A central challenge in financial economics is understanding how credit networks form under informational noise. We introduce the concept of topological capital, arguing that banks increasingly rely on topological certification, interpreting a borrower's connectivity as a primary proxy for creditworthiness. Using a novel dataset of bank-firm relationships manually extracted from Italian financial statements, we implement a multi-stage empirical framework, benchmarking empirical patterns against a maximum-entropy benchmark, to separate the determinants of credit access from those of loan volumes. Our results indicate that network topology systematically outperforms traditional fundamentals. In the link-formation stage, connectivity breeds further connectivity through an amplified preferential attachment mechanism. In the loan-sizing stage, network strength absorbs the explanatory power of balance-sheet metrics, documenting a profound network substitution effect where topological signals effectively replace physical collateral across all corporate segments. For SMEs, we identify a critical signal divergence: reported debt acts as a risk signal, while network footprint serves as market validation. Furthermore, we reveal a diversification paradox: while firms fragment debt to avoid hold-up risks, over-diversification leads to a complexity penalty that stagnates credit depth and inflates systemic Loss Given Default. Ultimately, our findings signal the twilight of the balance sheet as the primary anchor of corporate lending, calling for a shift toward topological macro-prudential supervision to manage vulnerabilities invisible to traditional bilateral indicators.