diff --git a/lumbda.py b/lumbda.py
index 8ed1fa0..77d5433 100644
--- a/lumbda.py
+++ b/lumbda.py
@@ -3438,7 +3438,11 @@ def make_global_env():
         return n
     d(S('/'), _div)
     d(S('quotient'),   lambda a, _: (lambda x, y: -(abs(int(x)) // abs(int(y))) if (x < 0) != (y < 0) else abs(int(x)) // abs(int(y)))(_num(a[0]), _num(a[1])))
-    d(S('remainder'),  lambda a, _: int(_num(a[0])) % int(_num(a[1])) * (1 if _num(a[0]) >= 0 else -1))
+    # R7RS: remainder has the sign of the dividend; uses truncated division.
+    # The previous impl did `signed_a % signed_b * sign(a)` which double-counted
+    # the sign of a (Python's % floors, so `-17 % 5 == 3`) and gave -3 for
+    # (-17, 5) instead of the correct -2. Use abs() on both sides, then re-sign.
+    d(S('remainder'),  lambda a, _: (abs(int(_num(a[0]))) % abs(int(_num(a[1])))) * (1 if _num(a[0]) >= 0 else -1))
     d(S('modulo'),     lambda a, _: int(_num(a[0])) % int(_num(a[1])))
     d(S('expt'),       lambda a, _: _num(a[0]) ** _num(a[1]))
     d(S('abs'),        lambda a, _: abs(_num(a[0])))
diff --git a/wasm/Makefile b/wasm/Makefile
index dba68ee..fac3c36 100644
--- a/wasm/Makefile
+++ b/wasm/Makefile
@@ -168,7 +168,7 @@ repl: build
 
 # ─── Tests ─────────────────────────────────────────────────────────
 
-test: test-unit test-integration test-functional-cross
+test: test-unit test-integration test-parity test-functional-cross
 
 test-unit: build
 	@echo "── wasm unit tests ──"
@@ -178,6 +178,15 @@ test-integration: build
 	@echo "── wasm integration tests (cross-tier diff) ──"
 	node tests/integration.mjs
 
+# Cross-tier parity probe — every expression in parity-corpus.mjs runs on
+# native python (reference), c-wasm, and asm-wasm. Fails on any unknown
+# divergence so a regression against whitepaper § normative claims gets
+# caught before merge. Known gaps (bignums on asm-wasm today) live in
+# KNOWN_DIVERGE; trim that list as the gaps close.
+test-parity: build
+	@echo "── wasm cross-tier parity probe ──"
+	node tests/parity-cross-tier.mjs
+
 # Cross-tier functional.lsp runner. C-wasm reaches full parity (205/205);
 # asm-wasm passes a documented growing subset and is exit-soft.
 test-functional-cross: build
diff --git a/wasm/asm/lumbda.wat b/wasm/asm/lumbda.wat
index e59093a..4da9349 100644
--- a/wasm/asm/lumbda.wat
+++ b/wasm/asm/lumbda.wat
@@ -2498,11 +2498,19 @@
           (then (local.set $sum (i32.sub (i32.const 0) (local.get $sum)))))
         (return (call $make_fixnum (local.get $sum)))))
 
-    ;; modulo
+    ;; modulo — R7RS: result has the sign of the divisor.
+    ;; i32.rem_s by itself gives remainder semantics (sign of dividend);
+    ;; we add the divisor if the rem and divisor disagree on sign.
     (if (i32.eq (local.get $id) (i32.const 23))
       (then
-        (return (call $make_fixnum (i32.rem_s (call $fixnum_val (local.get $a))
-                                                 (call $fixnum_val (local.get $b)))))))
+        (local.set $sum (i32.rem_s (call $fixnum_val (local.get $a))
+                                      (call $fixnum_val (local.get $b))))
+        (if (i32.and
+              (i32.ne (local.get $sum) (i32.const 0))
+              (i32.lt_s (i32.mul (local.get $sum) (call $fixnum_val (local.get $b)))
+                         (i32.const 0)))
+          (then (local.set $sum (i32.add (local.get $sum) (call $fixnum_val (local.get $b))))))
+        (return (call $make_fixnum (local.get $sum)))))
 
     ;; zero?
     (if (i32.eq (local.get $id) (i32.const 24))
diff --git a/wasm/dist-repl/asm/lumbda-asm.wasm b/wasm/dist-repl/asm/lumbda-asm.wasm
index 33def25..3a30eb5 100644
Binary files a/wasm/dist-repl/asm/lumbda-asm.wasm and b/wasm/dist-repl/asm/lumbda-asm.wasm differ
diff --git a/wasm/dist-repl/python/lumbda.py b/wasm/dist-repl/python/lumbda.py
index 8ed1fa0..77d5433 100644
--- a/wasm/dist-repl/python/lumbda.py
+++ b/wasm/dist-repl/python/lumbda.py
@@ -3438,7 +3438,11 @@ def make_global_env():
         return n
     d(S('/'), _div)
     d(S('quotient'),   lambda a, _: (lambda x, y: -(abs(int(x)) // abs(int(y))) if (x < 0) != (y < 0) else abs(int(x)) // abs(int(y)))(_num(a[0]), _num(a[1])))
-    d(S('remainder'),  lambda a, _: int(_num(a[0])) % int(_num(a[1])) * (1 if _num(a[0]) >= 0 else -1))
+    # R7RS: remainder has the sign of the dividend; uses truncated division.
+    # The previous impl did `signed_a % signed_b * sign(a)` which double-counted
+    # the sign of a (Python's % floors, so `-17 % 5 == 3`) and gave -3 for
+    # (-17, 5) instead of the correct -2. Use abs() on both sides, then re-sign.
+    d(S('remainder'),  lambda a, _: (abs(int(_num(a[0]))) % abs(int(_num(a[1])))) * (1 if _num(a[0]) >= 0 else -1))
     d(S('modulo'),     lambda a, _: int(_num(a[0])) % int(_num(a[1])))
     d(S('expt'),       lambda a, _: _num(a[0]) ** _num(a[1]))
     d(S('abs'),        lambda a, _: abs(_num(a[0])))
diff --git a/wasm/dist-repl/repl.css b/wasm/dist-repl/repl.css
index 8adf2e0..e476dac 100644
--- a/wasm/dist-repl/repl.css
+++ b/wasm/dist-repl/repl.css
@@ -1,11 +1,12 @@
 /* lumbda repl — grid-only layout. Inherits palette + base from style.css. */
 
 body.repl {
-  display: grid;
-  /* header (fixed)  scrolling-stream (everything else) */
-  grid-template-rows: auto 1fr;
-  height: 100vh;
-  overflow: hidden;
+  /* Body scrolls naturally. The prompt-bar is position: fixed so it
+   * stays glued to the viewport bottom; the transcript reserves bottom
+   * padding equal to the prompt-bar height so its last line isn't hidden
+   * underneath. */
+  min-height: 100vh;
+  overflow: auto;
 }
 
 /* ─── Lock screen overlay ──────────────────────────────────────── */
@@ -176,12 +177,13 @@ body.repl {
  * fresh sessions show the prompt up near the top and it drifts down
  * with each new entry. */
 .repl-stream {
-  overflow: auto;
-  padding: 0.5rem 1rem 0.8rem;
+  padding: 0.5rem 1rem 0;
   background: var(--code-bg);
   display: grid;
   grid-template-rows: auto auto auto;
   align-content: start;
+  /* Leave room for the fixed prompt bar at the viewport bottom. */
+  padding-bottom: calc(3.6rem + env(safe-area-inset-bottom, 0));
 }
 .transcript {
   font-family: var(--mono);
@@ -232,12 +234,16 @@ body.repl {
 /* ─── Prompt bar ───────────────────────────────────────────────── */
 
 .prompt-bar {
+  position: fixed;
+  left: 0; right: 0; bottom: 0;
+  z-index: 50;
   display: grid;
   grid-template-columns: auto 1fr auto auto;
   gap: 0.4rem;
   align-items: center;
-  padding: 0.3rem 0;
-  background: transparent;
+  padding: 0.5rem 1rem;
+  background: var(--code-bg);
+  border-top: 1px solid var(--rule);
 }
 .prompt-bar .prompt-sigil {
   color: var(--green);
diff --git a/wasm/dist-repl/repl.js b/wasm/dist-repl/repl.js
index 7062df8..7b2f8d5 100644
--- a/wasm/dist-repl/repl.js
+++ b/wasm/dist-repl/repl.js
@@ -287,7 +287,8 @@ function renderAll() {
         }
         transcriptEl.appendChild(block);
     }
-    replStream.scrollTop = replStream.scrollHeight;
+    // Body owns the scroll now; jump it to the latest entry.
+    window.scrollTo({ top: document.documentElement.scrollHeight, behavior: "instant" });
 }
 
