gw-04 — Verification

One command

cd gw-04-connection-management && bash scripts/verify.sh

Test	Invariant
`TestPoolReuse`	a put-then-get reuses the warm connection (`Created==1`, `Reused==1`)
`TestNoPoolIsAllChurn`	`maxIdle=0` → every request dials (`Created==100`) — pure churn baseline
`TestPoolingReducesChurn`	`maxIdle=8` → 100 cycles dial once, reuse 99 times
`TestIdleEvictionCausesChurn`	a too-short idle TTL evicts and re-dials — over-tuning re-creates churn
`TestPerLoopIndependence`	per-loop pools each dial their own conn (the `K×` trade-off), then reuse within a loop
`TestVanDerCorputKnownValues`	sequence is exactly `0, .5, .25, .75, .125, .625, .375, .875`
`TestSubsetConnectionMath`	subsetting cuts `N×M` to `N×subset` (≥10× here)
`TestSubsetBalance`	every origin is covered (no cold origins); max coverage within a sane band of ideal
`TestSubsetStabilityVsHashMod`	the ring is strictly more stable than hash-mod and does not reshuffle everything when one origin leaves

All under -race.

The demo prints, for 1000 origins / 500 gateways / subset 20:

500000 → 10000 connections (50× fewer),
coverage min/p50/max ≈ 5/10/15 against ideal 10,
on one origin leaving: ring ~11/500 vs hash-mod ~259/500 gateways changed.

No real sockets. The pool is abstracted over a Resource so churn is measured deterministically; wiring it to net.Conn/http.Transport is an exercise (GUIDE §6.1).
No live LB within the subset. P2C/outlier ejection over the subset is gw-06.
No debounced re-subsetting. Membership-churn debouncing is an exercise (GUIDE §6.3); production needs it so the fix doesn't cause churn.