diff --git a/.gitignore b/.gitignore
index eae9097..f4709d9 100644
--- a/.gitignore
+++ b/.gitignore
@@ -1 +1,2 @@
 /cover.out
+*.out
diff --git a/README.md b/README.md
index 5f4794b..d3cf58d 100644
--- a/README.md
+++ b/README.md
@@ -4,7 +4,7 @@
 
 [![Docs](https://img.shields.io/badge/docs-mkdocs--material-013243)](https://go-ndarray.github.io/docs/)
 [![License](https://img.shields.io/badge/license-BSD--3--Clause-blue)](LICENSE)
-[![Go](https://img.shields.io/badge/go-1.26.4%2B-00ADD8)](https://go.dev/dl/)
+[![Go](https://img.shields.io/badge/go-1.26.6%2B-00ADD8)](https://go.dev/dl/)
 [![Status](https://img.shields.io/badge/status-numpy%20parity%20(float64)-9a6700)](docs/plan-ndarray.md)
 
 **A pure-Go (CGO=0) NumPy-style N-dimensional array library.** Row-major
@@ -106,7 +106,8 @@ pure-Go `gonum` 4–10× (**[BENCHMARKS.md](BENCHMARKS.md)**). It is a
 > the suite on amd64, arm64, 386, and riscv64/loong64/ppc64le/s390x/arm under
 > qemu, on Linux, macOS and Windows, and compiles it for every `GOOS/GOARCH`
 > pair Go supports; v0.1.0 and v0.2.0 were also run on real amd64, arm64,
-> ppc64le, riscv64 and loong64 hardware. See **[docs/plan-ndarray.md](docs/plan-ndarray.md)**
+> ppc64le, riscv64 and loong64 hardware, v0.3.0 on real amd64, arm64, ppc64le
+> and loong64. See **[docs/plan-ndarray.md](docs/plan-ndarray.md)**
 > for the roadmap (more dtypes, more SIMD targets).
 
 ## Why this module?
@@ -117,8 +118,25 @@ pure-Go `gonum` 4–10× (**[BENCHMARKS.md](BENCHMARKS.md)**). It is a
 arch is therefore a durable foundation. The numeric loops live in
 `internal/kernels`, each with a pure-Go reference implementation;
 [go-asmgen](https://github.com/go-asmgen)-generated SIMD kernels replace them
-on amd64 and arm64 today, behind the same API and held to the same tests, and
-the other 64-bit targets are next.
+on amd64, arm64, ppc64le and loong64 today, behind the same API and held to the
+same tests; riscv64 and s390x are next.
+
+## Untrusted input
+
+Shapes, indices and data can come from someone else (a file, a request), so
+every operation answers a shape it cannot represent with an error wrapping
+`ErrShapeMismatch` instead of a panic or a wrong array. That covers results as
+well as inputs: `(2^32, 0) @ (0, 2^32)` holds no data, yet its result would
+have 2^64 elements, so `MatMul` refuses it, as NumPy does. The one exception
+is `Outer`, which has no error result: it panics when its result is too big,
+which takes operands of more than 2^30 elements each. An empty array whose
+other axis is huge, `(2^58, 0)`, costs nothing to reduce, concatenate or scan.
+
+The assembly kernels take raw pointers. Their Go wrappers check every operand
+the kernel reads or writes against the length it is given, so a mistake is an
+index panic in Go, never an access outside a slice; a test places each operand
+flush against an inaccessible page to prove the kernels themselves stay inside
+(see [SECURITY.md](SECURITY.md)).
 
 ## Example
 
diff --git a/SECURITY.md b/SECURITY.md
new file mode 100644
index 0000000..7cad1a7
--- /dev/null
+++ b/SECURITY.md
@@ -0,0 +1,67 @@
+# Security
+
+## Reporting
+
+Report a vulnerability privately through GitHub's **Report a vulnerability**
+button on this repository (Security → Advisories). Please do not open a public
+issue for it.
+
+## What the library guarantees
+
+go-ndarray is pure Go (`CGO_ENABLED=0`) except for its SIMD kernels, which are
+Plan 9 assembly generated by [go-asmgen](https://github.com/go-asmgen/asmgen)
+for amd64, arm64, ppc64le and loong64. Those kernels are the only code Go's
+bounds checks do not cover, so they are held to the following:
+
+- **Every wrapper checks the reach of its kernel.** Before an assembly call, the
+  Go wrapper indexes the last element of every operand the kernel reads or
+  writes (`internal/kernels/{reduce,gemm}_<arch>.go`). A caller's mistake is an
+  index-out-of-range panic in Go, never an access outside a slice.
+  `TestWrappersRefuseShortOperands` passes each wrapper an operand one element
+  short and requires the panic.
+- **The kernels stay inside their slices.** `TestKernelsStayInsideTheirSlices`
+  and `TestGemmMicroStaysInsideItsOperands` (`internal/kernels/fence_test.go`,
+  Linux and macOS) map each operand flush against a `PROT_NONE` page, once
+  ending at it and once starting after one, for every length from 1 to 70 and
+  every GEMM depth from 1 to 9. A read or write one element past either end is a
+  fault. The fence itself was checked by a kernel deliberately reading one
+  element too far, which faults on amd64 (4 KiB pages), arm64 (16 KiB), loong64
+  (16 KiB) and ppc64le (64 KiB). Prefetch instructions may point past the end:
+  they are hints and do not fault.
+- **Shapes are validated, results included.** A shape whose element count, or
+  whose size in bytes, does not fit in an `int` is an error wrapping
+  `ErrShapeMismatch`, even when a zero dimension makes it empty, as in NumPy.
+  This applies to the shapes operations compute: `MatMul`, `Dot`, `Inner`,
+  `Concatenate`, `Stack`, broadcasting and `Linspace`. `Outer` has no error
+  result and panics instead.
+- **Empty arrays cost nothing.** Operations on an empty array with a huge axis,
+  such as `(2^58, 0)`, return at once instead of walking that axis.
+  `TestEmptyArraysWithHugeAxesReturnPromptly` covers concatenation, the axis
+  reductions and the scans.
+
+The minimum Go version (`go` in `go.mod`) is kept on a release that fixes the
+standard library's known vulnerabilities; `govulncheck ./...` reports none.
+
+## Audit log
+
+**2026-10-04 (v0.3.0).**
+
+- `govulncheck` found no reachable vulnerability. At `go 1.26.4`, 10 standard
+  library vulnerabilities were in modules the library requires but did not
+  call; `go 1.26.6` fixes all of them.
+- Found and fixed:
+  - `Concatenate` summed the axis lengths without an overflow check, so 17
+    arrays of shape `(2^59, 0)` gave a **negative** dimension.
+  - `MatMul` of `(2^32, 0)` by `(0, 2^32)` returned a `(2^32, 2^32)` array whose
+    `Size()` was 0. A product wrapping to −1 panicked in `makeslice`.
+  - `Linspace` with a count above the limit panicked in `makeslice`.
+  - `Stack` of 9 arrays `(2^58, 0)` returned `(9, 2^58, 0)`, which `New`
+    rejects.
+  - Reducing `(2^58, 0)` over axis 0, concatenating it along its last axis, or
+    scanning `(0, 2^58)` walked the 2^58-long axis: effectively a hang.
+- Hardened: the operand checks in front of every assembly call (above). The
+  fence test found no out-of-bounds access in any kernel, on real amd64
+  (Zen 3), arm64, ppc64le (POWER9) and loong64 (3C5000L, with LASX).
+- Cost: none measurable. A single-core A/B on Zen 3 (10 interleaved rounds)
+  measured `MatMul` 256², `Dot1D` and `AddInto` 16 Ki within ±2%, inside the
+  run-to-run spread.
diff --git a/benchmarks/verify_test.go b/benchmarks/verify_test.go
index cad6850..260c342 100644
--- a/benchmarks/verify_test.go
+++ b/benchmarks/verify_test.go
@@ -37,7 +37,7 @@ func TestDumpForVerify(t *testing.T) {
 		put(tag+".mid", flat.At(flat.Size()/2))
 	}
 