 // ─── Input handling ─────────────────────────────────────────────────
diff --git a/wasm/repl/repl.css b/wasm/repl/repl.css
index 8adf2e0..e476dac 100644
--- a/wasm/repl/repl.css
+++ b/wasm/repl/repl.css
@@ -1,11 +1,12 @@
 /* lumbda repl — grid-only layout. Inherits palette + base from style.css. */
 
 body.repl {
-  display: grid;
-  /* header (fixed)  scrolling-stream (everything else) */
-  grid-template-rows: auto 1fr;
-  height: 100vh;
-  overflow: hidden;
+  /* Body scrolls naturally. The prompt-bar is position: fixed so it
+   * stays glued to the viewport bottom; the transcript reserves bottom
+   * padding equal to the prompt-bar height so its last line isn't hidden
+   * underneath. */
+  min-height: 100vh;
+  overflow: auto;
 }
 
 /* ─── Lock screen overlay ──────────────────────────────────────── */
@@ -176,12 +177,13 @@ body.repl {
  * fresh sessions show the prompt up near the top and it drifts down
  * with each new entry. */
 .repl-stream {
-  overflow: auto;
-  padding: 0.5rem 1rem 0.8rem;
+  padding: 0.5rem 1rem 0;
   background: var(--code-bg);
   display: grid;
   grid-template-rows: auto auto auto;
   align-content: start;
+  /* Leave room for the fixed prompt bar at the viewport bottom. */
+  padding-bottom: calc(3.6rem + env(safe-area-inset-bottom, 0));
 }
 .transcript {
   font-family: var(--mono);
@@ -232,12 +234,16 @@ body.repl {
 /* ─── Prompt bar ───────────────────────────────────────────────── */
 
 .prompt-bar {
+  position: fixed;
+  left: 0; right: 0; bottom: 0;
+  z-index: 50;
   display: grid;
   grid-template-columns: auto 1fr auto auto;
   gap: 0.4rem;
   align-items: center;
-  padding: 0.3rem 0;
-  background: transparent;
+  padding: 0.5rem 1rem;
+  background: var(--code-bg);
+  border-top: 1px solid var(--rule);
 }
 .prompt-bar .prompt-sigil {
   color: var(--green);
diff --git a/wasm/repl/repl.js b/wasm/repl/repl.js
index 7062df8..7b2f8d5 100644
--- a/wasm/repl/repl.js
+++ b/wasm/repl/repl.js
@@ -287,7 +287,8 @@ function renderAll() {
         }
         transcriptEl.appendChild(block);
     }
-    replStream.scrollTop = replStream.scrollHeight;
+    // Body owns the scroll now; jump it to the latest entry.
+    window.scrollTo({ top: document.documentElement.scrollHeight, behavior: "instant" });
 }
 
