One-dimensional crystals have long range translational invariance which manifests as long exciton diffusion lengths, but such intrinsic properties are often obscured by environmental perturbations. We use a first-passage approach to model single-walled carbon nanotube (SWCNT) exciton dynamics (including exciton-exciton annihilation and end effects) and compare it to results from both continuous-wave and multipulse ultrafast excitation experiments to extract intrinsic SWCNT properties. Excitons in suspended SWCNTs experience macroscopic diffusion lengths, on the order of the SWCNT length (1.3-4.7 μm), in sharp contrast to encapsulated samples. For these pristine samples, our model reveals intrinsic lifetimes (350-750 ps), diffusion constants (130-350 cm 2 /s), and absorption cross sections (2.1-3.6 × 10 −17 cm 2 /atom) among the highest previously reported.Semiconductor nanoscience has rapidly expanded since material engineering enabled control of the dimensionality, with two-dimensional (quantum well), one-dimensional (quantum wire), and zero-dimensional (quantum dot) systems now readily producible. These nanosystems have been particularly useful for optical applications due to their customizable electronic properties and, in contrast to bulk semiconductors, the electronic density of states (DOS) at the band gap is nonzero. In the case of quantum wires, the one-dimensional quantum confinement leads to Van Hove singularities, which are divergences in the DOS at the band gap. An example of a nearly ideal quantum wire is the single-walled carbon nanotube (SWCNT), which is a rolled graphene sheet with radial quantum confinement and translation invariance along the SWCNT axis. The one dimensionality of carriers in SWCNTs results in a strong Coulomb interaction which binds the electron-hole pair into an exciton with a binding energy approximately one third of the single particle band gap. 1,2 For many SWCNT samples, the exciton lifetime is dominated by end quenching, defects/adsorbates, and, when highly excited, interactions between excitons. These decay mechanisms are all strongly dependent on exciton transport, which is often modeled as diffusive, with an effective diffusion length determined by the sample quality. 3,4 The high likelihood of spatial overlap between diffusing excitons results in efficient Auger-like exciton-exciton annihilation (EEA) which limits the maximum exciton density well below the predictions of phase-space filling. 5 In addition to EEA, diffusion also allows quenching of excitons at the ends and defect sites, severely limiting the quantum efficiency for many samples. Interestingly, both diffusion driven end/defect quenching and EEA enable many realized and potential photonic applications. 6 At low exciton densities, the stochastic fluctuations of the optical emission intensity due to the adsorption and desorption of fluorescence quenchers has led to single molecule counting arrays and biological sensors. 7-9 At high exciton densities, the rapid relaxation of excitons due to EEA may give rise ...