-	x, y := vec(1 << 16), vec(1 << 16)
+	x, y := vec(1<<16), vec(1<<16)
 	r, _ := x.Add(y)
 	putArr("add", r)
 	r, _ = x.Mul(y)
diff --git a/cg.out b/cg.out
deleted file mode 100644
index c8640fc..0000000
--- a/cg.out
+++ /dev/null
@@ -1,2155 +0,0 @@
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diff --git a/cg1.out b/cg1.out
deleted file mode 100644
index ac2a2cd..0000000
--- a/cg1.out
+++ /dev/null
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diff --git a/cg4.out b/cg4.out
deleted file mode 100644
index c8640fc..0000000
--- a/cg4.out
+++ /dev/null
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diff --git a/cover2.out b/cover2.out
deleted file mode 100644
index 45634dd..0000000
--- a/cover2.out
+++ /dev/null
@@ -1,2155 +0,0 @@
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-github.com/go-ndarray/ndarray/internal/kernels/kernels.go:382.13,384.4 1 2
-github.com/go-ndarray/ndarray/internal/kernels/kernels.go:385.3,385.13 1 5
-github.com/go-ndarray/ndarray/internal/kernels/kernels.go:391.39,392.21 1 1
-github.com/go-ndarray/ndarray/internal/kernels/kernels.go:392.21,393.19 1 5
-github.com/go-ndarray/ndarray/internal/kernels/kernels.go:393.19,395.4 1 3
-github.com/go-ndarray/ndarray/internal/kernels/kernels.go:395.9,397.4 1 2
-github.com/go-ndarray/ndarray/internal/kernels/parallel.go:29.28,31.71 2 38
-github.com/go-ndarray/ndarray/internal/kernels/parallel.go:31.71,33.3 1 5
-github.com/go-ndarray/ndarray/internal/kernels/parallel.go:34.2,34.10 1 38
-github.com/go-ndarray/ndarray/internal/kernels/parallel.go:40.51,41.12 1 37
-github.com/go-ndarray/ndarray/internal/kernels/parallel.go:41.12,44.3 2 1
-github.com/go-ndarray/ndarray/internal/kernels/parallel.go:45.2,47.35 3 36
-github.com/go-ndarray/ndarray/internal/kernels/parallel.go:47.35,49.13 2 507
-github.com/go-ndarray/ndarray/internal/kernels/parallel.go:49.13,51.4 1 6
-github.com/go-ndarray/ndarray/internal/kernels/parallel.go:52.3,53.23 2 507
-github.com/go-ndarray/ndarray/internal/kernels/parallel.go:53.23,56.4 2 507
-github.com/go-ndarray/ndarray/internal/kernels/parallel.go:58.2,58.11 1 36
-github.com/go-ndarray/ndarray/internal/kernels/parallel.go:68.54,70.22 2 32
-github.com/go-ndarray/ndarray/internal/kernels/parallel.go:70.22,73.3 2 20
-github.com/go-ndarray/ndarray/internal/kernels/parallel.go:74.2,74.49 1 12
-github.com/go-ndarray/ndarray/internal/kernels/parallel.go:74.49,76.3 1 24
-github.com/go-ndarray/ndarray/internal/kernels/parallel.go:87.32,87.65 1 8
-github.com/go-ndarray/ndarray/internal/kernels/parallel.go:90.32,90.65 1 8
-github.com/go-ndarray/ndarray/internal/kernels/parallel.go:93.32,93.65 1 8
-github.com/go-ndarray/ndarray/internal/kernels/parallel.go:96.32,96.65 1 8
-github.com/go-ndarray/ndarray/internal/kernels/parallel.go:100.56,102.22 2 8
-github.com/go-ndarray/ndarray/internal/kernels/parallel.go:102.22,105.3 2 5
-github.com/go-ndarray/ndarray/internal/kernels/parallel.go:106.2,106.49 1 3
-github.com/go-ndarray/ndarray/internal/kernels/parallel.go:106.49,108.3 1 6
-github.com/go-ndarray/ndarray/internal/kernels/parallel.go:117.32,119.22 2 8
-github.com/go-ndarray/ndarray/internal/kernels/parallel.go:119.22,122.3 2 5
-github.com/go-ndarray/ndarray/internal/kernels/parallel.go:123.2,123.49 1 3
-github.com/go-ndarray/ndarray/internal/kernels/parallel.go:123.49,125.3 1 6
-github.com/go-ndarray/ndarray/internal/kernels/parallel.go:133.100,135.22 2 12
-github.com/go-ndarray/ndarray/internal/kernels/parallel.go:135.22,137.3 1 3
-github.com/go-ndarray/ndarray/internal/kernels/parallel.go:138.2,141.37 4 9
-github.com/go-ndarray/ndarray/internal/kernels/parallel.go:141.37,142.34 1 18
-github.com/go-ndarray/ndarray/internal/kernels/parallel.go:142.34,145.13 3 18
-github.com/go-ndarray/ndarray/internal/kernels/parallel.go:145.13,147.5 1 3
-github.com/go-ndarray/ndarray/internal/kernels/parallel.go:148.4,148.31 1 18
-github.com/go-ndarray/ndarray/internal/kernels/parallel.go:151.2,151.26 1 9
-github.com/go-ndarray/ndarray/internal/kernels/parallel.go:159.32,159.70 1 4
