The Momentum Invariant
In physics, momentum is mass times velocity — the quantity of motion a system possesses. A system with sufficient momentum resists perturbation. A system without it can be redirected by any external force.
An invariant is a quantity that remains constant across all reference frames. The speed of light is invariant — it does not change whether you are stationary or moving at half the speed of light. Invariants are not chosen. They are discovered. They are properties of the system itself.
Bitcoin has momentum. It is the economic energy flowing to miners that keeps the chain resistant to redirection. When that energy is sufficient, the cost of overpowering the network exceeds the rational incentive to try. When it is not, the chain can be bent.
Bitcoin has a Momentum Invariant. The network requires a minimum rate of security spend to remain resistant to attack. This rate is denominated in BTC — not dollars — because the security budget and the value it secures are expressed in the same unit. The requirement is identical whether Bitcoin is worth 10M. Price is the reference frame. The requirement does not change when you change it. Price cancels out.
The Momentum Invariant is not the security budget. The security budget is what miners earn. The Momentum Invariant is what miners must earn. The budget can be above, at, or below the invariant. When it falls below, the network’s security guarantee is degrading — whether or not anyone notices.
The exact value of the invariant is debated but bounded. Lyn Alden’s security modeling estimates 0.5%–1.5% of network value. A TopMonks analysis puts the safe minimum at 1%, with 0.5% as the bare floor. No credible research has proposed a figure below 0.5%. At that most generous threshold, the Momentum Invariant is approximately 2 BTC per block. That is the minimum sum of block reward subsidy and transaction fees that must flow to miners every block for the network to remain secure.
The invariant does not care what Bitcoin’s price is, what narrative the market believes, or what roadmap exists. It must be satisfied continuously. It is a property of the system.