diff --git a/lib/lua/runtime.sx b/lib/lua/runtime.sx
index cf711f0f..3089a8be 100644
--- a/lib/lua/runtime.sx
+++ b/lib/lua/runtime.sx
@@ -1425,6 +1425,35 @@
 (dict-set! math "min" lua-math-min)
 (dict-set! math "max" lua-math-max)
 (dict-set! math "fmod" lua-math-fmod)
+(dict-set! math "mod" lua-math-fmod)
+(define
+  lua-math-frexp
+  (fn (x)
+    (cond
+      ((= x 0) (list (quote lua-multi) 0 0))
+      (else
+        (let ((sign (if (< x 0) -1 1)) (ax (abs x)) (e 0))
+          (begin
+            (define
+              fr-up
+              (fn ()
+                (when (>= ax 1)
+                  (begin (set! ax (/ ax 2)) (set! e (+ e 1)) (fr-up)))))
+            (define
+              fr-dn
+              (fn ()
+                (when (< ax 0.5)
+                  (begin (set! ax (* ax 2)) (set! e (- e 1)) (fr-dn)))))
+            (fr-up)
+            (fr-dn)
+            (list (quote lua-multi) (* sign ax) e)))))))
+
+(define
+  lua-math-ldexp
+  (fn (m e) (* m (pow 2 e))))
+
+(dict-set! math "frexp" lua-math-frexp)
+(dict-set! math "ldexp" lua-math-ldexp)
 (dict-set! math "modf" lua-math-modf)
 (dict-set! math "random" lua-math-random)
 (dict-set! math "randomseed" lua-math-randomseed)
diff --git a/lib/lua/scoreboard.json b/lib/lua/scoreboard.json
index 1a4fbd86..7a854ad1 100644
--- a/lib/lua/scoreboard.json
+++ b/lib/lua/scoreboard.json
@@ -1,8 +1,8 @@
 {
   "totals": {
     "pass": 1,
-    "fail": 9,
-    "timeout": 6,
+    "fail": 12,
+    "timeout": 3,
     "skip": 8,
     "total": 24,
     "runnable": 16,
@@ -10,12 +10,12 @@
   },
   "top_failure_modes": [
     [
-      "timeout",
-      6
+      "other: Unhandled exception: \\\"Unhandled exception: \\\\\\\"assertion failed!\\\\\\\"\\",
+      7
     ],
     [
-      "other: Unhandled exception: \\\"Unhandled exception: \\\\\\\"assertion failed!\\\\\\\"\\",
-      5
+      "timeout",
+      3
     ],
     [
       "other: Unhandled exception: \\\"Unhandled exception: \\\\\\\"lua: attempt to call non-functio",
@@ -28,6 +28,10 @@
     [
       "undefined symbol: fat\\",
       1
+    ],
+    [
+      "other: Unhandled exception: \\\"Unhandled exception: \\\\\\\"lua: attempt to compare incompat",
+      1
     ]
   ],
   "results": [
@@ -47,7 +51,7 @@
       "name": "attrib.lua",
       "status": "fail",
       "reason": "other: Unhandled exception: \\\"Unhandled exception: \\\\\\\"lua: module 'C' not found\\\\\\\"\\",
-      "ms": 6985
+      "ms": 6723
     },
     {
       "name": "big.lua",
@@ -59,7 +63,7 @@
       "name": "calls.lua",
       "status": "fail",
       "reason": "undefined symbol: fat\\",
-      "ms": 5721
+      "ms": 5181
     },
     {
       "name": "checktable.lua",
@@ -71,7 +75,7 @@
       "name": "closure.lua",
       "status": "timeout",
       "reason": "per-test timeout",
-      "ms": 8008
+      "ms": 8004
     },
     {
       "name": "code.lua",
@@ -81,9 +85,9 @@
     },