-github.com/go-ndarray/ndarray/internal/kernels/parallel.go:163.64,165.2 1 8
-github.com/go-ndarray/ndarray/internal/kernels/parallel.go:179.76,181.26 2 16
-github.com/go-ndarray/ndarray/internal/kernels/parallel.go:181.26,184.3 2 8
-github.com/go-ndarray/ndarray/internal/kernels/parallel.go:193.2,193.15 1 8
-github.com/go-ndarray/ndarray/internal/kernels/parallel.go:193.15,196.3 2 2
-github.com/go-ndarray/ndarray/internal/kernels/parallel.go:197.2,198.15 2 6
-github.com/go-ndarray/ndarray/internal/kernels/parallel.go:198.15,200.3 1 4
-github.com/go-ndarray/ndarray/internal/kernels/parallel.go:201.2,201.41 1 6
-github.com/go-ndarray/ndarray/internal/kernels/parallel.go:201.41,205.3 3 190
-github.com/go-ndarray/ndarray/internal/kernels/parallel.go:214.32,214.62 1 4
-github.com/go-ndarray/ndarray/internal/kernels/parallel.go:219.32,219.62 1 4
-github.com/go-ndarray/ndarray/internal/kernels/reduce_arm64.go:24.35,25.17 1 22
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-github.com/go-ndarray/ndarray/internal/kernels/reduce_arm64.go:28.2,28.31 1 21
-github.com/go-ndarray/ndarray/internal/kernels/reduce_arm64.go:37.35,38.19 1 27
-github.com/go-ndarray/ndarray/internal/kernels/reduce_arm64.go:38.19,40.3 1 1
-github.com/go-ndarray/ndarray/internal/kernels/reduce_arm64.go:41.2,41.38 1 26
-github.com/go-ndarray/ndarray/internal/kernels/reduce_arm64.go:51.35,51.60 1 68
-github.com/go-ndarray/ndarray/internal/kernels/reduce_arm64.go:52.35,52.60 1 68
-github.com/go-ndarray/ndarray/internal/kernels/reduce_arm64.go:62.34,63.19 1 27
-github.com/go-ndarray/ndarray/internal/kernels/reduce_arm64.go:63.19,65.3 1 1
-github.com/go-ndarray/ndarray/internal/kernels/reduce_arm64.go:66.2,66.42 1 26
-github.com/go-ndarray/ndarray/internal/kernels/reduce_arm64.go:69.34,70.19 1 27
-github.com/go-ndarray/ndarray/internal/kernels/reduce_arm64.go:70.19,72.3 1 1
-github.com/go-ndarray/ndarray/internal/kernels/reduce_arm64.go:73.2,73.42 1 26
-github.com/go-ndarray/ndarray/internal/kernels/reduce_arm64.go:76.34,77.19 1 27
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-github.com/go-ndarray/ndarray/internal/kernels/reduce_arm64.go:80.2,80.42 1 26
-github.com/go-ndarray/ndarray/internal/kernels/reduce_arm64.go:86.34,86.52 1 27
-github.com/go-ndarray/ndarray/internal/kernels/reduce_unrolled.go:18.39,20.11 2 68
-github.com/go-ndarray/ndarray/internal/kernels/reduce_unrolled.go:20.11,22.3 1 18
-github.com/go-ndarray/ndarray/internal/kernels/reduce_unrolled.go:23.2,25.25 3 50
-github.com/go-ndarray/ndarray/internal/kernels/reduce_unrolled.go:25.25,30.3 4 40534
-github.com/go-ndarray/ndarray/internal/kernels/reduce_unrolled.go:31.2,32.19 2 50
-github.com/go-ndarray/ndarray/internal/kernels/reduce_unrolled.go:32.19,34.3 1 54
-github.com/go-ndarray/ndarray/internal/kernels/reduce_unrolled.go:35.2,35.10 1 50
-github.com/go-ndarray/ndarray/internal/kernels/reduce_unrolled.go:38.39,40.11 2 68
-github.com/go-ndarray/ndarray/internal/kernels/reduce_unrolled.go:40.11,42.3 1 18
-github.com/go-ndarray/ndarray/internal/kernels/reduce_unrolled.go:43.2,45.25 3 50
-github.com/go-ndarray/ndarray/internal/kernels/reduce_unrolled.go:45.25,50.3 4 40534
-github.com/go-ndarray/ndarray/internal/kernels/reduce_unrolled.go:51.2,52.19 2 50
-github.com/go-ndarray/ndarray/internal/kernels/reduce_unrolled.go:52.19,54.3 1 54
-github.com/go-ndarray/ndarray/internal/kernels/reduce_unrolled.go:55.2,55.10 1 50
diff --git a/creation.go b/creation.go
index dae2261..5959ef9 100644
--- a/creation.go
+++ b/creation.go
@@ -11,6 +11,9 @@ func Linspace(start, stop float64, num int) (*Array, error) {
 		return nil, fmt.Errorf("%w: linspace num must be non-negative, got %d",
 			ErrShapeMismatch, num)
 	}
+	if err := validateShape([]int{num}); err != nil {
+		return nil, err
+	}
 	data := make([]float64, num)
 	switch {
 	case num == 1:
diff --git a/go.mod b/go.mod
index a09a6bb..9578066 100644
--- a/go.mod
+++ b/go.mod
@@ -1,3 +1,3 @@
 module github.com/go-ndarray/ndarray
 
-go 1.26.4
+go 1.26.6
diff --git a/internal/kernels/asmgen/go.mod b/internal/kernels/asmgen/go.mod
index e2dc623..5ff3cf2 100644
--- a/internal/kernels/asmgen/go.mod
+++ b/internal/kernels/asmgen/go.mod
@@ -4,6 +4,6 @@
 // go-asmgen to (re)produce the committed .s files via `go generate`.
 module github.com/go-ndarray/ndarray/internal/kernels/asmgen
 
-go 1.26.4
+go 1.26.6
 
 require github.com/go-asmgen/asmgen v0.14.0
diff --git a/internal/kernels/fence_amd64_test.go b/internal/kernels/fence_amd64_test.go
new file mode 100644
index 0000000..7b32f75
--- /dev/null
+++ b/internal/kernels/fence_amd64_test.go
@@ -0,0 +1,9 @@
+package kernels
+
+// forEachFallback runs f again with the SSE2 kernels the FMA ones replace.
+func forEachFallback(f func()) {
+	saved := useFMA
+	useFMA = false
+	defer func() { useFMA = saved }()
+	f()
+}
diff --git a/internal/kernels/fence_fallback_test.go b/internal/kernels/fence_fallback_test.go
new file mode 100644
index 0000000..387527c
--- /dev/null
+++ b/internal/kernels/fence_fallback_test.go
@@ -0,0 +1,7 @@
+//go:build arm64 || ppc64le
+
+package kernels
+
+// forEachFallback has nothing to do: these kernels have no CPU-dependent
+// alternative.
+func forEachFallback(func()) {}
diff --git a/internal/kernels/fence_loong64_test.go b/internal/kernels/fence_loong64_test.go
new file mode 100644
index 0000000..e2f8dcb
--- /dev/null
+++ b/internal/kernels/fence_loong64_test.go
@@ -0,0 +1,9 @@
+package kernels
+
+// forEachFallback runs f again with the scalar kernel used without LASX.
+func forEachFallback(f func()) {
+	saved := useLASX
+	useLASX = false
+	defer func() { useLASX = saved }()
+	f()
+}
diff --git a/internal/kernels/fence_test.go b/internal/kernels/fence_test.go
new file mode 100644
index 0000000..94f6217
--- /dev/null
+++ b/internal/kernels/fence_test.go
@@ -0,0 +1,99 @@
+//go:build (amd64 || arm64 || ppc64le || loong64) && (linux || darwin)
+
+package kernels
+
+import (
+	"os"
+	"syscall"
+	"testing"
+	"unsafe"
+)
+
+// The assembly kernels take raw pointers and trust their Go wrappers for the
+// lengths: an off-by-one in a tail loop, or a load issued one iteration early,
+// reads or writes memory that is not the slice's. Go's bounds checks cannot see
+// inside a .s file, and a stray access into the rest of the heap goes unnoticed.
+//
+// A fence makes it fault instead. Each operand is placed flush against an
+// inaccessible page (PROT_NONE), once ending at the page and once starting
+// right after one, so an access a single element past either end is a
+// SIGSEGV. Prefetches are hints and do not fault, so the kernels' prefetching
+// past the end is allowed, as the hardware allows it.
+
+// fenced is a mapping of [guard | data | guard] whose data region holds at
+// least n float64s.
+type fenced struct {
+	mem  []byte
+	data []float64 // the whole region between the guards
+}
+
+func newFenced(t *testing.T, n int) *fenced {
+	t.Helper()
+	pg := os.Getpagesize()
+	dataBytes := (n*8 + pg - 1) / pg * pg
+	mem, err := syscall.Mmap(-1, 0, dataBytes+2*pg,
+		syscall.PROT_READ|syscall.PROT_WRITE, syscall.MAP_ANON|syscall.MAP_PRIVATE)
+	if err != nil {
+		t.Fatalf("mmap: %v", err)
+	}
+	t.Cleanup(func() { syscall.Munmap(mem) })
+	for _, g := range [][]byte{mem[:pg], mem[pg+dataBytes:]} {
+		if err := syscall.Mprotect(g, syscall.PROT_NONE); err != nil {
+			t.Fatalf("mprotect: %v", err)
+		}
+	}
+	d := unsafe.Slice((*float64)(unsafe.Pointer(&mem[pg])), dataBytes/8)
+	for i := range d {
+		d[i] = float64(i%7) + 1 // positive, so sqrt and div stay finite
+	}
+	return &fenced{mem: mem, data: d}
+}
+
+// head is n elements starting right after the leading guard; tail is n
+// elements ending right before the trailing guard.
+func (f *fenced) head(n int) []float64 { return f.data[:n:n] }
+func (f *fenced) tail(n int) []float64 { return f.data[len(f.data)-n:] }
+
+// fences returns, for n elements, the operand placements to try.
+func fences(t *testing.T, n int) [][]float64 {
+	f := newFenced(t, n)
+	return [][]float64{f.head(n), f.tail(n)}
+}
+
+func TestKernelsStayInsideTheirSlices(t *testing.T) {
+	for n := 1; n <= 70; n++ {
+		for _, a := range fences(t, n) {
+			for _, b := range fences(t, n) {
+				for _, dst := range fences(t, n) {
+					sumSIMD(a)
+					maxSIMD(a)
+					minSIMD(a)
+					dotSIMD(a, b)
+					sqrtSIMD(dst, a)
+					addBin(dst, a, b)
+					subBin(dst, a, b)
+					mulBin(dst, a, b)
+					divBin(dst, a, b)
+				}
+			}
+		}
+	}
+}
+
+func TestGemmMicroStaysInsideItsOperands(t *testing.T) {
+	run := func() {
+		for kc := 1; kc <= 9; kc++ {
+			for _, ldc := range []int{NR, NR + 3, 64} {
+				for _, pa := range fences(t, kc*MR) {
+					for _, pb := range fences(t, kc*NR) {
+						for _, dst := range fences(t, (MR-1)*ldc+NR) {
+							gemmMicro(kc, pa, pb, dst, ldc)
+						}
+					}
+				}
+			}
+		}
+	}
+	run()
+	forEachFallback(run)
+}
diff --git a/internal/kernels/gemm_amd64.go b/internal/kernels/gemm_amd64.go
index 9053cba..718e792 100644
--- a/internal/kernels/gemm_amd64.go
+++ b/internal/kernels/gemm_amd64.go
@@ -32,6 +32,7 @@ var useFMA = hasFMA()
 // dst[0:], whose rows are ldc apart. pa, pb hold at least kc*MR and kc*NR packed
 // (zero-padded) doubles; dst has at least (MR-1)*ldc + NR elements.
 func gemmMicro(kc int, pa, pb, dst []float64, ldc int) {
+	_, _, _ = pa[kc*MR-1], pb[kc*NR-1], dst[(MR-1)*ldc+NR-1] // the kernel's whole reach
 	if useFMA {
 		gemmMicro6x8FMA(kc, &pa[0], &pb[0], &dst[0], ldc)
 		return
@@ -52,6 +53,7 @@ func dotSIMD(a, b []float64) float64 {
 	if !useFMA || len(a) == 0 {
 		return dotRange(a, b)
 	}
+	_ = b[len(a)-1] // the kernel reads len(a) of b
 	return dotFMA(&a[0], &b[0], len(a))
 }
 
