diff --git a/CHANGELOG.md b/CHANGELOG.md
index 34851869..d0d90e4e 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -7,6 +7,10 @@ and this project follows [Semantic Versioning](https://semver.org/).
 
 ## [Unreleased]
 
+### Changed
+
+- **BREAKING:** The serialized `Preconditioner` wire format changed (v12 → v13) with the `approx-chol` 0.4 → 0.5 bump; 0.3.0 bytes no longer decode.
+
 ### Fixed
 
 - A design carrying varying slopes on two distinct factors could fail preconditioner construction with `matrix is not symmetric`, when rounding left the two triangles of the exact Schur complement unequal (#229).
diff --git a/Cargo.lock b/Cargo.lock
index 21cdd58e..2d272ab3 100644
--- a/Cargo.lock
+++ b/Cargo.lock
@@ -25,9 +25,9 @@ checksum = "940b3a0ca603d1eade50a4846a2afffd5ef57a9feac2c0e2ec2e14f9ead76000"
 
 [[package]]
 name = "approx-chol"
-version = "0.4.0"
+version = "0.5.0"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "ceecf5e5bb6136d3c335eec5aac88f17b284b68e22d710ebeec66417fa410830"
+checksum = "affa21d606ec089747ab3ef1baff8feac12b5c115e42d4451b01668c9acded56"
 dependencies = [
  "num-traits",
  "rand 0.10.2",
diff --git a/crates/within/Cargo.toml b/crates/within/Cargo.toml
index aff769f6..97b48c75 100644
--- a/crates/within/Cargo.toml
+++ b/crates/within/Cargo.toml
@@ -12,7 +12,7 @@ categories.workspace = true
 
 [dependencies]
 schwarz-precond = { workspace = true, features = ["serde"] }
-approx-chol = { version = "0.4.0", features = ["serde"] }
+approx-chol = { version = "0.5.0", features = ["serde"] }
 serde = { workspace = true, features = ["rc"] }
 postcard.workspace = true
 ndarray = "0.17"
diff --git a/crates/within/tests/fixtures/preconditioner_v11.postcard b/crates/within/tests/fixtures/preconditioner_v11.postcard
deleted file mode 100644
index 845123af..00000000
Binary files a/crates/within/tests/fixtures/preconditioner_v11.postcard and /dev/null differ
diff --git a/crates/within/tests/fixtures/preconditioner_v13.postcard b/crates/within/tests/fixtures/preconditioner_v13.postcard
new file mode 100644
index 00000000..6f8e07a2
Binary files /dev/null and b/crates/within/tests/fixtures/preconditioner_v13.postcard differ
diff --git a/crates/within/tests/wire_format_fixture.rs b/crates/within/tests/wire_format_fixture.rs
index 1c708114..d7f9865d 100644
--- a/crates/within/tests/wire_format_fixture.rs
+++ b/crates/within/tests/wire_format_fixture.rs
@@ -5,9 +5,9 @@
 
 use within::{Effect, LsmrOptions, Preconditioner, PreconditionerConfig, Solver};
 
-const WIRE_FORMAT_VERSION: u32 = 12;
-const PRECOND_BYTES: &[u8] = include_bytes!("fixtures/preconditioner_v12.postcard");
-const PRE_BUMP_BYTES: &[u8] = include_bytes!("fixtures/preconditioner_v11.postcard");
+const WIRE_FORMAT_VERSION: u32 = 13;
+const PRECOND_BYTES: &[u8] = include_bytes!("fixtures/preconditioner_v13.postcard");
+const PRE_BUMP_BYTES: &[u8] = include_bytes!("fixtures/preconditioner_v12.postcard");
 
 fn fixture_problem() -> (Vec<u32>, Vec<u32>, Vec<f64>, Vec<f64>) {
     // The frustrated (f-slope, g) pair pins a signed operator with Scaled coords and a Cover.
@@ -96,7 +96,7 @@ fn pre_bump_fixture_no_longer_decodes() {
 }
 
 /// Generate the wire-format fixture. Run with `--ignored` to overwrite
-/// `crates/within/tests/fixtures/preconditioner_v12.postcard`. Intended for
+/// `crates/within/tests/fixtures/preconditioner_v13.postcard`. Intended for
 /// intentional wire-format bumps only; CI runs the non-ignored tests above.
 #[test]
 #[ignore]
@@ -117,7 +117,7 @@ fn regenerate_wire_format_fixture() {
     let bytes = postcard::to_stdvec(prec).expect("serialize");
 
     let mut path = PathBuf::from(env!("CARGO_MANIFEST_DIR"));
-    path.push("tests/fixtures/preconditioner_v12.postcard");
+    path.push("tests/fixtures/preconditioner_v13.postcard");
     let mut out = std::fs::File::create(&path).expect("create fixture file");
     out.write_all(&bytes).expect("write fixture bytes");
     eprintln!("wrote {} bytes to {}", bytes.len(), path.display());