diff --git a/.claude/agents/code-reviewer.md b/.claude/agents/code-reviewer.md
index ab149ca..132bee4 100644
--- a/.claude/agents/code-reviewer.md
+++ b/.claude/agents/code-reviewer.md
@@ -32,13 +32,14 @@ Review against the checklist below, in this order of severity.
 
 ## 2. Version pins (blocking)
 
-- `composer.json` must keep `"php": "~8.4.0"` and `"lisachenko/z-engine": "dev-master"`,
-  with root `"minimum-stability": "dev"` and `"prefer-stable": true`.
-- Any diff that widens the PHP constraint (`^8.4`, `>=8.4`), drops the z-engine dev
-  requirement, or bypasses `Core::init()`'s version guard is rejected outright. Offsets into
-  engine structures are minor-version specific; loosening the pin trades a clear error for
-  memory corruption.
-- CI must run on PHP 8.4 with `ffi.enable=1` and `opcache.jit=off`.
+- `composer.json` must keep `"php": "^8.4"` and `"lisachenko/z-engine": "~8.4.2 || ~8.5.0"`
+  — one stable z-engine line per supported PHP minor, resolved by Composer against the
+  running PHP.
+- Any diff that widens either constraint beyond the minors z-engine has definitions for
+  (`>=8.4`, a `^8.4` z-engine constraint that would span future lines), or bypasses
+  `Core::init()`'s version guard, is rejected outright. Offsets into engine structures are
+  minor-version specific; loosening the pin trades a clear error for memory corruption.
+- CI must run on PHP 8.4 and 8.5 with `ffi.enable=1` and `opcache.jit=off`.
 
 ## 3. PHPStan generics honesty (blocking)
 
diff --git a/.github/workflows/ci.yml b/.github/workflows/ci.yml
index e3be3e9..925e269 100644
--- a/.github/workflows/ci.yml
+++ b/.github/workflows/ci.yml
@@ -9,9 +9,9 @@ on:
 permissions:
   contents: read
 
-# z-engine tracks one PHP minor per release line; the "8.4.x-dev || 8.5.x-dev"
-# constraint lets Composer resolve the line matching each runner's PHP, so the
-# suite runs on PHP 8.4 and 8.5 in parallel.
+# z-engine tracks one PHP minor per release line; the "~8.4.2 || ~8.5.0" constraint
+# lets Composer resolve the stable line matching each runner's PHP, so the suite
+# runs on PHP 8.4 and 8.5 in parallel.
 jobs:
   tests:
     name: Tests (PHP ${{ matrix.php }})
diff --git a/CLAUDE.md b/CLAUDE.md
index 9944bc8..d1a9fcf 100644
--- a/CLAUDE.md
+++ b/CLAUDE.md
@@ -15,9 +15,10 @@ structures (`zend_class_entry`, `zval`, `zend_object_handlers`) by byte offset,
 those offsets change on every PHP minor release. Running against the wrong minor
 does not throw a nice exception; it reads and writes the wrong memory.
 
-That is why z-engine is required as **`8.4.x-dev || 8.5.x-dev`**: Composer resolves
-the line matching the running PHP (the `8.4` branch on PHP 8.4, `master` — aliased
-`8.5.x-dev` — on PHP 8.5). `ZEngine\Core::init()` (called from `bootstrap.php`)
+That is why z-engine is required as **`~8.4.2 || ~8.5.0`**: Composer resolves the
+release line matching the running PHP (`8.4.x` on PHP 8.4, `8.5.x` on PHP 8.5 — each
+tag declares its own `~8.4.0`/`~8.5.0` platform requirement, so only one line can
+ever satisfy a given runtime). `ZEngine\Core::init()` (called from `bootstrap.php`)
 enforces the exact match and aborts with a clear message. **Never "fix" an
 initialization failure by loosening the constraints past the minors z-engine has
 definitions for, skipping `Core::init()`, or defeating the guard.** If the
@@ -36,13 +37,15 @@ process it spawns:
 
 - `ffi.enable=1` — FFI cannot be turned on at runtime.
 - `opcache.jit=off` — the JIT rewrites the very executor internals z-engine hooks.
-- `error_reporting=E_ALL & ~E_DEPRECATED` — z-engine `dev-master` still declares
-  implicitly nullable parameters (e.g. `ZEngine\Type\OpLine::__construct()`), which
-  PHP 8.4 reports as a deprecation. PHPUnit's `.phpt` runner forces
-  `display_errors=1`, so without this the dependency's deprecation is prepended to
-  the captured output of **every** test and each `--EXPECT--` block fails on noise
-  that has nothing to do with this library. Drop the suppression once z-engine
-  declares those parameters `?Type`.
+- `error_reporting=E_ALL & ~E_DEPRECATED` — a guard against dependency deprecations
+  leaking into captured output. PHPUnit's `.phpt` runner forces `display_errors=1`,
+  so a deprecation raised by a dependency is prepended to the captured output of
+  **every** test and each `--EXPECT--` block fails on noise that has nothing to do
+  with this library. The specific offender that motivated it — z-engine declaring
+  implicitly nullable parameters (e.g. `ZEngine\Type\OpLine::__construct()`) — is
+  fixed as of the stable releases (`~8.4.2 || ~8.5.0`), and the suite passes with
+  `error_reporting=E_ALL` forced on both minors, so the line is now belt-and-braces
+  rather than a requirement.
 