 // ─── Input handling ─────────────────────────────────────────────────
diff --git a/wasm/tests/parity-corpus.mjs b/wasm/tests/parity-corpus.mjs
new file mode 100644
index 0000000..18dd2f9
--- /dev/null
+++ b/wasm/tests/parity-corpus.mjs
@@ -0,0 +1,131 @@
+// wasm/tests/parity-corpus.mjs
+// The cross-tier parity corpus. Each entry is one expression; we expect
+// every tier to produce the same output. Entries are tagged with the
+// whitepaper section / R7RS concept they exercise so a regression can be
+// traced to the normative claim it violates.
+//
+// `expected` is set to the python tier's output (the reference, per
+// "Exact rational arithmetic uses Python's Fraction type"); we mark the
+// known-divergent ones with `knownDiverge: ["asm"]` so the suite remains
+// green while documenting the gap.
+
+export const CORPUS = [
+    // ─── numeric tower: rationals ────────────────────────────────────
+    { tag: "rat-div",     src: "(/ 67 7)",            expected: "67/7" },
+    { tag: "rat-div-one", src: "(/ 1 3)",             expected: "1/3" },
+    { tag: "rat-div-exact", src: "(/ 6 2)",           expected: "3" },
+    { tag: "rat-add",     src: "(+ 1/3 1/6)",         expected: "1/2" },
+    { tag: "rat-mul",     src: "(* 2/3 3/4)",         expected: "1/2" },
+    { tag: "rat-sub",     src: "(- 3/4 1/2)",         expected: "1/4" },
+    { tag: "rat-mixed-add", src: "(+ 1 1/2)",         expected: "3/2" },
+    { tag: "rat-eq-norm", src: "(= 1/2 2/4)",         expected: "#t" },
+    { tag: "rat-eq-int",  src: "(= 3 6/2)",           expected: "#t" },
+    { tag: "rat-lt",      src: "(< 1/3 1/2)",         expected: "#t" },
+    { tag: "number?-rat", src: "(number? 1/3)",       expected: "#t" },
+    { tag: "integer?-rat", src: "(integer? 1/3)",     expected: "#f" },
+    { tag: "integer?-int", src: "(integer? 6/2)",     expected: "#t" },
+
+    // ─── numeric tower: bignums (whitepaper §2.1 claim) ──────────────
+    { tag: "expt-2-100", src: "(expt 2 100)",
+      expected: "1267650600228229401496703205376" },
+    { tag: "expt-3-50",  src: "(expt 3 50)",
+      expected: "717897987691852588770249" },
+    { tag: "big-arith", src: "(* 12345678901234567890 12345678901234567890)",
+      expected: "152415787532388367501905199875019052100" },
+
+    // ─── division semantics ──────────────────────────────────────────
+    { tag: "quotient-pos",  src: "(quotient 17 5)",        expected: "3" },
+    { tag: "quotient-neg",  src: "(quotient -17 5)",       expected: "-3" },
+    { tag: "remainder-pos", src: "(remainder 17 5)",       expected: "2" },
+    { tag: "remainder-neg", src: "(remainder -17 5)",      expected: "-2" },
+    { tag: "modulo-pos",    src: "(modulo 17 5)",          expected: "2" },
+    { tag: "modulo-neg",    src: "(modulo -17 5)",         expected: "3" },
+
+    // ─── arithmetic edge cases ───────────────────────────────────────
+    { tag: "neg-arith",  src: "(- 5)",                  expected: "-5" },
+    { tag: "empty-add",  src: "(+)",                    expected: "0" },
+    { tag: "empty-mul",  src: "(*)",                    expected: "1" },
+    { tag: "multi-arith", src: "(+ 1 2 3 4 5)",         expected: "15" },
+    { tag: "abs-pos",    src: "(abs 5)",                expected: "5" },
+    { tag: "abs-neg",    src: "(abs -5)",               expected: "5" },
+    { tag: "min",        src: "(min 5 3 8 1 7)",        expected: "1" },
+    { tag: "max",        src: "(max 5 3 8 1 7)",        expected: "8" },
+
+    // ─── booleans / truthiness ───────────────────────────────────────
+    { tag: "if-true",    src: "(if #t 'yes 'no)",       expected: "yes" },
+    { tag: "if-false",   src: "(if #f 'yes 'no)",       expected: "no" },
+    { tag: "if-zero",    src: "(if 0 'truthy 'falsy)",  expected: "truthy" },
+    { tag: "if-nil",     src: "(if '() 'truthy 'falsy)", expected: "truthy" },
+    { tag: "if-empty-str", src: "(if \"\" 'truthy 'falsy)", expected: "truthy" },
+    { tag: "not-#f",     src: "(not #f)",               expected: "#t" },
+    { tag: "not-#t",     src: "(not #t)",               expected: "#f" },
+    { tag: "not-zero",   src: "(not 0)",                expected: "#f" },
+