diff --git a/internal/kernels/gemm_arm64.go b/internal/kernels/gemm_arm64.go
index 53bd211..51402f0 100644
--- a/internal/kernels/gemm_arm64.go
+++ b/internal/kernels/gemm_arm64.go
@@ -23,6 +23,7 @@ const (
 // kc*MR and kc*NR packed (zero-padded) doubles; dst has at least (MR-1)*ldc + NR
 // elements. Bit-identical to the scalar ikj accumulation (see gemmEdge).
 func gemmMicro(kc int, pa, pb, dst []float64, ldc int) {
+	_, _, _ = pa[kc*MR-1], pb[kc*NR-1], dst[(MR-1)*ldc+NR-1] // the kernel's whole reach
 	gemmMicro4x8(kc, &pa[0], &pb[0], &dst[0], ldc)
 }
 
@@ -31,6 +32,7 @@ func dotSIMD(a, b []float64) float64 {
 	if len(a) == 0 {
 		return 0
 	}
+	_ = b[len(a)-1] // the kernel reads len(a) of b
 	return dotNEON(&a[0], &b[0], len(a))
 }
 
diff --git a/internal/kernels/gemm_loong64.go b/internal/kernels/gemm_loong64.go
index f926b6f..076e7e1 100644
--- a/internal/kernels/gemm_loong64.go
+++ b/internal/kernels/gemm_loong64.go
@@ -14,6 +14,7 @@ const (
 
 func gemmMicro(kc int, pa, pb, dst []float64, ldc int) {
 	if useLASX {
+		_, _, _ = pa[kc*MR-1], pb[kc*NR-1], dst[(MR-1)*ldc+NR-1] // the kernel's whole reach
 		gemmMicro8x8LASX(kc, &pa[0], &pb[0], &dst[0], ldc)
 		return
 	}
@@ -47,6 +48,7 @@ func dotSIMD(a, b []float64) float64 {
 	if !useLASX || len(a) == 0 {
 		return dotRange(a, b)
 	}
+	_ = b[len(a)-1] // the kernel reads len(a) of b
 	return dotLASX(&a[0], &b[0], len(a))
 }
 
diff --git a/internal/kernels/gemm_ppc64le.go b/internal/kernels/gemm_ppc64le.go
index fc53ee9..7f14907 100644
--- a/internal/kernels/gemm_ppc64le.go
+++ b/internal/kernels/gemm_ppc64le.go
@@ -16,6 +16,7 @@ const (
 // gemmMicro adds the MR x NR tile sum_p pa[p*MR..]*pb[p*NR..] into the C block
 // at dst[0:], whose rows are ldc apart.
 func gemmMicro(kc int, pa, pb, dst []float64, ldc int) {
+	_, _, _ = pa[kc*MR-1], pb[kc*NR-1], dst[(MR-1)*ldc+NR-1] // the kernel's whole reach
 	gemmMicro8x8VSX(kc, &pa[0], &pb[0], &dst[0], ldc)
 }
 
