Dirac's 1951 reformulation of Weyl geometry required imposing a gauge-fixing condition to recover constant masses, revealing that historical path-independence must be externally stipulated, not derived.

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Constant masses(as a physical property that needs to be maintained): The property that particles have a fixed, unchanging weight or mass; in some theories, masses can appear to vary depending on conditions, so physicists have to impose rules to keep them constant.
Dirac(as the originator of constraint analysis methods): Paul Dirac was a famous 20th-century physicist who developed mathematical methods for understanding how the laws of physics work, especially in quantum mechanics and relativity.
Externally stipulated(as a distinction between what must be assumed versus what can be proven): Imposed or declared from outside the system as a requirement, rather than coming naturally from the theory itself; it means you have to add it by hand rather than deriving it mathematically.
Gauge-fixing condition(as a mathematical technique in physics): A mathematical constraint or rule you have to add to a theory to pin down specific values and make predictions work out; it's like choosing a reference point so your measurements make sense.

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