+    // ─── equality ────────────────────────────────────────────────────
+    { tag: "eq?-int",    src: "(eq? 1 1)",              expected: "#t" },
+    { tag: "eq?-symbol", src: "(eq? 'a 'a)",            expected: "#t" },
+    { tag: "equal?-list", src: "(equal? '(1 2 3) '(1 2 3))", expected: "#t" },
+    { tag: "equal?-str", src: "(equal? \"abc\" \"abc\")", expected: "#t" },
+
+    // ─── pairs / lists ───────────────────────────────────────────────
+    { tag: "cons",       src: "(cons 1 2)",             expected: "(1 . 2)" },
+    { tag: "list",       src: "(list 1 2 3)",           expected: "(1 2 3)" },
+    { tag: "length",     src: "(length '(a b c d))",    expected: "4" },
+    { tag: "reverse",    src: "(reverse '(1 2 3))",     expected: "(3 2 1)" },
+    { tag: "append",     src: "(append '(1 2) '(3 4))", expected: "(1 2 3 4)" },
+    { tag: "map",        src: "(map (lambda (x) (* x x)) '(1 2 3 4))",
+      expected: "(1 4 9 16)" },
+    { tag: "filter-odd", src: "(filter odd? '(1 2 3 4 5))",
+      expected: "(1 3 5)" },
+    { tag: "fold-left",  src: "(fold-left + 0 '(1 2 3 4 5))", expected: "15" },
+
+    // ─── strings ─────────────────────────────────────────────────────
+    { tag: "str-len",    src: "(string-length \"hello\")", expected: "5" },
+    { tag: "str-append", src: "(string-append \"foo\" \"bar\")",
+      expected: "foobar" },
+    { tag: "substring",  src: "(substring \"hello world\" 6 11)",
+      expected: "world" },
+    { tag: "str-upcase", src: "(string-upcase \"hello\")", expected: "HELLO" },
+    { tag: "str-num",    src: "(string->number \"42\")", expected: "42" },
+    { tag: "num-str",    src: "(number->string 42)",     expected: "42" },
+
+    // ─── characters ──────────────────────────────────────────────────
+    { tag: "char-int",   src: "(char->integer #\\A)",    expected: "65" },
+    { tag: "int-char",   src: "(integer->char 65)",      expected: "A" },
+    { tag: "char-alpha", src: "(char-alphabetic? #\\a)", expected: "#t" },
+
+    // ─── vectors ─────────────────────────────────────────────────────
+    { tag: "vec-make",   src: "(vector 1 2 3)",         expected: "#(1 2 3)" },
+    { tag: "vec-len",    src: "(vector-length (vector 1 2 3))", expected: "3" },
+    { tag: "vec-ref",    src: "(vector-ref (vector 10 20 30) 1)", expected: "20" },
+
+    // ─── special forms ──────────────────────────────────────────────
+    { tag: "let-basic",  src: "(let ((x 3) (y 4)) (+ x x y))", expected: "10" },
+    { tag: "let*-shadow", src: "(let* ((x 1) (x (+ x 10)) (x (* x 2))) x)",
+      expected: "22" },
+    { tag: "letrec",     src: "(letrec ((f (lambda (n) (if (= n 0) 1 (* n (f (- n 1))))))) (f 5))",
+      expected: "120" },
+    { tag: "named-let",  src: "(let loop ((i 0) (acc 0)) (if (= i 10) acc (loop (+ i 1) (+ acc i))))",
+      expected: "45" },
+    { tag: "cond-else",  src: "(cond ((= 1 2) 'no) (else 'yes))", expected: "yes" },
+    { tag: "case-match", src: "(case 2 ((1) 'one) ((2 3) 'two-three) (else 'big))",
+      expected: "two-three" },
+    { tag: "when",       src: "(when (> 3 1) 'yes)",     expected: "yes" },
+    { tag: "and-pass",   src: "(and 1 2 3)",             expected: "3" },
+    { tag: "or-first",   src: "(or #f 7 8)",             expected: "7" },
+
+    // ─── deep recursion / TCO ───────────────────────────────────────
+    { tag: "tco-loop",   src: "(let loop ((i 0)) (if (= i 50000) i (loop (+ i 1))))",
+      expected: "50000" },
+    { tag: "mutual-tco", src: "(define (a n) (if (= n 0) 'done-a (b (- n 1)))) (define (b n) (if (= n 0) 'done-b (a (- n 1)))) (a 100000)",
+      expected: "done-a" },
+];
+
+// Tiers where each tag is known to diverge today. Keep this short and
+// remove entries as the gaps close — that's how we track "% to parity".
+export const KNOWN_DIVERGE = {
+    // Asm-WASM has 31-bit fixnum num/den rationals; no bignums yet.
+    "expt-2-100":   ["asm"],
+    "expt-3-50":    ["asm"],
+    "big-arith":    ["asm"],
+};
diff --git a/wasm/tests/parity-cross-tier.mjs b/wasm/tests/parity-cross-tier.mjs
new file mode 100644
index 0000000..5210118
--- /dev/null
+++ b/wasm/tests/parity-cross-tier.mjs
@@ -0,0 +1,134 @@
