Current climate-finance regulation — TCFD scenario analysis, NGFS stress tests, ECB climate scenarios — treats climate risk as an input to financial risk: a scenario that stresses asset values. It does not model the coupling topology: the feedback between the physical climate system and the financial obligation network. This feedback creates irresolvable conflict cycles — the Climate Deep — that are invisible to both climate modellers (who treat finance as exogenous) and financial regulators (who treat climate as a scenario). This paper extends the Deep Framework (Islands/$H^0$, Flatland/$H^1$, The Deep/$H^2$) to the joint climate-finance system. The three strata become: Islands risk ($H^0$), the physical viability of assets under climate change (stranded assets, physical damage), partially addressed by TCFD and NGFS; Flatland risk ($H^1$), the carbon and supply-chain loops that couple financial flows to emissions (fossil fuel debt, transition loops), addressed by carbon pricing and supply-chain due diligence but not their network topology; and the Climate Deep ($H^2$), tipping cascade conflict cycles — the irresolvable interactions between climate tipping elements and financial obligations that no bilateral instrument can resolve. The central result is the Climate-Finance Coupling Theorem: $H^2(\mathcal{F}_{\mathrm{climate}} \times \mathcal{F}_{\mathrm{finance}})$ can be non-zero even when $H^2(\mathcal{F}_{\mathrm{climate}}) = 0$ and $H^2(\mathcal{F}_{\mathrm{finance}}) = 0$ separately. A conflict cycle can form at the coupling between two individually manageable systems. Managing financial obligations and climate outcomes separately — however rigorously — can still produce a globally irresolvable conflict cycle at the interface. The proof follows from the Mayer-Vietoris long exact sequence: the connecting homomorphism $\delta: H^1 \to H^2$ can be non-trivial even when both factors have trivial $H^2$. The canonical example is the stranded asset conflict cycle: fossil fuel revenues fund sovereign debt service ($A \to B$), sovereign carbon policy determines the rate of Amazonian deforestation ($B \to C$), and Amazonian tipping accelerates physical risk to the fossil fuel sector ($C \to A$). Each bilateral link is individually manageable; the triangle is not. Carney's three channels — physical, liability, and transition risk — map precisely onto the three strata: Islands, Flatland, and The Deep. Existing instruments address the first two. Transition risk at the network level is the Climate Deep, and no regulatory instrument currently measures or addresses it. The resolution instrument required to fill $H^2$ holes in the joint sheaf is a Level 6 supranational authority: an institution that can simultaneously restructure sovereign debt, fossil fuel obligations, and climate commitments. The Paris Agreement is the closest approximation — but it has no balance sheet, no enforcement mechanism, and cannot force the quadrilateral resolution that the Climate Deep requires. Companion papers: Beyond Basel — the Deep Framework for Systemic Risk Regulation (doi:10.5281/zenodo.20700006), Systemic Risk as $H^2$ (doi:10.5281/zenodo.20642908), Tipping Points are Topological (doi:10.5281/zenodo.20653285). Keywords: climate finance, tipping cascades, stranded assets, Deep Framework, sheaf cohomology, systemic risk, Tragedy of the Horizon, Mark Carney, TCFD, NGFS, Paris Agreement, Mayer-Vietoris, coupling theorem, Islands Flatland Deep, physical risk, transition risk, liability risk, supranational resolution, fossil fuel, sovereign debt