1.Model` : the indexing data of an N=1 sector — a chiral index type,
+    an anti-chiral (barred) index type, and an equivalence `equiv` between them.
+- `SUSY.N1.ChiralScalarConfiguration` : the physical scalar configuration space
+    `C → ℂ`, where `C` is the finite type indexing the chiral scalars — the only
+    field data in the sector.
+
+-/
+
+@[expose] public section
+
+noncomputable section
+
+namespace SUSY.N1
+
+/-- The indexing data of an N=1 sector: a chiral index type `ChiralIndexingType`,
+an anti-chiral (barred) index type `AntiChiralIndexingType`, and a bijection
+`equiv` between them. -/
+structure Model (ChiralIndexingType : Type*) [Fintype ChiralIndexingType]
+    (AntiChiralIndexingType : Type*) [Fintype AntiChiralIndexingType] where
+  /-- The correspondence between chiral and anti-chiral (barred) labels. -/
+  equiv : ChiralIndexingType ≃ AntiChiralIndexingType
+
+/-- The chiral scalar configuration: an assignment of complex values to each
+chiral label. An `abbrev` so unification applies Mathlib's `α → ℂ` calculus
+lemmas directly. -/
+abbrev ChiralScalarConfiguration (ChiralIndexingType : Type*) := ChiralIndexingType → ℂ
+
+end SUSY.N1
+
+end
+
+end