+// wasm/tests/parity-cross-tier.mjs
+// For every CORPUS entry, run the source on every tier (native python,
+// c-wasm, asm-wasm) and report mismatches against the expected output.
+// Known divergences (KNOWN_DIVERGE) are tolerated but printed in yellow
+// so the gap is visible without breaking the build.
+//
+// Python tier runs via the host's python3 lumbda.py because the Pyodide
+// loader needs a browser context. That keeps this test fast (no 10MB
+// CDN download) while still pinning behavior to the reference tier.
+
+import fs from "node:fs";
+import path from "node:path";
+import { execFileSync } from "node:child_process";
+import { fileURLToPath } from "node:url";
+import { CORPUS, KNOWN_DIVERGE } from "./parity-corpus.mjs";
+
+const here = path.dirname(fileURLToPath(import.meta.url));
+const dist = path.resolve(here, "..", "dist");
+const repoRoot = path.resolve(here, "..", "..");
+
+const state = { ok: 0, fail: 0, knownDiverge: 0, failures: [] };
+
+function check(tag, tier, expected, got, isKnown) {
+    const passed = got === expected;
+    if (passed) state.ok++;
+    else if (isKnown) state.knownDiverge++;
+    else { state.fail++; state.failures.push({ tag, tier, expected, got }); }
+    const status = passed
+        ? "✓"
+        : isKnown
+            ? "~"   // known divergence
+            : "✗";
+    const label = `${status} ${tier.padEnd(6)} ${tag}`;
+    if (!passed) {
+        const detail = `expected ${JSON.stringify(expected)} · got ${JSON.stringify(got)}`;
+        console.log(`  ${label} — ${detail}`);
+    }
+}
+
+// Wrap each test source so the result is printed via display (uniform
+// across tiers — no write quoting, no "is this the last expression"
+// behavior to depend on). The source may contain multiple top-level
+// forms (e.g. defines), so we put the final expression in a (begin ...)
+// and display its result.
+function wrap(src) {
+    // The source's last sub-expression is what we want to display.
+    // We rely on the tiers each evaluating the lot and `(display ...)`
+    // emitting display semantics on the value.
+    return `(display (begin ${src})) (newline)`;
+}
+
+// ─── tier adapters ─────────────────────────────────────────────────
+function nativePython(src) {
+    const tmp = `/tmp/parity-${process.pid}.lsp`;
+    fs.writeFileSync(tmp, wrap(src) + "\n");
+    try {
+        return execFileSync("python3", [path.join(repoRoot, "lumbda.py"), tmp], {
+            encoding: "utf8", timeout: 30000,
+        }).trim();
+    } finally { try { fs.unlinkSync(tmp); } catch {} }
+}
+
+async function withAsmTier() {
+    const wasmBytes = fs.readFileSync(path.join(dist, "asm", "lumbda-asm.wasm"));
+    const importObj = { env: { bend_call() { return 0; } } };
+    const { instance } = await WebAssembly.instantiate(wasmBytes, importObj);
+    const exp = instance.exports;
+    exp.lumbda_init();
+    return (src) => {
+        const bytes = new TextEncoder().encode(wrap(src));
+        new Uint8Array(exp.memory.buffer).set(bytes, exp.lumbda_source_ptr());
+        try { exp.lumbda_eval(bytes.length); }
+        catch (e) { return `THREW: ${e.message}`; }
+        return new TextDecoder().decode(
+            new Uint8Array(exp.memory.buffer, exp.lumbda_output_ptr(), exp.lumbda_output_len())
+        ).trim();
+    };
+}
+
+async function withCTier() {
+    const factoryURL = "file://" + path.join(dist, "c", "lumbda-c.js");
+    const createLumbdaC = (await import(factoryURL)).default;
+    let out = [];
+    const m = await createLumbdaC({
+        locateFile: (p) => path.join(dist, "c", p),
+        print: (line) => out.push(line),
+        printErr: () => {},
+    });
+    m.cwrap("lumbda_wasm_init", null, [])();
+    const _eval = m.cwrap("lumbda_wasm_eval", "number", ["string"]);
+    const _free = m.cwrap("lumbda_wasm_free_result", null, ["number"]);
+    return (src) => {
+        out = [];
+        const r = _eval(wrap(src));
+        if (r) { const msg = m.UTF8ToString(r); _free(r); return msg; }
+        return out.join("\n").trim();
+    };
+}
+
+(async () => {
+    console.log("─".repeat(70));
+    console.log("Cross-tier parity probe — python (ref) vs c-wasm vs asm-wasm");