@@ -25,6 +26,7 @@ func dotSIMD(a, b []float64) float64 {
 	if len(a) == 0 {
 		return 0
 	}
+	_ = b[len(a)-1] // the kernel reads len(a) of b
 	return dotVSX(&a[0], &b[0], len(a))
 }
 
diff --git a/internal/kernels/guard_test.go b/internal/kernels/guard_test.go
new file mode 100644
index 0000000..e639256
--- /dev/null
+++ b/internal/kernels/guard_test.go
@@ -0,0 +1,33 @@
+//go:build amd64 || arm64 || ppc64le || loong64
+
+package kernels
+
+import "testing"
+
+// The wrappers check the operands the assembly reads against the length it is
+// given, so a caller's mistake is an index panic in Go rather than an access
+// past a slice inside the kernel.
+func TestWrappersRefuseShortOperands(t *testing.T) {
+	long, short := make([]float64, 8), make([]float64, 7)
+	ldc := NR
+	for name, f := range map[string]func(){
+		"sqrt src": func() { sqrtSIMD(long, short) },
+		"add a":    func() { addBin(long, short, long) },
+		"sub b":    func() { subBin(long, long, short) },
+		"mul a":    func() { mulBin(long, short, long) },
+		"div b":    func() { divBin(long, long, short) },
+		"dot b":    func() { dotSIMD(long, short) },
+		"gemm pa":  func() { gemmMicro(1, make([]float64, MR-1), make([]float64, NR), make([]float64, (MR-1)*ldc+NR), ldc) },
+		"gemm pb":  func() { gemmMicro(1, make([]float64, MR), make([]float64, NR-1), make([]float64, (MR-1)*ldc+NR), ldc) },
+		"gemm dst": func() { gemmMicro(1, make([]float64, MR), make([]float64, NR), make([]float64, (MR-1)*ldc+NR-1), ldc) },
+	} {
+		func() {
+			defer func() {
+				if recover() == nil {
+					t.Errorf("%s: a short operand was accepted", name)
+				}
+			}()
+			f()
+		}()
+	}
+}
diff --git a/internal/kernels/reduce_amd64.go b/internal/kernels/reduce_amd64.go
index bfeff79..4524233 100644
--- a/internal/kernels/reduce_amd64.go
+++ b/internal/kernels/reduce_amd64.go
@@ -28,6 +28,7 @@ func sqrtSIMD(dst, src []float64) {
 	if len(dst) == 0 {
 		return
 	}
+	_ = src[len(dst)-1] // the kernel reads len(dst) of src
 	sqrtSSE2(&dst[0], &src[0], len(dst))
 }
 
@@ -56,6 +57,7 @@ func addBin(dst, a, b []float64) {
 	if len(dst) == 0 {
 		return
 	}
+	_, _ = a[len(dst)-1], b[len(dst)-1] // the kernel reads len(dst) of each
 	addSSE2(&dst[0], &a[0], &b[0], len(dst))
 }
 
@@ -63,6 +65,7 @@ func subBin(dst, a, b []float64) {
 	if len(dst) == 0 {
 		return
 	}
+	_, _ = a[len(dst)-1], b[len(dst)-1] // the kernel reads len(dst) of each
 	subSSE2(&dst[0], &a[0], &b[0], len(dst))
 }
 
@@ -70,6 +73,7 @@ func mulBin(dst, a, b []float64) {
 	if len(dst) == 0 {
 		return
 	}
+	_, _ = a[len(dst)-1], b[len(dst)-1] // the kernel reads len(dst) of each
 	mulSSE2(&dst[0], &a[0], &b[0], len(dst))
 }
 
@@ -77,6 +81,7 @@ func divBin(dst, a, b []float64) {
 	if len(dst) == 0 {
 		return
 	}
+	_, _ = a[len(dst)-1], b[len(dst)-1] // the kernel reads len(dst) of each
 	divSSE2(&dst[0], &a[0], &b[0], len(dst))
 }
 
diff --git a/internal/kernels/reduce_arm64.go b/internal/kernels/reduce_arm64.go
index 8a0d348..02f1317 100644
--- a/internal/kernels/reduce_arm64.go
+++ b/internal/kernels/reduce_arm64.go
@@ -38,6 +38,7 @@ func sqrtSIMD(dst, src []float64) {
 	if len(dst) == 0 {
 		return
 	}
+	_ = src[len(dst)-1] // the kernel reads len(dst) of src
 	sqrtNEON(&dst[0], &src[0], len(dst))
 }
 
@@ -63,6 +64,7 @@ func addBin(dst, a, b []float64) {
 	if len(dst) == 0 {
 		return
 	}
+	_, _ = a[len(dst)-1], b[len(dst)-1] // the kernel reads len(dst) of each
 	addNEON(&dst[0], &a[0], &b[0], len(dst))
 }
 
@@ -70,6 +72,7 @@ func subBin(dst, a, b []float64) {
 	if len(dst) == 0 {
 		return
 	}
+	_, _ = a[len(dst)-1], b[len(dst)-1] // the kernel reads len(dst) of each
 	subNEON(&dst[0], &a[0], &b[0], len(dst))
 }
 
@@ -77,6 +80,7 @@ func mulBin(dst, a, b []float64) {
 	if len(dst) == 0 {
 		return
 	}
+	_, _ = a[len(dst)-1], b[len(dst)-1] // the kernel reads len(dst) of each
 	mulNEON(&dst[0], &a[0], &b[0], len(dst))
 }
 
diff --git a/internal/kernels/reduce_loong64.go b/internal/kernels/reduce_loong64.go
index 5fce39d..d5b12ae 100644
--- a/internal/kernels/reduce_loong64.go
+++ b/internal/kernels/reduce_loong64.go
@@ -37,6 +37,7 @@ func sqrtSIMD(dst, src []float64) {
 		sqrtScalar(dst, src)
 		return
 	}
+	_ = src[len(dst)-1] // the kernel reads len(dst) of src
 	sqrtLASX(&dst[0], &src[0], len(dst))
 }
 
