feat: add interactive exploration of Shannon's capacity formula with Plotly graphs

- Implemented bandwidth sensitivity and power sensitivity plots.
- Created a contour map for bit rate multiplying factors.
- Added input parameters for C/N and bandwidth with validation.
- Displayed computed results and sensitivity analysis metrics.
- Integrated interactive graphs for user exploration.
- Included background information section for user guidance.

core/database.py

@@ -0,0 +1,107 @@
+"""
+Database module for managing user contributions.
+
+Uses parameterized queries (no SQL injection) and context managers.
+"""
+
+import sqlite3
+import os
+from datetime import datetime
+
+
+DB_DIR = os.path.join(os.path.dirname(os.path.dirname(__file__)), "data")
+
+
+def _get_db_path(db_name: str) -> str:
+    os.makedirs(DB_DIR, exist_ok=True)
+    return os.path.join(DB_DIR, db_name)
+
+
+def _init_db(db_path: str):
+    with sqlite3.connect(db_path) as conn:
+        conn.execute(
+            """CREATE TABLE IF NOT EXISTS contributions (
+                num INTEGER PRIMARY KEY,
+                name TEXT NOT NULL,
+                title TEXT NOT NULL,
+                keywords TEXT,
+                text TEXT NOT NULL,
+                date TEXT NOT NULL,
+                password TEXT DEFAULT ''
+            )"""
+        )
+
+
+def write_contribution(
+    db_name: str, name: str, title: str, keywords: str, text: str, password: str = ""
+) -> int:
+    """Write a new contribution. Returns the new contribution ID."""
+    db_path = _get_db_path(db_name)
+    _init_db(db_path)
+
+    with sqlite3.connect(db_path) as conn:
+        cursor = conn.cursor()
+        cursor.execute("SELECT COALESCE(MAX(num), 0) FROM contributions")
+        next_id = cursor.fetchone()[0] + 1
+
+        cursor.execute(
+            "INSERT INTO contributions (num, name, title, keywords, text, date, password) "
+            "VALUES (?, ?, ?, ?, ?, ?, ?)",
+            (next_id, name, title, keywords, text, datetime.now().strftime("%Y-%m-%d"), password),
+        )
+    return next_id
+
+
+def search_contributions(
+    db_name: str,
+    name_filter: str = "",
+    title_filter: str = "",
+    keywords_filter: str = "",
+    content_filter: str = "",
+    limit: int = 50,
+) -> list[dict]:
+    """Search contributions with optional filters. Returns list of dicts."""
+    db_path = _get_db_path(db_name)
+    if not os.path.isfile(db_path):
+        return []
+
+    _init_db(db_path)
+
+    with sqlite3.connect(db_path) as conn:
+        conn.row_factory = sqlite3.Row
+        cursor = conn.cursor()
+        cursor.execute(
+            """SELECT num, name, title, keywords, text, date, password
+               FROM contributions
+               WHERE name LIKE ? AND title LIKE ? AND keywords LIKE ? AND text LIKE ?
+               ORDER BY num DESC
+               LIMIT ?""",
+            (
+                f"%{name_filter}%",
+                f"%{title_filter}%",
+                f"%{keywords_filter}%",
+                f"%{content_filter}%",
+                limit,
+            ),
+        )
+        return [dict(row) for row in cursor.fetchall()]
+
+
+def delete_contribution(db_name: str, num: int, password: str) -> bool:
+    """Delete a contribution if the password matches. Returns True on success."""
+    db_path = _get_db_path(db_name)
+    if not os.path.isfile(db_path):
+        return False
+
+    with sqlite3.connect(db_path) as conn:
+        cursor = conn.cursor()
+        cursor.execute(
+            "SELECT password FROM contributions WHERE num = ?", (num,)
+        )
+        row = cursor.fetchone()
+        if row is None:
+            return False
+        if row[0] != password:
+            return False
+        cursor.execute("DELETE FROM contributions WHERE num = ?", (num,))
+    return True