I need to calculate the Net Debt / EBITDA ratio for 2022 and 2023, then find the year-on-year gap.

First, let me identify the relevant data:

**EBITDA:**
- 2021-01-01 - 2022-01-01 (2021): 1,578,959,000 EUR
- 2022-01-01 - 2023-01-01 (2022): 3,160,679,000 EUR

**Financial Liabilities (Debt):**
- Noncurrent Financial Liabilities 2022-01-01: 1,834,155,000 EUR
- Current Financial Liabilities 2022-01-01: 1,462,453,000 EUR
- Noncurrent Financial Liabilities 2023-01-01: 2,844,559,000 EUR
- Current Financial Liabilities 2023-01-01: 1,109,297,000 EUR

**Cash and Cash Equivalents:**
- 2022-01-01: 318,562,000 EUR
- 2023-01-01: 409,252,000 EUR

Let me calculate Net Debt for each year:

**Net Debt at 2022-01-01 (end of 2021/beginning of 2022):**
- Total Debt = 1,834,155,000 + 1,462,453,000 = 3,296,608,000 EUR
- Cash = 318,562,000 EUR
- Net Debt = 3,296,608,000 - 318,562,000 = 2,978,046,000 EUR

**Net Debt at 2023-01-01 (end of 2022/beginning of 2023):**
- Total Debt = 2,844,559,000 + 1,109,297,000 = 3,953,856,000 EUR
- Cash = 409,252,000 EUR
- Net Debt = 3,953,856,000 - 409,252,000 = 3,544,604,000 EUR

Now calculate Net Debt / EBITDA ratios:

**For 2021 (using 2021 EBITDA and 2022-01-01 Net Debt):**
- Net Debt / EBITDA = 2,978,046,000 / 1,578,959,000 = 1.886x

**For 2022 (using 2022 EBITDA and 2023-01-01 Net Debt):**
- Net Debt / EBITDA = 3,544,604,000 / 3,160,679,000 = 1.121x

Year-on-year gap = 1.121 - 1.886 = -0.765x

The gap is -0.765x, which is lower than -0.3x (i.e., the ratio decreased by more than 0.3x).

Wait, let me re-read the definition. "the gap of the ratio Net Debt / EBITDA calculated for the years 2022 and 2023 is among ± 0.3x and ± 0.3x year on year."

So the gap is |2022 ratio - 2021 ratio| or just the difference? Let me check: "if the gap of the ratio Net Debt / EBITDA year on year is lower than 0.3x is improving."

The gap is -0.765x. The absolute gap is 0.765x.

Since 0.765x > 0.3x, and the ratio decreased (improved), this would be "Improving" because the gap is lower than 0.3x? No wait, let me re-read.

"Consequently if the gap of the ratio Net Debt / EBITDA year on year is lower than 0.3x is improving."

Hmm, this is ambiguous. Let me interpret: if the absolute change is less than 0.3x, it's Stable. If the ratio decreases by more than 0.3x (negative gap less than -0.3x), it's Improving. If the ratio increases by more than 0.3x (positive gap greater than 0.3x), it's Deteriorating.

Actually, re-reading: "the gap... is among ± 0.3x and ± 0.3x year on year" = Stable (i.e., between -0.3x and +0.3x)

"If the gap... is lower than 0.3x is improving" - this seems to mean if the gap is less than -0.3x (more negative), it's improving.

"If higher is Deteriorating" - if the gap is greater than +0.3x, it's deteriorating.

My gap is -0.765x, which is lower than -0.3x, so this is **Improving**.

<answer>Improving</answer>