@@ -49,6 +50,7 @@ func addBin(dst, a, b []float64) {
 		Add(dst, a, b)
 		return
 	}
+	_, _ = a[len(dst)-1], b[len(dst)-1] // the kernel reads len(dst) of each
 	addLASX(&dst[0], &a[0], &b[0], len(dst))
 }
 
@@ -57,6 +59,7 @@ func subBin(dst, a, b []float64) {
 		Sub(dst, a, b)
 		return
 	}
+	_, _ = a[len(dst)-1], b[len(dst)-1] // the kernel reads len(dst) of each
 	subLASX(&dst[0], &a[0], &b[0], len(dst))
 }
 
@@ -65,6 +68,7 @@ func mulBin(dst, a, b []float64) {
 		Mul(dst, a, b)
 		return
 	}
+	_, _ = a[len(dst)-1], b[len(dst)-1] // the kernel reads len(dst) of each
 	mulLASX(&dst[0], &a[0], &b[0], len(dst))
 }
 
@@ -73,6 +77,7 @@ func divBin(dst, a, b []float64) {
 		Div(dst, a, b)
 		return
 	}
+	_, _ = a[len(dst)-1], b[len(dst)-1] // the kernel reads len(dst) of each
 	divLASX(&dst[0], &a[0], &b[0], len(dst))
 }
 
diff --git a/internal/kernels/reduce_ppc64le.go b/internal/kernels/reduce_ppc64le.go
index c62df0c..9f18d70 100644
--- a/internal/kernels/reduce_ppc64le.go
+++ b/internal/kernels/reduce_ppc64le.go
@@ -26,6 +26,7 @@ func sqrtSIMD(dst, src []float64) {
 	if len(dst) == 0 {
 		return
 	}
+	_ = src[len(dst)-1] // the kernel reads len(dst) of src
 	sqrtVSX(&dst[0], &src[0], len(dst))
 }
 
@@ -38,24 +39,28 @@ func minSIMD(a []float64) float64 { return minUnrolled(a) }
 // kernels, each lane one IEEE operation, bit-identical to the scalar oracle.
 func addBin(dst, a, b []float64) {
 	if len(dst) > 0 {
+		_, _ = a[len(dst)-1], b[len(dst)-1] // the kernel reads len(dst) of each
 		addVSX(&dst[0], &a[0], &b[0], len(dst))
 	}
 }
 
 func subBin(dst, a, b []float64) {
 	if len(dst) > 0 {
+		_, _ = a[len(dst)-1], b[len(dst)-1] // the kernel reads len(dst) of each
 		subVSX(&dst[0], &a[0], &b[0], len(dst))
 	}
 }
 
 func mulBin(dst, a, b []float64) {
 	if len(dst) > 0 {
+		_, _ = a[len(dst)-1], b[len(dst)-1] // the kernel reads len(dst) of each
 		mulVSX(&dst[0], &a[0], &b[0], len(dst))
 	}
 }
 
 func divBin(dst, a, b []float64) {
 	if len(dst) > 0 {
+		_, _ = a[len(dst)-1], b[len(dst)-1] // the kernel reads len(dst) of each
 		divVSX(&dst[0], &a[0], &b[0], len(dst))
 	}
 }
diff --git a/linalg.go b/linalg.go
index c1137dd..10d5e67 100644
--- a/linalg.go
+++ b/linalg.go
@@ -40,6 +40,10 @@ func (a *Array) MatMul(b *Array) (*Array, error) {
 		return nil, fmt.Errorf("%w: MatMul %v x %v inner dims differ",
 			ErrLinalg, a.shape, b.shape)
 	}
+	// (m, 0) @ (0, n) holds no data, yet its m*n result can overflow.
+	if err := validateShape([]int{a.shape[0], b.shape[1]}); err != nil {
+		return nil, err
+	}
 	return matmul2D(a, b, a.shape[0], a.shape[1], b.shape[1]), nil
 }
 
diff --git a/manipulation.go b/manipulation.go
index 6eada76..cfd7639 100644
--- a/manipulation.go
+++ b/manipulation.go
@@ -102,9 +102,20 @@ func Concatenate(arrays []*Array, axis int) (*Array, error) {
 					ErrShapeMismatch, arr.shape, first.shape, d)
 			}
 		}
+		// Sum with an overflow guard: every length is at most maxSize, but
+		// enough of them would wrap axisTotal negative.
+		if arr.shape[ax] > maxSize-axisTotal {
+			return nil, fmt.Errorf("%w: concatenate along axis %d is too big",
+				ErrShapeMismatch, ax)
+		}
 		axisTotal += arr.shape[ax]
 	}
 	out[ax] = axisTotal
+	// Zero-size operands do not bound the result: (2^58, 0) stacked 9 times is
+	// (9, 2^58, 0), which numpy rejects as too big.
+	if err := validateShape(out); err != nil {
+		return nil, err
+	}
 	return concatInto(arrays, ax, out), nil
 }
 
