This paper presents a new algorithm for learning the structure of Hamiltonians from real-time evolution. The goal is to recover an unknown local Hamiltonian $ H = \sum_{a=1}^{m} \lambda_{a} E_{a} $ on n qubits, given the ability to apply $ e^{-iHt} $ for any t > 0. The algorithm achieves Heisenberg-limited scaling in error, with total evolution time $ \mathcal{O}(\log(n)/\varepsilon) $ and constant time resolution. It works for any Hamiltonian where the sum of terms interacting with a qubit has bounded norm, and does not require prior knowledge of the interaction structure or interaction terms. The algorithm improves upon previous methods by achieving optimal error scaling and constant time resolution, even when all interactions are unknown. It also extends to Hamiltonians with power-law decay, achieving better scaling than the standard limit of $ 1/\varepsilon^{2} $. The algorithm uses a bootstrapping framework to iteratively improve estimates of the Hamiltonian's coefficients, leveraging a novel bound on Trotter error to achieve constant time resolution. It also employs a Goldreich–Levin-like approach to efficiently identify large coefficients of the Hamiltonian. The algorithm is efficient in both quantum and classical resources, with a total evolution time of $ \mathcal{O}(\log(n)/\varepsilon) $ and a classical overhead of $ \widetilde{\mathcal{O}}(n^{2}\mathfrak{r}^{3}\log(1/\varepsilon)) $. It can be applied to Hamiltonians with long-range interactions and is robust to errors in the quantum circuit. The algorithm is also efficient in terms of the number of experiments required, with $ \widetilde{\mathcal{O}}(\mathfrak{r}^{2}\log(n)\log(1/\varepsilon)) $ quantum circuits. The algorithm is applicable to a wide range of Hamiltonians, including those with geometrically local interactions and those with power-law decay.This paper presents a new algorithm for learning the structure of Hamiltonians from real-time evolution. The goal is to recover an unknown local Hamiltonian $ H = \sum_{a=1}^{m} \lambda_{a} E_{a} $ on n qubits, given the ability to apply $ e^{-iHt} $ for any t > 0. The algorithm achieves Heisenberg-limited scaling in error, with total evolution time $ \mathcal{O}(\log(n)/\varepsilon) $ and constant time resolution. It works for any Hamiltonian where the sum of terms interacting with a qubit has bounded norm, and does not require prior knowledge of the interaction structure or interaction terms. The algorithm improves upon previous methods by achieving optimal error scaling and constant time resolution, even when all interactions are unknown. It also extends to Hamiltonians with power-law decay, achieving better scaling than the standard limit of $ 1/\varepsilon^{2} $. The algorithm uses a bootstrapping framework to iteratively improve estimates of the Hamiltonian's coefficients, leveraging a novel bound on Trotter error to achieve constant time resolution. It also employs a Goldreich–Levin-like approach to efficiently identify large coefficients of the Hamiltonian. The algorithm is efficient in both quantum and classical resources, with a total evolution time of $ \mathcal{O}(\log(n)/\varepsilon) $ and a classical overhead of $ \widetilde{\mathcal{O}}(n^{2}\mathfrak{r}^{3}\log(1/\varepsilon)) $. It can be applied to Hamiltonians with long-range interactions and is robust to errors in the quantum circuit. The algorithm is also efficient in terms of the number of experiments required, with $ \widetilde{\mathcal{O}}(\mathfrak{r}^{2}\log(n)\log(1/\varepsilon)) $ quantum circuits. The algorithm is applicable to a wide range of Hamiltonians, including those with geometrically local interactions and those with power-law decay.