+    console.log("─".repeat(70));
+
+    const runAsm = await withAsmTier();
+    const runC = await withCTier();
+
+    for (const entry of CORPUS) {
+        const knownOn = KNOWN_DIVERGE[entry.tag] || [];
+        const isAsmKnown = knownOn.includes("asm");
+        const isCKnown   = knownOn.includes("c");
+        const isPyKnown  = knownOn.includes("python");
+
+        const py  = nativePython(entry.src);
+        const cw  = runC(entry.src);
+        const aw  = runAsm(entry.src);
+
+        check(entry.tag, "py-ref", entry.expected, py,  isPyKnown);
+        check(entry.tag, "c-wasm", entry.expected, cw,  isCKnown);
+        check(entry.tag, "asm",    entry.expected, aw,  isAsmKnown);
+    }
+
+    console.log("─".repeat(70));
+    console.log(`  passing      : ${state.ok}`);
+    console.log(`  known diverge: ${state.knownDiverge}  (tracked in KNOWN_DIVERGE)`);
+    console.log(`  fail         : ${state.fail}`);
+    if (state.fail > 0) {
+        console.log("\nUnknown divergences (fix or add to KNOWN_DIVERGE):");
+        for (const f of state.failures) {
+            console.log(`  ${f.tier} ${f.tag}: expected ${JSON.stringify(f.expected)} got ${JSON.stringify(f.got)}`);
+        }
+    }
+    process.exit(state.fail ? 1 : 0);
+})();
diff --git a/www/playground/asm/lumbda-asm.wasm b/www/playground/asm/lumbda-asm.wasm
index 33def25..3a30eb5 100644
Binary files a/www/playground/asm/lumbda-asm.wasm and b/www/playground/asm/lumbda-asm.wasm differ
diff --git a/www/playground/python/lumbda.py b/www/playground/python/lumbda.py
index 8ed1fa0..77d5433 100644
--- a/www/playground/python/lumbda.py
+++ b/www/playground/python/lumbda.py
@@ -3438,7 +3438,11 @@ def make_global_env():
         return n
     d(S('/'), _div)
     d(S('quotient'),   lambda a, _: (lambda x, y: -(abs(int(x)) // abs(int(y))) if (x < 0) != (y < 0) else abs(int(x)) // abs(int(y)))(_num(a[0]), _num(a[1])))
-    d(S('remainder'),  lambda a, _: int(_num(a[0])) % int(_num(a[1])) * (1 if _num(a[0]) >= 0 else -1))
+    # R7RS: remainder has the sign of the dividend; uses truncated division.
+    # The previous impl did `signed_a % signed_b * sign(a)` which double-counted
+    # the sign of a (Python's % floors, so `-17 % 5 == 3`) and gave -3 for
+    # (-17, 5) instead of the correct -2. Use abs() on both sides, then re-sign.
+    d(S('remainder'),  lambda a, _: (abs(int(_num(a[0]))) % abs(int(_num(a[1])))) * (1 if _num(a[0]) >= 0 else -1))
     d(S('modulo'),     lambda a, _: int(_num(a[0])) % int(_num(a[1])))
     d(S('expt'),       lambda a, _: _num(a[0]) ** _num(a[1]))
     d(S('abs'),        lambda a, _: abs(_num(a[0])))
diff --git a/www/repl/asm/lumbda-asm.wasm b/www/repl/asm/lumbda-asm.wasm
index 33def25..3a30eb5 100644
Binary files a/www/repl/asm/lumbda-asm.wasm and b/www/repl/asm/lumbda-asm.wasm differ
diff --git a/www/repl/python/lumbda.py b/www/repl/python/lumbda.py
index 8ed1fa0..77d5433 100644
--- a/www/repl/python/lumbda.py
+++ b/www/repl/python/lumbda.py
@@ -3438,7 +3438,11 @@ def make_global_env():
         return n
     d(S('/'), _div)
     d(S('quotient'),   lambda a, _: (lambda x, y: -(abs(int(x)) // abs(int(y))) if (x < 0) != (y < 0) else abs(int(x)) // abs(int(y)))(_num(a[0]), _num(a[1])))
-    d(S('remainder'),  lambda a, _: int(_num(a[0])) % int(_num(a[1])) * (1 if _num(a[0]) >= 0 else -1))
+    # R7RS: remainder has the sign of the dividend; uses truncated division.
+    # The previous impl did `signed_a % signed_b * sign(a)` which double-counted
+    # the sign of a (Python's % floors, so `-17 % 5 == 3`) and gave -3 for
+    # (-17, 5) instead of the correct -2. Use abs() on both sides, then re-sign.
+    d(S('remainder'),  lambda a, _: (abs(int(_num(a[0]))) % abs(int(_num(a[1])))) * (1 if _num(a[0]) >= 0 else -1))
     d(S('modulo'),     lambda a, _: int(_num(a[0])) % int(_num(a[1])))
     d(S('expt'),       lambda a, _: _num(a[0]) ** _num(a[1]))
     d(S('abs'),        lambda a, _: abs(_num(a[0])))
diff --git a/www/repl/repl.css b/www/repl/repl.css
index 8adf2e0..e476dac 100644
--- a/www/repl/repl.css
+++ b/www/repl/repl.css
@@ -1,11 +1,12 @@
 /* lumbda repl — grid-only layout. Inherits palette + base from style.css. */
 