@@ -116,6 +127,10 @@ func concatInto(arrays []*Array, ax int, out []int) *Array {
 	outer := prod(out[:ax])
 	axisTotal := out[ax]
 	data := wsOf(arrays...).alloc(outer*axisTotal*inner, false) // every slab is copied in
+	if len(data) == 0 {
+		// Nothing to copy, but outer alone can be 2^58: do not walk it.
+		return &Array{data: data, shape: out, strides: rowMajorStrides(out), ws: wsOf(arrays...)}
+	}
 	// Column offset (in the joined axis) where the next array's slab begins.
 	colBase := 0
 	for _, arr := range arrays {
diff --git a/ndarray.go b/ndarray.go
index 14ea223..f2423d5 100644
--- a/ndarray.go
+++ b/ndarray.go
@@ -873,7 +873,11 @@ func (a *Array) reduceAxis(
 	// zero copy; only strided views pay a materialise. The kernel only reads src.
 	src := a.contiguousData()
 	dst := a.alloc(outer*inner, true)
-	kernels.RunAxisP(kernel, dst, src, outer, axisLen, inner)
+	// An empty result, (2^58, 0) reduced over axis 0, would still walk the
+	// 2^58-long axis: skip the kernel, there is nothing to compute.
+	if len(dst) > 0 {
+		kernels.RunAxisP(kernel, dst, src, outer, axisLen, inner)
+	}
 	shape := a.reduceShape(axis, keepdims)
 	return &Array{data: dst, shape: shape, strides: rowMajorStrides(shape), ws: a.ws}, nil
 }
diff --git a/reductions.go b/reductions.go
index 826175c..1400a69 100644
--- a/reductions.go
+++ b/reductions.go
@@ -56,7 +56,11 @@ func (a *Array) scanAxis(
 	outer, axisLen, inner := a.reduceLayout(axis)
 	src := a.materialize()
 	dst := a.alloc(len(src), false)
-	kernel(dst, src, outer, axisLen, inner)
+	// An empty array can still have a huge axis, (0, 2^58), and the kernel
+	// walks outer*axisLen*inner: skip it rather than loop over nothing.
+	if len(dst) > 0 {
+		kernel(dst, src, outer, axisLen, inner)
+	}
 	shape := append([]int(nil), a.shape...)
 	return &Array{data: dst, shape: shape, strides: rowMajorStrides(shape), ws: a.ws}, nil
 }
diff --git a/result_shape_test.go b/result_shape_test.go
new file mode 100644
index 0000000..429ff96
--- /dev/null
+++ b/result_shape_test.go
@@ -0,0 +1,95 @@
+package ndarray
+
+import (
+	"errors"
+	"strconv"
+	"testing"
+	"time"
+)
+
+// hugeAxis is a quarter of the largest size: 2^58 on 64-bit, 2^26 on 32-bit.
+const hugeAxis = (maxSize + 1) / 4
+
+// A result whose shape cannot be represented is an error, as it is for New,
+// even when no operand holds any data: zero-size operands bound nothing.
+// Before, these wrapped: Concatenate produced a negative dimension, MatMul a
+// shape whose Size() was 0, and the rest panicked in makeslice.
+func TestResultShapeOverflow(t *testing.T) {
+	must := func(a *Array, err error) *Array {
+		t.Helper()
+		if err != nil {
+			t.Fatal(err)
+		}
+		return a
+	}
+	// Sizes derive from the word size, so the test compiles and means the
+	// same on 32-bit targets: big*big overflows maxSize, slab*4 exceeds it.
+	big := 1 << (strconv.IntSize / 2)
+	wide, tall := must(New(big, 0)), must(New(0, big))
+	slab := must(New(hugeAxis, 0))
+	many := func(n int) []*Array {
+		s := make([]*Array, n)
+		for i := range s {
+			s[i] = slab
+		}
+		return s
+	}
+	for name, f := range map[string]func() (*Array, error){
+		"MatMul (2^32,0)@(0,2^32)": func() (*Array, error) { return wide.MatMul(tall) },
+		"MatMul m*n wraps to -1":   func() (*Array, error) { return must(New(big+1, 0)).MatMul(must(New(0, big-1))) },
+		"Dot 2-D":                  func() (*Array, error) { return wide.Dot(tall) },
+		"Linspace 2^62":            func() (*Array, error) { return Linspace(0, 1, maxSize+1) },
+		"Concatenate sum wraps":    func() (*Array, error) { return Concatenate(many(33), 0) },
+		"Stack 9 of (2^58,0)":      func() (*Array, error) { return Stack(many(9), 0) },
+	} {
+		a, err := f()
+		if !errors.Is(err, ErrShapeMismatch) {
+			t.Errorf("%s: got %v, %v; want ErrShapeMismatch", name, a, err)
+		}
+	}
+	// Up to the limit (maxSize = 2^60-1 elements, as for New) is accepted:
+	// 3 x 2^58 fits, 4 x 2^58 = 2^60 does not.
+	if _, err := Concatenate(many(3), 0); err != nil {
+		t.Errorf("Concatenate 3 of (2^58,0): %v", err)
+	}
+	if _, err := Concatenate(many(4), 0); !errors.Is(err, ErrShapeMismatch) {
+		t.Errorf("Concatenate 4 of (2^58,0) = (2^60,0): got %v, want ErrShapeMismatch", err)
+	}
+}
+
+// An empty array can have a huge axis, (2^58, 0), and an operation that walks
+// that axis without doing anything still takes years. Concatenate, the axis
+// reductions and the scans did; each must now return at once.
+func TestEmptyArraysWithHugeAxesReturnPromptly(t *testing.T) {
+	const H = hugeAxis
+	for _, sh := range [][]int{{H, 0}, {0, H}, {H, 0, 3}, {3, H, 0}, {H, 1, 0}} {
+		a, err := New(sh...)
+		if err != nil {
+			t.Fatal(err)
+		}
+		ops := []func() (*Array, error){
+			func() (*Array, error) { return Concatenate([]*Array{a, a}, -1) },
+			func() (*Array, error) { return Concatenate([]*Array{a, a}, 0) },
+			func() (*Array, error) { return a.SumAxis(0, false) },
+			func() (*Array, error) { return a.MaxAxis(0, true) },
+			func() (*Array, error) { return a.MeanAxis(0, false) },
+			func() (*Array, error) { return a.ArgMaxAxis(0, false) },
+			func() (*Array, error) { return a.CumSum(0) },
+			func() (*Array, error) { return a.CumProd(-1) },
+		}
+		done := make(chan struct{})
+		go func() {
+			defer close(done)
+			for _, op := range ops {
+				if r, err := op(); err == nil && r.Size() != 0 {
+					t.Errorf("%v: a result with %d elements from an empty array", sh, r.Size())
+				}
+			}
+		}()
+		select {
+		case <-done:
+		case <-time.After(30 * time.Second):
+			t.Fatalf("%v: an operation on an empty array is walking its huge axis", sh)
+		}
+	}
+}