Metadata-generate the logarithmic scales; fold Percent/Gain into the linear metadata

CLAUDE.md

@@ -52,7 +52,7 @@ These are now baked into the generator and enforced by tests. **Do not reopen wi
 2. **Dimensionless and angular quantities have both `Ratio` (V0) and `SignedRatio` (V1) bases.** Ratios that semantically must be non-negative (e.g. `RefractiveIndex`, `MachNumber`, `SpecificGravity`) are V0 overloads of `Ratio`.
 3. **Semantic overloads widen implicitly to their base, narrow explicitly from it.** A `Weight` is implicitly a `ForceMagnitude`; the reverse requires `Weight.From(forceMagnitude)` or an explicit cast.
 4. **Physical constraints are enforced structurally via the V0 (magnitude) form.** `Vector0` factories run `Vector0Guards.EnsureNonNegative` and throw `ArgumentException` on a negative value. That covers absolute zero (Temperature is V0, so Kelvin must be ≥ 0), non-negative frequency, non-negative absolute pressure, etc. A V0 *overload* can opt into a stricter rule by declaring `physicalConstraints: { "minExclusive": "0" }` in `dimensions.json` (#51); the generator then emits `Vector0Guards.EnsurePositive` and rejects zero too. Used today for `Wavelength`, `Period`, and `HalfLife` — quantities for which zero is unphysical.
-5. **Logarithmic-scale quantities are hand-written companions, not generated dimensions.** Decibel scales (`SoundPressureLevel`, `SoundIntensityLevel`, `SoundPowerLevel`, `DirectionalityIndex`, the audio-engineering `Decibels`) and `PH` don't obey linear arithmetic, so they live as self-contained `readonly record struct`s that convert to and from their linear generated counterparts (`SoundPressure`, `SoundIntensity`, `SoundPower`, `Ratio`, `Concentration`). Adding a new log-scale quantity means writing such a companion, not a `dimensions.json` entry.
+5. **Logarithmic-scale quantities are generated from `logarithmic.json`, not declared as dimensions.** Decibel scales (`Decibels`, `SoundPressureLevel`, `SoundIntensityLevel`, `SoundPowerLevel`, `DirectionalityIndex`), pitch intervals (`Cents`, `Semitones`), and `PH` don't obey linear arithmetic, so they are emitted by `LogarithmicScalesGenerator` as standalone `readonly partial record struct`s built around `scale = multiplier · log_base(linear / reference)`, converting to and from their linear generated counterparts (`Gain`, `Ratio`, `SoundPressure`, `SoundIntensity`, `SoundPower`, `Concentration`). Bespoke members (named constants like `PH.Neutral`, cross-scale conversions like `Cents`↔`Semitones`) live in hand-written partials next to the metadata-generated core. Adding a new log-scale quantity means adding a `logarithmic.json` entry, plus a partial only if it needs bespoke members.
 
 ### Physical constants
 
@@ -152,6 +152,7 @@ var converted = sourceString.As<SourceType, TargetType>();
   - **SEM002** — schema-level validation issue (missing `name`/`symbol`, empty `availableUnits`, duplicate type names, no vector forms declared).
   - **SEM003** — a relationship's explicit `forms` list references a vector form not declared on a participating dimension. Use `forms` to constrain a relationship to specific vector forms (e.g. `crossProducts: [{ "other": "Length", "result": "Torque", "forms": [3] }]`); when omitted, the legacy "emit at every common form" behaviour is preserved.
   - **SEM004** — a dimension's `availableUnits` array references a unit name that isn't declared anywhere in `units.json`. Without the diagnostic the generator silently emits an identity-conversion `From{Unit}` factory, which is wrong for any non-base unit; SEM004 catches the typo at build time.
+  - **SEM005** — schema-level validation issue in `logarithmic.json` (missing or duplicate scale names, a conversion with no linear type).
 - See `docs/physics-generator.md` for the full schema and an end-to-end "add a dimension" walk-through.
 