     {
       "name": "constructs.lua",
-      "status": "timeout",
-      "reason": "per-test timeout",
-      "ms": 8007
+      "status": "fail",
+      "reason": "other: Unhandled exception: \\\"Unhandled exception: \\\\\\\"lua: attempt to compare incompat",
+      "ms": 7350
     },
     {
       "name": "db.lua",
@@ -95,13 +99,13 @@
       "name": "errors.lua",
       "status": "fail",
       "reason": "other: Unhandled exception: \\\"Unhandled exception: \\\\\\\"assertion failed!\\\\\\\"\\",
-      "ms": 4667
+      "ms": 3439
     },
     {
       "name": "events.lua",
-      "status": "timeout",
-      "reason": "per-test timeout",
-      "ms": 8007
+      "status": "fail",
+      "reason": "other: Unhandled exception: \\\"Unhandled exception: \\\\\\\"assertion failed!\\\\\\\"\\",
+      "ms": 7915
     },
     {
       "name": "files.lua",
@@ -119,13 +123,13 @@
       "name": "literals.lua",
       "status": "fail",
       "reason": "other: Unhandled exception: \\\"Unhandled exception: \\\\\\\"assertion failed!\\\\\\\"\\",
-      "ms": 2950
+      "ms": 2141
     },
     {
       "name": "locals.lua",
       "status": "fail",
       "reason": "other: Unhandled exception: \\\"Unhandled exception: \\\\\\\"lua: attempt to call non-functio",
-      "ms": 2366
+      "ms": 1799
     },
     {
       "name": "main.lua",
@@ -137,19 +141,19 @@
       "name": "math.lua",
       "status": "fail",
       "reason": "other: Unhandled exception: \\\"Unhandled exception: \\\\\\\"lua: attempt to call non-functio",
-      "ms": 4991
+      "ms": 4738
     },
     {
       "name": "nextvar.lua",
-      "status": "timeout",
-      "reason": "per-test timeout",
-      "ms": 8007
+      "status": "fail",
+      "reason": "other: Unhandled exception: \\\"Unhandled exception: \\\\\\\"assertion failed!\\\\\\\"\\",
+      "ms": 7818
     },
     {
       "name": "pm.lua",
       "status": "fail",
       "reason": "other: Unhandled exception: \\\"Unhandled exception: \\\\\\\"assertion failed!\\\\\\\"\\",
-      "ms": 6697
+      "ms": 6478
     },
     {
       "name": "sort.lua",
@@ -161,19 +165,19 @@
       "name": "strings.lua",
       "status": "fail",
       "reason": "other: Unhandled exception: \\\"Unhandled exception: \\\\\\\"assertion failed!\\\\\\\"\\",
-      "ms": 4493
+      "ms": 4339
     },
     {
       "name": "vararg.lua",
       "status": "fail",
       "reason": "other: Unhandled exception: \\\"Unhandled exception: \\\\\\\"assertion failed!\\\\\\\"\\",
-      "ms": 2541
+      "ms": 2343
     },
     {
       "name": "verybig.lua",
       "status": "pass",
       "reason": "",
-      "ms": 1187
+      "ms": 1064
     }
   ]
 }
\ No newline at end of file
diff --git a/lib/lua/scoreboard.md b/lib/lua/scoreboard.md
index a1db5ec8..979c973e 100644
--- a/lib/lua/scoreboard.md
+++ b/lib/lua/scoreboard.md
@@ -1,15 +1,16 @@
 # Lua-on-SX conformance scoreboard
 
