diff --git a/mathstream/README.md b/mathstream/README.md
index e3abb68..6602dd5 100644
--- a/mathstream/README.md
+++ b/mathstream/README.md
@@ -10,7 +10,7 @@ source venv/bin/activate
 pip install -e .
 ```
 
-Create digit files anywhere you like (the examples below use `instance/log`), then construct `StreamNumber` objects, and call the helpers:
+Create digit files anywhere you like (the examples below use `instance/log`), or supply ad-hoc literals, then construct `StreamNumber` objects and call the helpers:
 
 ```python
 from mathstream import (
@@ -26,8 +26,8 @@ from mathstream import (
 )
 
 a = StreamNumber("instance/log/huge.txt")
-b = StreamNumber("instance/log/tiny.txt")
-e = StreamNumber("instance/log/exponent.txt")
+b = StreamNumber(literal="34567")
+e = StreamNumber(literal="3")
 
 print("sum =", "".join(add(a, b).stream()))
 print("difference =", "".join(sub(a, b).stream()))
@@ -43,7 +43,7 @@ Each arithmetic call writes its result back into `instance/log` (configurable vi
 
 ## Core Concepts
 
-- **StreamNumber(path)** – Wraps a digit text file. The file may include an optional leading sign (`+` or `-`). Whitespace is ignored; digits must otherwise be contiguous.
+- **StreamNumber(path | literal=...)** – Wraps a digit text file or creates one for an integer literal inside `LOG_DIR`. Literal operands are persisted as `literal_<hash>.txt`, so repeated runs reuse the same staged file (note that `clear_logs()` removes these cache files too).
 - **`.stream(chunk_size)`** – Yields strings of digits with the provided chunk size. Operations in `mathstream.engine` consume these streams to avoid loading the entire number at once.
 - **Automatic staging** – Outputs are stored under `LOG_DIR` with hashes based on input file paths, letting you compose operations without manual bookkeeping.
 - **Sign-aware** – Addition, subtraction, multiplication, division (`//` behavior), modulo, and exponentiation (non-negative exponents) all respect operand sign. Division/modulo follow Python’s floor-division rules.
diff --git a/mathstream/number.py b/mathstream/number.py
index a3cc79e..22d1cf4 100644
--- a/mathstream/number.py
+++ b/mathstream/number.py
@@ -1,13 +1,55 @@
 import hashlib
 from pathlib import Path
+from typing import Optional, Union
 
 LOG_DIR = Path("./instance/log")
 
+
+def _ensure_log_dir() -> None:
+    LOG_DIR.mkdir(parents=True, exist_ok=True)
+
+
+def _canonicalize_literal(value: str) -> str:
+    raw = value.strip()
+    if not raw:
+        raise ValueError("Literal value cannot be empty.")
+
+    sign = ""
+    digits = raw
+    if raw[0] in "+-":
+        sign = "-" if raw[0] == "-" else ""
+        digits = raw[1:]
+
+    if not digits or not digits.isdigit():
+        raise ValueError(f"Literal must be an integer string, got: {value!r}")
+
+    digits = digits.lstrip("0") or "0"
+    if digits == "0":
+        sign = ""
+    return f"{sign}{digits}"
+
+
 class StreamNumber:
-    def __init__(self, file_path):
-        self.path = Path(file_path)
-        if not self.path.exists():
-            raise FileNotFoundError(self.path)
+    def __init__(
+        self,
+        file_path: Optional[Union[str, Path]] = None,
+        *,
+        literal: Optional[str] = None,
+    ):
+        if (file_path is None) == (literal is None):
+            raise ValueError("Provide exactly one of file_path or literal.")
+
+        if literal is not None:
+            normalized = _canonicalize_literal(literal)
+            _ensure_log_dir()
+            literal_hash = hashlib.sha1(normalized.encode()).hexdigest()[:10]
+            self.path = LOG_DIR / f"literal_{literal_hash}.txt"
+            self.path.write_text(normalized, encoding="utf-8")
+        else:
+            self.path = Path(file_path)
+            if not self.path.exists():
+                raise FileNotFoundError(self.path)
+
         self.hash = hashlib.sha1(str(self.path).encode()).hexdigest()[:10]
 
     def __repr__(self):
@@ -21,6 +63,7 @@ class StreamNumber:
 
     def write_stage(self, stage, data: str):
         """Write intermediate stage result."""
+        _ensure_log_dir()
         stage_file = LOG_DIR / f"{self.hash}_stage_{stage}.bin"
         with open(stage_file, "wb") as f:
             f.write(data.encode())
diff --git a/test.py b/test.py
index 69d8e60..26c13b7 100644
--- a/test.py
+++ b/test.py
@@ -52,6 +52,8 @@ def main() -> None:
     negative = write_number("negative", "-1200")
     exponent = write_number("power", "5")
     negative_divisor = write_number("neg_divisor", "-34567")
+    literal_even = StreamNumber(literal="2000")
+    literal_odd = StreamNumber(literal="-3")
 
     # Showcase the core operations.
     total = add(big, small)
@@ -63,6 +65,7 @@ def main() -> None:
     neg_mod_pos = mod(negative, small)
     pos_mod_neg = mod(small, negative)
     neg_mod_neg = mod(negative, negative_divisor)
+    literal_combo = add(literal_even, literal_odd)
 
     print("Operands stored under:", NUMBERS_DIR)
     check("huge + tiny", total, "98765432123491356")
@@ -74,10 +77,13 @@ def main() -> None:
     check("negative % tiny", neg_mod_pos, "33367")
     check("tiny % negative", pos_mod_neg, "-233")
     check("negative % neg_divisor", neg_mod_neg, "-1200")
+    check("literal_even + literal_odd", literal_combo, "1997")
     check_bool("is_even(negative)", is_even(negative), True)
     check_bool("is_even(tiny)", is_even(small), False)
     check_bool("is_odd(tiny)", is_odd(small), True)
     check_bool("is_odd(negative)", is_odd(negative), False)
+    check_bool("is_even(literal_even)", is_even(literal_even), True)
+    check_bool("is_odd(literal_odd)", is_odd(literal_odd), True)
 
 
 if __name__ == "__main__":