 This file is the entry point. For deeper material:

Semantics.Quantities/Acoustics/DirectionalityIndex.cs

@@ -4,82 +4,16 @@
 
 namespace ktsu.Semantics.Quantities;
 
-using System.Globalization;
 using System.Numerics;
 
 /// <summary>
-/// Represents a directivity index (DI) in decibels — how much more intense a
-/// source or receiver is on-axis than its spherical average.
+/// Bespoke members of <see cref="DirectionalityIndex{T}"/>; the logarithmic core
+/// is generated from <c>logarithmic.json</c>.
 /// </summary>
-/// <remarks>
-/// <c>DI = 10·log10(I_axis / I_average)</c>. Like all decibel scales it is a
-/// hand-written companion rather than a generated linear quantity.
-/// </remarks>
 /// <typeparam name="T">The floating-point storage type.</typeparam>
-/// <param name="Value">The index in decibels.</param>
-public readonly record struct DirectionalityIndex<T>(T Value) : IComparable<DirectionalityIndex<T>>
+public readonly partial record struct DirectionalityIndex<T>
 	where T : struct, INumber<T>
 {
 	/// <summary>Gets the index of an omnidirectional source (0 dB).</summary>
 	public static DirectionalityIndex<T> Omnidirectional => new(T.Zero);
-
-	/// <summary>
-	/// Creates an index from a raw decibel value.
-	/// </summary>
-	/// <param name="decibels">The index in decibels.</param>
-	/// <returns>A new <see cref="DirectionalityIndex{T}"/>.</returns>
-	public static DirectionalityIndex<T> FromDecibels(T decibels) => new(decibels);
-
-	/// <summary>
-	/// Creates an index from the linear on-axis-to-average intensity ratio using <c>DI = 10·log10(ratio)</c>.
-	/// </summary>
-	/// <param name="ratio">The intensity ratio.</param>
-	/// <returns>A new <see cref="DirectionalityIndex{T}"/>.</returns>
-	public static DirectionalityIndex<T> FromIntensityRatio(Ratio<T> ratio)
-	{
-		ArgumentNullException.ThrowIfNull(ratio);
-		double linear = double.CreateChecked(ratio.Value);
-		return new(T.CreateChecked(10.0 * Math.Log10(linear)));
-	}
-
-	/// <summary>
-	/// Converts this index to the linear intensity ratio using <c>ratio = 10^(DI/10)</c>.
-	/// </summary>
-	/// <returns>The on-axis-to-average intensity <see cref="Ratio{T}"/>.</returns>
-	public Ratio<T> ToIntensityRatio()
-	{
-		double db = double.CreateChecked(Value);
-		return Ratio<T>.Create(T.CreateChecked(Math.Pow(10.0, db / 10.0)));
-	}
-
-	/// <inheritdoc/>
-	public int CompareTo(DirectionalityIndex<T> other) => Value.CompareTo(other.Value);
-
-	/// <summary>Determines whether one index is less than another.</summary>
-	/// <param name="left">The left index.</param>
-	/// <param name="right">The right index.</param>
-	/// <returns><see langword="true"/> if <paramref name="left"/> is less than <paramref name="right"/>.</returns>
-	public static bool operator <(DirectionalityIndex<T> left, DirectionalityIndex<T> right) => left.CompareTo(right) < 0;
-
-	/// <summary>Determines whether one index is greater than another.</summary>
-	/// <param name="left">The left index.</param>
-	/// <param name="right">The right index.</param>
-	/// <returns><see langword="true"/> if <paramref name="left"/> is greater than <paramref name="right"/>.</returns>
-	public static bool operator >(DirectionalityIndex<T> left, DirectionalityIndex<T> right) => left.CompareTo(right) > 0;
-
-	/// <summary>Determines whether one index is less than or equal to another.</summary>
-	/// <param name="left">The left index.</param>
-	/// <param name="right">The right index.</param>
-	/// <returns><see langword="true"/> if <paramref name="left"/> is less than or equal to <paramref name="right"/>.</returns>
-	public static bool operator <=(DirectionalityIndex<T> left, DirectionalityIndex<T> right) => left.CompareTo(right) <= 0;
-
-	/// <summary>Determines whether one index is greater than or equal to another.</summary>
-	/// <param name="left">The left index.</param>
-	/// <param name="right">The right index.</param>
-	/// <returns><see langword="true"/> if <paramref name="left"/> is greater than or equal to <paramref name="right"/>.</returns>
-	public static bool operator >=(DirectionalityIndex<T> left, DirectionalityIndex<T> right) => left.CompareTo(right) >= 0;
-
-	/// <summary>Returns a culture-invariant string representation of this index.</summary>
-	/// <returns>The index formatted with a <c> dB</c> suffix.</returns>
-	public override string ToString() => string.Create(CultureInfo.InvariantCulture, $"{Value} dB");
 }