Urban decarbonization requires scaling rooftop solar across millions of fragmented producers, yet cities face a fundamental tension: energy data is easily manipulated, and economic incentives often reward speculation rather than actual infrastructure deployment. We present SolarChain, a platform that resolves both problems by anchoring digital accountability to the thermodynamic limits of solar energy conversion. Using real-time meteorological data, geospatial coordinates, and first-principles calculations of solar yield, the system establishes a hard physical boundary for every panel's maximum possible output; any reported generation exceeding this limit is automatically rejected before entering the shared ledger. This trustless verification enables a peer-to-peer marketplace with programmatic reward structures that continuously reinvest value into equipment maintenance and market liquidity, preventing the speculative hoarding that typically destabilizes blockchain-based marketplaces. When electricity is consumed, the corresponding digital credits are permanently retired in direct proportion to physical energy dissipation, creating an auditable one-to-one mapping between urban consumption and carbon accounting. Deployed across heterogeneous city nodes, the prototype demonstrates resilience against data injection attacks while lowering capital barriers for community-level solar expansion. Beyond energy, the framework offers a general model for coordinating economic activity with physical law in any domain where distributed infrastructure demands both data integrity and sustainable investment. We release the data and code as open-access on GitHub.