 **Pass rate:** 1/16 runnable (6.2%)
-fail=9 timeout=6 skip=8 total=24
+fail=12 timeout=3 skip=8 total=24
 
 ## Top failure modes
 
-- **6x** timeout
-- **5x** other: Unhandled exception: \"Unhandled exception: \\\"assertion failed!\\\"\
+- **7x** other: Unhandled exception: \"Unhandled exception: \\\"assertion failed!\\\"\
+- **3x** timeout
 - **2x** other: Unhandled exception: \"Unhandled exception: \\\"lua: attempt to call non-functio
 - **1x** other: Unhandled exception: \"Unhandled exception: \\\"lua: module 'C' not found\\\"\
 - **1x** undefined symbol: fat\
+- **1x** other: Unhandled exception: \"Unhandled exception: \\\"lua: attempt to compare incompat
 
 ## Per-test results
 
@@ -17,25 +18,25 @@ fail=9 timeout=6 skip=8 total=24
 |---|---|---|---:|
 | all.lua | skip | driver uses dofile to chain other tests | 0 |
 | api.lua | skip | requires testC (C debug library) | 0 |
-| attrib.lua | fail | other: Unhandled exception: \"Unhandled exception: \\\"lua: module 'C' not found\\\"\ | 6985 |
+| attrib.lua | fail | other: Unhandled exception: \"Unhandled exception: \\\"lua: module 'C' not found\\\"\ | 6723 |
 | big.lua | timeout | per-test timeout | 8008 |
-| calls.lua | fail | undefined symbol: fat\ | 5721 |
+| calls.lua | fail | undefined symbol: fat\ | 5181 |
 | checktable.lua | skip | internal debug helpers | 0 |
-| closure.lua | timeout | per-test timeout | 8008 |
+| closure.lua | timeout | per-test timeout | 8004 |
 | code.lua | skip | bytecode inspection via debug library | 0 |
-| constructs.lua | timeout | per-test timeout | 8007 |
+| constructs.lua | fail | other: Unhandled exception: \"Unhandled exception: \\\"lua: attempt to compare incompat | 7350 |
 | db.lua | skip | debug library | 0 |
-| errors.lua | fail | other: Unhandled exception: \"Unhandled exception: \\\"assertion failed!\\\"\ | 4667 |
-| events.lua | timeout | per-test timeout | 8007 |
+| errors.lua | fail | other: Unhandled exception: \"Unhandled exception: \\\"assertion failed!\\\"\ | 3439 |
+| events.lua | fail | other: Unhandled exception: \"Unhandled exception: \\\"assertion failed!\\\"\ | 7915 |
 | files.lua | skip | io library | 0 |
 | gc.lua | skip | collectgarbage / finalisers | 0 |
-| literals.lua | fail | other: Unhandled exception: \"Unhandled exception: \\\"assertion failed!\\\"\ | 2950 |
-| locals.lua | fail | other: Unhandled exception: \"Unhandled exception: \\\"lua: attempt to call non-functio | 2366 |
+| literals.lua | fail | other: Unhandled exception: \"Unhandled exception: \\\"assertion failed!\\\"\ | 2141 |
+| locals.lua | fail | other: Unhandled exception: \"Unhandled exception: \\\"lua: attempt to call non-functio | 1799 |
 | main.lua | skip | standalone interpreter driver | 0 |
-| math.lua | fail | other: Unhandled exception: \"Unhandled exception: \\\"lua: attempt to call non-functio | 4991 |
-| nextvar.lua | timeout | per-test timeout | 8007 |
-| pm.lua | fail | other: Unhandled exception: \"Unhandled exception: \\\"assertion failed!\\\"\ | 6697 |
+| math.lua | fail | other: Unhandled exception: \"Unhandled exception: \\\"lua: attempt to call non-functio | 4738 |
+| nextvar.lua | fail | other: Unhandled exception: \"Unhandled exception: \\\"assertion failed!\\\"\ | 7818 |
+| pm.lua | fail | other: Unhandled exception: \"Unhandled exception: \\\"assertion failed!\\\"\ | 6478 |
 | sort.lua | timeout | per-test timeout | 8007 |
-| strings.lua | fail | other: Unhandled exception: \"Unhandled exception: \\\"assertion failed!\\\"\ | 4493 |
-| vararg.lua | fail | other: Unhandled exception: \"Unhandled exception: \\\"assertion failed!\\\"\ | 2541 |
-| verybig.lua | pass | - | 1187 |
+| strings.lua | fail | other: Unhandled exception: \"Unhandled exception: \\\"assertion failed!\\\"\ | 4339 |
+| vararg.lua | fail | other: Unhandled exception: \"Unhandled exception: \\\"assertion failed!\\\"\ | 2343 |
+| verybig.lua | pass | - | 1064 |
diff --git a/plans/lua-on-sx.md b/plans/lua-on-sx.md
index 929b6a93..8637c26e 100644
--- a/plans/lua-on-sx.md
+++ b/plans/lua-on-sx.md
@@ -82,6 +82,7 @@ Each item: implement → tests → tick box → update progress log.
 
 _Newest first. Agent appends on every commit._
 
+- 2026-04-25: lua: scoreboard iteration — `math.mod` (Lua 5.0 alias for `fmod`), `math.frexp` (mantissa/exponent split), `math.ldexp` (m·2^e). math.lua moves past line-103 `math.mod` call. Timeouts 6→3, asserts 5→7. 393/393 green.
 - 2026-04-25: lua: scoreboard iteration — `unpack(t, i, j)` now treats explicit nil for `i` or `j` as missing (defaults to 1 and `#t`). vararg.lua-style `unpack(args, 1, args.n)` works when `args.n` is nil. Asserts 4→5, timeouts 8→6 (more tests reach assertions instead of timing out). 393/393 green.
 - 2026-04-25: lua: scoreboard iteration — extended `string.format`. New `%x`/`%X`/`%o` (hex/octal), `%c` (codepoint→char via `lua-char-one`), `%q` (basic quote), width N (`%5d`), zero-pad (`%05d`), left-align (`%-5d`), `%.Ns` precision. Helpers `lua-fmt-pad` and `lua-fmt-int-base`. 393/393 green (+6 format tests).
 - 2026-04-25: lua: scoreboard iteration — `lua-eval-ast` now SKIPS the top-level guard when the parsed chunk has no top-level `return` (recursive AST walk via `lua-has-top-return?` that descends through control-flow but stops at function-body boundaries). Without the guard, top-level user defines leak to the SX top env, and `loadstring`-captured closures can find them. Verified: `function fat(x)...loadstring("return fat(...)")...end; x=fat(5)` works (was undefined). Most PUC-Rio tests still have top-level returns elsewhere, so they still need the guard. Scoreboard unchanged at 1/16 but unblocks future work.