The navigational system of the fruit fly is a crown jewel of systems neuroscience due to the work of some seminal neuroscientists (Larry Abbott, Gaby Maimon, Vivek Jayaraman, Barbara Webb), but it is an unfinished story. A fly that leaves a drop of food and wanders in the dark can always find its way back. To do that it has to keep a running sum of every step it has taken, a process called path integration. The neurons that report each step are known, but the neurons that add the steps up have never been found. There are two ways a brain can hold a sum like that. The usual answer is that some neurons holds it in activations and sustains these activations by exciting each other in a loop tuned so precisely that the signal neither fades nor blows up. Most models of navigation assumes this, and it is how RNNs and LLMs hold state too. The other answer is that nothing keeps firing at all. Each step is encoded into synaptic strengths (aka weights), and the sum of all synaptic strengths is the sum of the journey. A few papers have suggested the fly works this way but nobody has pointed to any candidate neurons, until now. Four neuron types, hΔH, hΔA, hΔI and hΔG, have no known functions, but we found that they have every ingredient option 2 needs. They receive input from neurons that report each step taken, they receive velocity-sensitive dopamine input that could gate memory writing, and they receive a reward-sensitive octopamine neuron that could reset the synaptic weights at food arrival. Simulations confirm this is a viable candidate for path integration. This is the key finding, but we have posted 3 other findings in links below. We tried to be exhaustive with published papers but may have very well missed some key published results, so inviting the cogniscenti to engage. Background, methods, experiments, results, as well as relevant citations: Panoramic circuit view: GH repo: