diff --git a/.github/workflows/release-binaries.yml b/.github/workflows/release-binaries.yml
index d9ca9fa..9745707 100644
--- a/.github/workflows/release-binaries.yml
+++ b/.github/workflows/release-binaries.yml
@@ -14,7 +14,7 @@ on:
         description: "The release tag the binaries are built from and attached to (e.g. 0.1.3)"
         required: true
       platform:
-        description: "The openkal-platform whose hosted arrangement builds the tools: the one whose version group holds the implementations the tag pins (0.1.5: 0.19.0; 0.1.6: 0.19.1; 0.1.7: 0.19.2; 0.1.8: 0.20.0; 0.1.9: 0.20.1; 0.3.0: 0.21.0; 0.3.1: 0.21.1; 0.4.0: 0.23.0)"
+        description: "The openkal-platform whose hosted arrangement builds the tools: the one whose version group holds the implementations the tag pins (0.1.5: 0.19.0; 0.1.6: 0.19.1; 0.1.7: 0.19.2; 0.1.8: 0.20.0; 0.1.9: 0.20.1; 0.3.0: 0.21.0; 0.3.1: 0.21.1; 0.4.1: 0.23.0)"
         required: true
         default: "0.21.0"
       mcpp_ref:
@@ -34,7 +34,7 @@ env:
   # the dispatch beside the tag: a tag's tools pin exact implementations, and the
   # platform is the one whose version group holds them (0.1.4: 0.18.0; 0.1.5:
   # 0.19.0, openkal-linux 0.19.0; 0.1.6: 0.19.1; 0.1.7: 0.19.2; 0.1.8: 0.20.0; 0.1.9: 0.20.1;
-  # 0.3.0: 0.21.0; 0.3.1: 0.21.1; 0.4.0: 0.23.0).
+  # 0.3.0: 0.21.0; 0.3.1: 0.21.1; 0.4.1: 0.23.0).
   PLATFORM_VERSION: ${{ github.event.inputs.platform }}
   XLINGS_VERSION: v2026.10.26.1
   XLINGS_NON_INTERACTIVE: '1'
diff --git a/README.md b/README.md
index 0aa6a9e..f2d2579 100644
--- a/README.md
+++ b/README.md
@@ -101,6 +101,12 @@ resource preference or named values the initialisers read differ from those the
 made under does not use it, and an initialiser that asks for anything else of the start is
 refused a snapshot. openkal-musl 0.27.0 takes part. `OKRUN_SNAPSHOT=0` runs the initialisers.
 
+**Over openkal-macos 0.21.2** (0.4.1): the runner on macOS is built over an implementation whose
+sleep suspends the context and whose monotonic granularity is the same at every start. Under 0.21.0
+the wait it suspends with failed at once for a word whose page was not yet present, and an image's
+sleep on macOS was a spin of the processor for its whole length; the granularity was measured at
+each start, and a snapshot compared among the implementation's facts was declined when it differed.
+
 ## What a start spends
 
 A program's resource preference (openkal 0.23: balanced, performance, economy) decides what
diff --git a/bind/mcpp.toml b/bind/mcpp.toml
index 372be7c..62c4c1c 100644
--- a/bind/mcpp.toml
+++ b/bind/mcpp.toml
@@ -1,7 +1,7 @@
 [package]
 namespace   = "mcpplibs"
 name        = "openkal-bind"
-version     = "0.4.0"
+version     = "0.4.1"
 # `mcpp::xpkg_request', `mcpp::decision' (protocol 15).
 mcpp        = ">=2026.10.1.3"
 description = "A build plugin: a library published as an ok image (.okso) and a C header is called from a program of any system, through a binding generated from the header and libokrun."
diff --git a/docs/bind.md b/docs/bind.md
index 5b05b17..2cf0266 100644
--- a/docs/bind.md
+++ b/docs/bind.md
@@ -24,10 +24,10 @@ sources      = []
 include_dirs = ["include"]
 
 [target.'cfg(not(os = "openkal"))'.dependencies]
-openkal-run = "0.4.0"
+openkal-run = "0.4.1"
 
 [build-dependencies]
-openkal-bind = "0.4.0"
+openkal-bind = "0.4.1"
 ```
 
 ```cpp
@@ -109,4 +109,5 @@ llvm toolchain's clang converts the call.
 | 0.3.1 | No change of its own; released with the archive, whose runner admits a remembered okb member by its shape without reading it. |
 | 0.3.2 | No change of its own; released with the archive, whose runner is built over openkal 0.22's implementations: a started program is given the system's null device at a position (`KAL_SPAWN_NULL_*`). |
 | 0.4.0 | No change of its own; released with the archive, whose loader places an image at the base `okld place` chose for it (openkal 0.23, `kal_exec_alloc_at`) and then applies only the relocations that name a symbol. |
+| 0.4.1 | No change of its own; released with the archive, whose runner on macOS is built over openkal-macos 0.21.2 (a sleep is no longer a spin of the processor; the granularity is the same at every start). |
 | 0.1.9 | No change of its own; released with the archive, whose runner on macOS is built over openkal-macos 0.17.1 (`kal_task_current` without a system call). |
diff --git a/ld/mcpp.toml b/ld/mcpp.toml
index 3f81510..5810579 100644
--- a/ld/mcpp.toml
+++ b/ld/mcpp.toml
@@ -1,7 +1,7 @@
 [package]
 namespace   = "mcpplibs"
 name        = "openkal-ld"
-version     = "0.4.0"
+version     = "0.4.1"
 description = "libokld: the ok format (openkal image format) --- its definition, a reader of bytes, a checker, a signer, and a loader. Freestanding: no C library, no exceptions."
 license     = "Apache-2.0"
 authors     = ["mcpplibs"]
diff --git a/run/mcpp.toml b/run/mcpp.toml
index c54008c..c590bc2 100644
--- a/run/mcpp.toml
+++ b/run/mcpp.toml
@@ -1,7 +1,7 @@
 [package]
 namespace   = "mcpplibs"
 name        = "openkal-run"
-version     = "0.4.0"
+version     = "0.4.1"
 description = "libokrun: the runner's core --- an ok image's names bound to this process's one openkal implementation, in the image's calling convention, and its entry entered."
 license     = "Apache-2.0"
 authors     = ["mcpplibs"]
@@ -18,7 +18,7 @@ openkal-ld = { path = "../ld" }
 openkal-linux = "0.24.0"
 
 [target.macos.dependencies]
-openkal-macos = "0.21.0"
+openkal-macos = "0.21.2"
 
 [target.windows.dependencies]
 openkal-windows = "0.19.0"
diff --git a/tools/mcpp.toml b/tools/mcpp.toml
index 1de3a6b..950b120 100644
--- a/tools/mcpp.toml
+++ b/tools/mcpp.toml
@@ -1,7 +1,7 @@
 [package]
 namespace   = "mcpplibs"
 name        = "openkal-tools"
-version     = "0.4.0"
+version     = "0.4.1"
 description = "okrun, which runs an ok image on this system, and okld, the format's tool on a build machine (check, note, sign, inspect)."
 license     = "Apache-2.0"
 authors     = ["mcpplibs"]