Sensitivity's dimensional formula matches neither V/Pa nor A/Pa, and the .NET generator emits the operator the C++ projection refuses

[matt-edmondson]

The metadata

Semantics.SourceGenerators/Metadata/dimensions.json:

"name": "Sensitivity",
"symbol": "M⁻¹ L⁻¹ T² I",
"dimensionalFormula": { "mass": -1, "length": -1, "time": 2, "electricCurrent": 1 },
"availableUnits": ["VoltPerPascal"],
"integrals": [ { "other": "Pressure", "result": "ElectricPotential" } ]

Its only unit is VoltPerPascal, symbol V/Pa (units.json:890-893). Working the exponents out:

	M	L	T	I
declared	−1	−1	2	1
V/Pa — what the unit says	0	3	−1	−1
A/Pa — what CLAUDE.md says is declared	−1	+1	2	1

The declared vector is neither. CLAUDE.md's own account ("declared as A/Pa, M⁻¹L⁻¹T²I") is itself inconsistent — A/Pa has length +1, not −1.

The relationship then computes Sensitivity × Pressure = L⁻² I, against ElectricPotential = M L² T⁻³ I⁻¹.

Checking every integrals / derivatives / dotProducts / crossProducts entry in the file: exactly four are dimensionally false, matching the set CLAUDE.md documents. Three are the rotational/angle cluster, which is structurally unfixable and correctly explained. This is the fourth, and it is not.

What ships

The C++ projection refuses it — Semantics.Cpp/QuantityVocabulary.cs:216-222, asserted by Semantics.Cpp.Test/CppQuantityGeneratorTests.cs:190-203.

The .NET generator has no dimensional check at all. SEM001 verifies only that names resolve; there is no exponent arithmetic anywhere in Semantics.SourceGenerators. So the operator is emitted into committed generated source:

// Semantics.Quantities/Generated/…/QuantitiesGenerator/Sensitivity.g.cs:123
public static VoltageMagnitude<T> operator *(Sensitivity<T> left, Pressure<T> right) =>
    VoltageMagnitude<T>.Create(left.Quantity * right.Quantity);

A caller writing sensitivity * pressure gets a VoltageMagnitude back — type-checked, and silently wrong by a factor carrying units of m⁻⁵·kg⁻¹·s⁴·A².

Why it matters

The point of the type system is that a dimensionally wrong product does not compile. Here it does, and yields a named quantity.

It also means the two projections of one metadata file disagree about what the vocabulary contains — at exactly the place the library promises they do not.

Suggested fix

Two separable pieces:

(a) Fix the metadata. This is a physics call between:

• V/Pa — {"length": 3, "time": -1, "electricCurrent": -1}, matching the declared unit and making the relationship true; or
• A/Pa — {"mass": -1, "length": 1, "time": 2, "electricCurrent": 1}, which requires both the unit and the relationship to change.

The symbol string needs updating either way, and CLAUDE.md's description of the bug needs its sign corrected.

(b) Port the exponent check to the .NET generator as a new SEM00x, so the two sides cannot diverge again. The arithmetic already exists in Semantics.Cpp/DimensionVector.cs; today a false relationship is caught only if it happens to reach the C++ projection.

Part (b) is the more durable half — (a) fixes one entry, (b) makes the next one impossible to miss.

[matt-edmondson]

Triage

Priority: High Effort: Medium

What needs to be done: Sensitivity's declared dimensional formula matches neither its own unit (V/Pa) nor the A/Pa reading CLAUDE.md describes (which is itself internally inconsistent about the sign). The C++ projection catches this and refuses to emit the Sensitivity × Pressure = ElectricPotential operator, but the .NET generator has no dimensional-consistency check at all, so it emits the operator into committed generated source — a type-checked but dimensionally false physics relationship that silently ships.

Suggested next steps / acceptance criteria:

• (a) Physics decision + metadata fix: pick the correct formula for Sensitivity — either V/Pa with {length: 3, time: -1, electricCurrent: -1} (matches the declared unit, makes the relationship true) or A/Pa with {mass: -1, length: 1, time: 2, electricCurrent: 1} (requires changing the unit too) — and correct the symbol string and CLAUDE.md's description to match. This step needs a maintainer/physics call before implementation, not just a code change.
• (b) Port the exponent-consistency check from Semantics.Cpp/DimensionVector.cs into the .NET generator as a new SEM00x diagnostic, so this class of divergence is caught at generation time for every relationship, not just the ones that happen to reach the C++ projection.

Blockers / dependencies: Part (a) is blocked on a physics decision (which of the two formulas is correct) — flag for maintainer input. Part (b) is independent and can proceed without waiting on (a); it's the more durable fix since it prevents the next such error from being invisible on the .NET side.

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