di's arity gate is the last mute diagnostic, and NeedsGate is the proven replacement

[btravers]

From the 2026-08-23 DX audit. Generalizes #83, which is the same finding scoped
to tapped — this covers the mechanism everywhere it survives.

The problem

Module.build and Module.scoped gate unmet dependencies with a conditional
rest tuple, and an arity error carries no type:

error TS2554: Expected 5 arguments, but got 2.

Neither the UNSATISFIED DEPENDENCIES label nor the missing ports reach the
message. This is the worst diagnostic in the framework, and the prose knows it:
the root CLAUDE.md, packages/di/CLAUDE.md, docs/explanation/compile-time-wiring.md
and docs/reference/di/entry-points.md all carry paragraphs explaining what the
bare arity line actually means and how to hand-spell the phantom arguments to
make the port print. Four documents apologizing for one gate is the measure of
the cost. GHC treats custom type errors as first-class; the marker technique is
this repo's equivalent, and every OTHER gate already uses it.

The replacement is proven in-repo

#50's NeedsGate rides an intersection whose failure branch is an object with
one required property, and the diagnostic ends on the port (measured):

Property '"UNDECLARED NEEDS — name it in `needs`"' is missing in type
  '{ provides: [...]; }' but required in type
  '{ readonly "UNDECLARED NEEDS — name it in `needs`": Logger; }'.

The same shape now guards routerFor's scope gate (#90) and start's
StartGate. The arity tuple predates all of them.

The work

• Module.build(module) / Module.scoped(module, use): replace the
  ..._missing rest tuple with a marker intersected onto the module
  parameter — unknown when Needs (minus Scope, for scoped) is never,
  the named-property object otherwise.
• tapped (tapped's gate is an arity error: the last rest tuple #83): same move, which closes that issue.
• Every @ts-expect-error — UNSATISFIED DEPENDENCIES arm in the type tests
  re-measured; examples/order-application/src/needs-gate.test-d.ts pins the
  new sentence.
• The four apology paragraphs shrink to one line each, stating what now prints.

Risks worth measuring first

The rest tuple has one property the intersection must not lose: it fires on the
CALL, not on the argument, so --pretty's related-information span differs.
And Module<X, E, N>'s covariant _needs must still refuse the laundered
assignment — the marker sits beside that check, not instead of it. Both are a
scratch-file measurement before the sweep, per house rules.