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-# Case study: a latent bug the verification harness caught
-
-This documents a real defect that the verification work found **on the very
-first run** of the new `make verify` target — before any of the heavier layers
-(TLA+, Gobra) were even involved. It is a good illustration of *why* wiring
-these checks into a gate pays off: the bug had been sitting in the repository
-undetected because the existing tests could never trigger it.
-
-## TL;DR
-
-- **Where:** `search/hash.go`, the `Hash.hash` method.
-- **What:** `key << 10`, where `key` has a generic integer type, silently
-  evaluates to `0` for narrow key types (`int8`/`uint8`), discarding a whole
-  term of the hash mix.
-- **Who found it:** `go vet`'s shift analyzer, run as part of `make verify`.
-- **Why the tests missed it:** every test instantiates the hash with 64-bit
-  `int` keys, where the shift is perfectly fine — so the bug is *latent*.
-- **Fix:** compute the mix in a full-width `int64`.
-
-## The offending code
-
-Before:
-
-```go
-func (h *Hash[K,V]) hash(key K) int {
-	i := key + key*2 + key<<10 + key>>2
-	if i < 0 {
-		i = -i
-	}
-	return int(i) % h.capacity
-}
-```
-
-`K` is a type parameter constrained by `ds.Integer` (`ds/types.go`), which
-embeds `constraints.Integer` — i.e. `K` may be **any** of `int, int8, int16,
-int32, int64, uint, uint8, …`. The intent of `key<<10` is clearly to spread the
-key's low bits up into the high bits so that keys differing only in their low
-bits land in different buckets.
-
-## What the tool reported
-
-```
-$ make verify
-go vet ./...
-search/hash.go:29:21: key (may be 8 bits) too small for shift of 10
-```
-
-`go vet` bundles a *shift* analyzer that is, in effect, a lightweight formal
-check: for every shift expression it computes a conservative lower bound on the
-bit width of the left operand and flags any shift whose count is `>=` that
-width. Here the narrowest type `K` can take is `int8` (8 bits), and `10 >= 8`,
-so the analyzer proves that *for at least one legal instantiation* the shift is
-degenerate.
-
-## Why it is genuinely a bug (Go shift semantics)
-
-This is not a false positive. The Go specification defines non-constant left
-shifts operationally:
-
-> Shifts behave as if the left operand is shifted `n` times by 1 for a shift
-> count of `n`. […] There is no upper limit on the shift count.
-
-For an 8-bit value, shifting "one bit at a time" ten times pushes **every**
-original bit out of the value's width. The result is therefore always `0`. So
-for `K = int8`/`uint8`:
-
-```
-key<<10  ==  0    // always, for every key
-```
-
-and the hash silently collapses to `key + key*2 + key>>2` — the high-bit mixing
-the author intended is simply gone.
-
-Two subtleties worth recording:
-
-1. **It is width-dependent, not universally broken.** For `int16` the count
-   `10 < 16`, so the term is fine; for 32-/64-bit types it is obviously fine.
-   `go vet` still (correctly) flags the expression because it must be sound for
-   *all* instantiations, and `int8` is in the constraint set. The narrowest
-   type is what governs safety.
-
-2. **It is a quality/portability bug, not a memory-safety or a Set-contract
-   violation.** The hash table stays *functionally correct* even for `int8`
-   keys: `Put`, `Get`, and `Del` all call the same `hash`, and collisions are
-   resolved by chaining in the per-bucket `Elementary` list. What degrades is
-   the *distribution* — more keys collide into the same bucket, turning the
-   intended O(1) operations toward O(n). So the failure mode is silent
-   performance rot for narrow-key instantiations, exactly the kind of thing that
-   never shows up as a failing assertion.
-
-## Why no test caught it
-
-Every instantiation in the test suite uses `int` keys:
-
-```go
-test[int,int](NewHash[int,int](i*2), i, t)   // search/search_test.go
-```
-
-`int` is 64 bits on this platform, so `key<<10` behaves as intended and all
-tests pass. There is no `Hash[int8, …]` anywhere, so the degenerate path is
-never exercised. A property test or a fuzz run over `int` keys would *also* miss
-it — the bug lives in the *type dimension*, not the value dimension, and only a
-tool that reasons about the type (like `go vet`) or an actual narrow-type
-instantiation can surface it. This is precisely the class of latent defect that
-static analysis is good at and dynamic testing is blind to.
-
-## The fix
-
-Perform the mixing in a full-width `int64`, then reduce:
-
-```go
-func (h *Hash[K,V]) hash(key K) int {
-	// Mix the key in a full-width int64 rather than in K. K is any ds.Integer,
-	// so for a narrow type (e.g. int8) the "key<<10" term would shift past the
-	// type width and vanish to 0, destroying the intended high-bit mixing (and
-	// go vet rightly flags it). Widening to int64 first keeps the result
-	// identical for 64-bit int keys while making the mix well-defined for every
-	// integer width.
-	i := int64(key)
-	i = i + i*2 + i<<10 + i>>2
-	if i < 0 {
-		i = -i
-	}
-	return int(i) % h.capacity
-}
-```
-
-Why this is the right fix:
-
-- **Behavior-preserving for the code that exists.** For `K = int` (64-bit), the
-  arithmetic is byte-for-byte identical to before — `int64(key)` is a no-op
-  widening, and every operation stays in 64 bits — so every existing test still
-  passes unchanged.
-- **Correct for the code that might exist.** For narrow `K`, the key is widened
-  *before* the shift, so `i<<10` now mixes real bits instead of vanishing. The
-  hash finally does for `int8` keys what it always did for `int` keys.
-- **It silences the analyzer for the right reason.** `int64` is 64 bits, `10 <
-  64`, so the shift is provably well-defined for the actual operand type. We are
-  not suppressing the warning; we are removing the condition that made it true.
-
-An `int64` cast rather than the value's own width also documents intent: "this
-mixing is meant to happen in a wide register, independent of the key type."
-
-> Residual note, left as-is: `if i < 0 { i = -i }` still has the classic
-> `-math.MinInt64` overflow corner. It predates this change, is astronomically
-> unlikely for these inputs, and is out of scope here — recorded for honesty.
-
-## How this maps to the verification layers
-
-This defect was caught by **Layer 2** of the harness (see
-[`verification.md`](verification.md)) — `go vet` inside `make verify`. It is the
-cheapest layer, and it found a bug that the paper proofs (Layer 0, which focus
-on the sorts) and the property tests (Layer 1, which only ever run `int`) did
-not. The lesson is the ordering of the layers is not the ordering of their
-value: a one-line static check surfaced a real, shipped-in latent bug that no
-amount of value-space testing would have. Cheap, broad checks first; deep proofs
-where they earn their keep.