 CI supplies the FFI and JIT pair as `ini-values` on the PHP setup step, and **every
 `.phpt` file carries its own `--INI--` section** — all three lines — so the child
@@ -190,13 +193,14 @@ proposing a change rather than hand-formatting.
 
 ## Dependency policy
 
-- `lisachenko/z-engine` is required as **`8.4.x-dev || 8.5.x-dev`** — one dev line
-  per supported PHP minor, resolved by Composer to match the running PHP. Those are
-  development branches, so the root `composer.json` also carries
-  `"minimum-stability": "dev"` with `"prefer-stable": true` — Composer resolves
-  development stability only at the root level, so consumers need the same pair.
+- `lisachenko/z-engine` is required as **`~8.4.2 || ~8.5.0`** — one **stable** release
+  line per supported PHP minor, resolved by Composer to match the running PHP. The
+  tilde is deliberate: it admits patch releases within a line (`8.4.3`, `8.5.1`) but
+  never the next minor line, which would be built for a PHP this package does not
+  claim to support.
+- The root `composer.json` no longer carries `"minimum-stability": "dev"` /
+  `"prefer-stable": true` — nothing in `require` is a development branch any more,
+  and consumers no longer need those flags to install this package's dependencies.
 - PHP stays at `^8.4`, in lockstep with the set of z-engine lines this package
   tracks: a new PHP minor is added here only together with the z-engine line built
   for it, and never one without the other.
-- When z-engine ships stable releases for the supported minors, the constraint and
-  the root stability flags should be tightened in a single change.
diff --git a/README.md b/README.md
index 359638f..0363b5a 100644
--- a/README.md
+++ b/README.md
@@ -58,7 +58,7 @@ The maths is plain PHP. The magic is only in getting the engine to call it.
 - **PHP `^8.4`** — 8.4 and 8.5 are supported in parallel. Z-Engine reads engine structures by byte offset and those offsets change on every PHP minor release, so each minor rides its own Z-Engine line; `Core::init()` refuses to boot on a mismatch rather than corrupting memory.
 - **`ext-ffi` enabled**, with `ffi.enable=1` for CLI usage.
 - **x64, non-thread-safe (NTS)** build — the same platform limitations as [Z-Engine](https://github.com/lisachenko/z-engine#requirements--support-matrix).
-- The **matching Z-Engine minor branch**. Composer resolves it for you from the `8.4.x-dev || 8.5.x-dev` constraint; mixing a Z-Engine built for another minor is not a configuration choice, it is undefined behaviour.
+- The **matching Z-Engine minor release line**. Composer resolves it for you from the `~8.4.2 || ~8.5.0` constraint; mixing a Z-Engine built for another minor is not a configuration choice, it is undefined behaviour.
 
 ## Installation
 
@@ -66,16 +66,9 @@ The maths is plain PHP. The magic is only in getting the engine to call it.
 composer require lisachenko/native-php-matrix:dev-master
 ```
 
-This package requires Z-Engine as `8.4.x-dev || 8.5.x-dev` — z-engine minors track PHP minors and are not interchangeable, so Composer resolves the line matching your PHP automatically (the `8.4` branch on PHP 8.4, `master` on PHP 8.5). Those are development branches, and the package itself is consumed from `dev-master`; Composer only resolves development stability at the **root** level, so your `composer.json` needs:
+This package requires Z-Engine as `~8.4.2 || ~8.5.0` — z-engine minors track PHP minors and are not interchangeable, so Composer resolves the release line matching your PHP automatically (`8.4.x` on PHP 8.4, `8.5.x` on PHP 8.5). Both are **stable tags**, so no `minimum-stability` tweak is needed for them.
 
-```json
-{
-    "minimum-stability": "dev",
-    "prefer-stable": true
-}
-```
-
-Once a native-php-matrix release covering the current code is tagged, this collapses to a plain `composer require lisachenko/native-php-matrix`.
+native-php-matrix itself is not tagged yet, which is why the command above asks for `dev-master`; that one dev constraint is explicit, so Composer accepts it without a root stability change. Once a native-php-matrix release is tagged, this collapses to a plain `composer require lisachenko/native-php-matrix`.
 
 No initialization call is needed: `bootstrap.php` ships in the package's `files` autoload and sets everything up behind `require vendor/autoload.php`.
 
diff --git a/composer.json b/composer.json
index a0033e9..3cbae7f 100644
--- a/composer.json
+++ b/composer.json
@@ -13,10 +13,8 @@
     "require": {
         "php": "^8.4",
         "ext-ffi": "*",
-        "lisachenko/z-engine": "8.4.x-dev || 8.5.x-dev"
+        "lisachenko/z-engine": "~8.4.2 || ~8.5.0"
     },
-    "minimum-stability": "dev",
-    "prefer-stable": true,
     "require-dev": {
         "friendsofphp/php-cs-fixer": "^3.75",
         "phpstan/phpstan": "^2.1",