Relating low-level executable code to a high-level account of its behavior has been a central concern of programming-language research for decades. From formally verified compilers to translation validators, certifying compilers, and proof-carrying code, each approach chooses between laborious but foundational mechanized proofs and automation that costs completeness, generality, and an increased trusted base. Recently, large language models (LLMs) have begun to change the economics of formal verification. Agentic proof development is now capable of producing machine-checked proofs at a scale and speed that were previously out of reach. In this paper, we evaluate the capabilities of LLMs to produce foundational, machine-checked proofs of refinement between executable code and its high-level specification, as post hoc, per-artifact certificates. We study this in the context of the Ethereum Virtual Machine (EVM), a low-level virtual machine that executes smart contracts on the Ethereum blockchain. We build EquiVM, a foundational framework in Lean comprising an executable EVM semantics and a specification language that characterizes the intended behavior of smart contracts, but commits to no source language or compilation toolchain. In EquiVM, refinement is stated for deployed bytecode of arbitrary provenance, interaction with unknown code is part of the semantics, and each proof is a replayable, machine-checked certificate. No previous technique achieves this combination. Using frontier commercial LLMs, twenty-three real-world contracts are proved end to end with minimal human guidance, among them most of the MakerDAO stablecoin system, at up to a hundred million tokens and a hundred hours of proof time per contract. We conclude that foundational mechanized proofs can now be bought at the price of tokens, and that this shift can reshape how verification frameworks are architected.