diff --git a/README.md b/README.md
index 21c14b1..3b0fb2e 100644
--- a/README.md
+++ b/README.md
@@ -13,8 +13,18 @@ text, err := extract.Text(doc, 1)     // the page as words, lines put back toget
 runs, err := extract.Runs(doc, 1)     // every piece, with its place and its size
 imgs, err := extract.Images(doc, 1)   // every picture, and where it lands
 tabs, err := extract.Tables(doc, 1)   // the grids its text lines up into
+
+lines := extract.Lines(runs)          // the runs gathered into their lines
+s     := extract.Join(lines[0])       // one line's pieces, spaced as words
 ```
 
+`Lines` and `Join` are exported because the rule has to be the **same** rule:
+`Text` uses them to put a page's text back together, and anything reading
+structure out of a page — where a paragraph ends, which line is a heading, as
+[`document`](https://github.com/go-pdfkit/document) does — has to agree with it
+line for line, or the two disagree about what the page says. A test asserts
+that agreement rather than trusting it.
+
 Pure Go, no C. It builds for `GOOS=js/wasm` and every architecture the fleet
 targets.
 
diff --git a/extract.go b/extract.go
index 64951f1..6103f66 100644
--- a/extract.go
+++ b/extract.go
@@ -174,3 +174,19 @@ func wantsSpace(prev, next Run, gap float64) bool {
 	}
 	return gap > space*0.3
 }
+
+// Lines gathers runs into the lines they were drawn on, down the page and then
+// left to right within each line. A line is allowed to wobble by a fraction of
+// its own height, which is what a superscript does.
+//
+// It is exported because the rule has to be the SAME rule: [Assemble] uses it
+// to put a page's text back together, and anything that reads structure out of
+// a page — where a paragraph ends, which line is a heading — has to agree with
+// it line for line or the two disagree about what the page says.
+func Lines(runs []Run) [][]Run { return groupIntoLines(runs) }
+
+// Join puts one line's pieces back together, with a space wherever the gap
+// between two of them is wide enough to be one and nothing where it is only
+// kerning. It is [Assemble] for a single line, and exported for the same
+// reason [Lines] is.
+func Join(line []Run) string { return joinLine(line) }
diff --git a/tables_test.go b/tables_test.go
index 5e40813..2cc7369 100644
--- a/tables_test.go
+++ b/tables_test.go
@@ -563,3 +563,36 @@ func type3Page(t *testing.T, size int, content string) *reader.Document {
 		})
 	})
 }
+
+// ⛔ Lines and Join are exported so that the rule is the SAME rule. The
+// control is that they agree with Assemble, which is what the rest of the
+// fleet already reads a page with: if the two could disagree, a caller reading
+// structure out of a page would be reading a different page from the one
+// Text reports.
+func TestLinesAndJoinAgreeWithAssemble(t *testing.T) {
+	d := pageWith(t, strings.Join([]string{
+		"BT /F1 10 Tf 20 150 Td (Name) Tj 40 0 Td (Age) Tj ET",
+		"BT /F1 10 Tf 20 130 Td (Ada) Tj 40 0 Td (36) Tj ET",
+		"BT /F1 10 Tf 20 110 Td (one two) Tj ET",
+	}, "\n"), nil)
+	runs, err := Runs(d, 1)
+	if err != nil {
+		t.Fatal(err)
+	}
+	lines := Lines(runs)
+	if len(lines) != 3 {
+		t.Fatalf("%d lines, want 3", len(lines))
+	}
+	var joined []string
+	for _, line := range lines {
+		joined = append(joined, Join(line))
+	}
+	if got, want := strings.Join(joined, "\n"), Assemble(runs); got != want {
+		t.Errorf("Lines+Join read\n%q\nAssemble read\n%q", got, want)
+	}
+	// And the pieces are in reading order, which is what a caller walking
+	// them depends on.
+	if Join(lines[0]) != "Name Age" {
+		t.Errorf("the first line reads %q", Join(lines[0]))
+	}
+}