Proposition: Fixed-presentation uniqueness and two rejection tests

Once realization, charts, overlap components, frame, and seam are fixed, incompatible proposed values of one transition cannot both be accepted.

For $\mu \ne \nu$ in $I$, keeping $J_{\nu }$ at a packet declaring $\mu$ fails packet/seam matching, although it still fixes the reference worldsheet pointwise. In spectral norm,

For $\delta \ne 0$, the affine map

preserves the worldsheet as a set but fails pointwise fixation. The same distinctions survive coherent affine conjugation.

Proof. Acceptance requires equality with the single map (eq:transition). The rotation norm follows from

The interval is shorter than $2\pi$, so different deficits give different oriented rotations. A time-shifted map sends $(\tau ,0,\zeta )$ to $(\tau +\delta ,0,\zeta )$, not the same point. Conjugation is injective and transports these equalities.