 body.repl {
-  display: grid;
-  /* header (fixed)  scrolling-stream (everything else) */
-  grid-template-rows: auto 1fr;
-  height: 100vh;
-  overflow: hidden;
+  /* Body scrolls naturally. The prompt-bar is position: fixed so it
+   * stays glued to the viewport bottom; the transcript reserves bottom
+   * padding equal to the prompt-bar height so its last line isn't hidden
+   * underneath. */
+  min-height: 100vh;
+  overflow: auto;
 }
 
 /* ─── Lock screen overlay ──────────────────────────────────────── */
@@ -176,12 +177,13 @@ body.repl {
  * fresh sessions show the prompt up near the top and it drifts down
  * with each new entry. */
 .repl-stream {
-  overflow: auto;
-  padding: 0.5rem 1rem 0.8rem;
+  padding: 0.5rem 1rem 0;
   background: var(--code-bg);
   display: grid;
   grid-template-rows: auto auto auto;
   align-content: start;
+  /* Leave room for the fixed prompt bar at the viewport bottom. */
+  padding-bottom: calc(3.6rem + env(safe-area-inset-bottom, 0));
 }
 .transcript {
   font-family: var(--mono);
@@ -232,12 +234,16 @@ body.repl {
 /* ─── Prompt bar ───────────────────────────────────────────────── */
 
 .prompt-bar {
+  position: fixed;
+  left: 0; right: 0; bottom: 0;
+  z-index: 50;
   display: grid;
   grid-template-columns: auto 1fr auto auto;
   gap: 0.4rem;
   align-items: center;
-  padding: 0.3rem 0;
-  background: transparent;
+  padding: 0.5rem 1rem;
+  background: var(--code-bg);
+  border-top: 1px solid var(--rule);
 }
 .prompt-bar .prompt-sigil {
   color: var(--green);
diff --git a/www/repl/repl.js b/www/repl/repl.js
index 7062df8..7b2f8d5 100644
--- a/www/repl/repl.js
+++ b/www/repl/repl.js
@@ -287,7 +287,8 @@ function renderAll() {
         }
         transcriptEl.appendChild(block);
     }
-    replStream.scrollTop = replStream.scrollHeight;
+    // Body owns the scroll now; jump it to the latest entry.
+    window.scrollTo({ top: document.documentElement.scrollHeight, behavior: "instant" });
 }
 
 // ─── Input handling ─────────────────────────────────────────────────