diff --git a/paperforge/worker/ocr_math.py b/paperforge/worker/ocr_math.py
index 0cbecbcc..76ab4d62 100644
--- a/paperforge/worker/ocr_math.py
+++ b/paperforge/worker/ocr_math.py
@@ -18,6 +18,13 @@ def normalize_inline_math_delimiters(text: str) -> str:
     return text
 
 
+_RELOP_PATTERN = re.compile(
+    r'(?:\\geq|\\leq|\\sim|\\approx|\\gg|\\ll|>|<)\s*$'
+)
+
+_GREEK_LETTER = re.compile(r'\\(?:[a-zA-Z]+)')
+
+
 def normalize_math_prose_boundaries(text: str) -> str:
     result: list[str] = []
     dollar_count = 0
@@ -31,14 +38,43 @@ def normalize_math_prose_boundaries(text: str) -> str:
         if ch == '$':
             dollar_count += 1
             is_opening = (dollar_count % 2 == 1)
-            if is_opening and i > 0 and text[i - 1].isalnum() and text[i - 1] not in '-–—':
-                result.append(' $')
+            if is_opening:
+                if i > 0 and text[i - 1].isalnum() and text[i - 1] not in '-–—':
+                    result.append(' $')
+                else:
+                    result.append('$')
             else:
                 result.append('$')
         else:
             result.append(ch)
         i += 1
-    return ''.join(result)
+
+    text = ''.join(result)
+
+    def _after_space(m: re.Match) -> str:
+        content = m.group(1)
+        nxt = m.group(2)
+
+        if nxt.isdigit():
+            return f"${content}$ {nxt}"
+
+        if _RELOP_PATTERN.search(content):
+            return f"${content}$ {nxt}"
+
+        if _GREEK_LETTER.fullmatch(content.strip()):
+            return f"${content}${nxt}"
+
+        if nxt.islower():
+            return f"${content}$ {nxt}"
+
+        return f"${content}${nxt}"
+
+    text = re.sub(
+        r'(?<!\$)\$([^$]+?)\$(?!\$)([a-zA-Z0-9])',
+        _after_space,
+        text,
+    )
+    return text
 
 
 def normalize_display_math(text: str) -> str:
diff --git a/tests/test_ocr_render_stabilization.py b/tests/test_ocr_render_stabilization.py
index 80af91a7..dfb2ef99 100644
--- a/tests/test_ocr_render_stabilization.py
+++ b/tests/test_ocr_render_stabilization.py
@@ -649,7 +649,7 @@ def test_stabilize_tail_zone_references_kept_separate() -> None:
 def test_normalize_ocr_math_text_delimiter_spacing() -> None:
     from paperforge.worker.ocr_math import normalize_ocr_math_text
     assert normalize_ocr_math_text("$ ^{8,49} $") == "$^{8,49}$"
-    assert normalize_ocr_math_text("$ \\\\mu $m") == "$\\\\mu$m"
+    assert normalize_ocr_math_text(r"$ \mu $m") == r"$\mu$m"
 
 
 def test_normalize_ocr_math_text_citation_superscript() -> None:
@@ -666,8 +666,28 @@ def test_normalize_ocr_math_text_prose_boundary() -> None:
 
 def test_normalize_ocr_math_text_hyphen_preserved() -> None:
     from paperforge.worker.ocr_math import normalize_ocr_math_text
-    result = normalize_ocr_math_text("TGF-$\\\\beta$")
-    assert "TGF-$\\\\beta$" in result
+    result = normalize_ocr_math_text(r"TGF-$\beta$")
+    assert r"TGF-$\beta$" in result
+
+
+def test_normalize_ocr_math_text_relop_followed_by_digit() -> None:
+    from paperforge.worker.ocr_math import normalize_ocr_math_text
+    assert normalize_ocr_math_text(r"$\geq$100") == r"$\geq$ 100"
+    assert normalize_ocr_math_text(r"$\leq$0.5") == r"$\leq$ 0.5"
+    assert normalize_ocr_math_text(r"$\sim$1000") == r"$\sim$ 1000"
+    assert normalize_ocr_math_text(r"$\approx$3.14") == r"$\approx$ 3.14"
+
+
+def test_normalize_ocr_math_text_relop_followed_by_unit() -> None:
+    from paperforge.worker.ocr_math import normalize_ocr_math_text
+    result = normalize_ocr_math_text(r"$\sim$1000Scm^{-1}")
+    assert r"$\sim$ 1000Scm^{-1}" in result
+
+
+def test_normalize_ocr_math_text_greek_letter_compound_preserved() -> None:
+    from paperforge.worker.ocr_math import normalize_ocr_math_text
+    assert normalize_ocr_math_text(r"NF-$\kappa$B") == r"NF-$\kappa$B"
+    assert normalize_ocr_math_text(r"TGF-$\beta$") == r"TGF-$\beta$"
 
 
 def test_normalize_ocr_math_text_display_math() -> None: