impulse

the proven change in focus that a neuron delivers to the cybergraph via a cyber/signal. mathematically $\Delta\phi^*$ — a sparse vector of (particle_id, $\Delta\phi^*$) pairs representing how the focus distribution $\phi^*$ shifts when the signal's cyberlinks are applied

in physics, impulse is force applied over time that changes momentum ($J = \Delta p$). in neuroscience, the nerve impulse is the action potential that propagates through a network and changes downstream potentials. in cyber, the impulse is the neuron's proven push on collective focus — discrete, has magnitude, delivered at a specific moment, and propagates through the cybergraph

computation

the neuron computes the impulse by running the tri-kernel locally on their $O(\log(1/\varepsilon))$-hop neighborhood, adding their cyberlinks, and measuring how $\phi^*$ shifts. the locality theorem guarantees effects beyond that radius are below $\varepsilon$ — most entries are zero, so the sparse representation is compact

each $\Delta\phi^*$ entry is a fixed-point Goldilocks field element, and the local recompute runs the same fixed $T(\varepsilon)$ steps as the global pass (see arithmetic) — so the neighborhood result agrees bit for bit with the global $\phi^*$ restricted to the neighborhood, which is what lets one proof certify the shift

the result is whatever the math says. there is no target, no threshold, no minimum. a link to a well-connected particle in a sparse region produces a larger impulse than a redundant link in a dense cluster. the neuron discovers their contribution by computing it

proof

the impulse is accompanied by a stark proof $\sigma$ that certifies correctness against the current BBG root. the proof covers the entire cyber/signal — all cyberlinks in the batch, all conviction box movements, and the resulting $\Delta\phi^*$ — in a single recursive verification. any node checks $\sigma$ in $O(\log n)$ without recomputing the tri-kernel

reward

the impulse proof doubles as a reward claim. if $\|\Delta\phi^*\| > 0$ and $\sigma$ is valid, the neuron self-mints $CYB proportional to the proven shift. no aggregator decides the reward — the proof IS the mining. see cyber/rewards for the full reward specification

conservation

total minting per epoch is bounded by the actual global $\Delta\phi^*$, verifiable from consecutive headers. if the sum of individual impulses exceeds the actual shift (overlapping neighborhoods), all claims are scaled proportionally

see cyber/signal, focus, cyber/rewards, cyber/network

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