This paper establishes the non-invariance of temporal labelling within the YU–TIME framework. In Paper 1, temporal ordering was constructed without invoking time as a primitive parameter, demonstrating that ordering arises from constraint structure via the Local Monotonic Constraint Relation (LMCR). Building on this, the present work shows that temporal labels such as “yesterday” are not intrinsic properties of configurations but depend on the choice of admissible projection. We formalize temporal labelling as a projection-dependent function and prove that no projection-independent temporal labelling function exists. This result, termed the Aruna Reddy “Yesterday” Paradox, demonstrates that temporal meaning itself is non-invariant, even when ordering is well-defined. The paper introduces the space of admissible projections, establishes a Projection Separation Lemma, and shows that divergence of temporal labels is structurally inevitable under non-unique projections. The work further develops the operational interpretation of time through projection mechanisms, grounding the framework in physical processes such as clocks and records. Temporal classification is shown to be representation-dependent, while underlying structural relations remain invariant. This paper extends the YU–TIME program from the construction of ordering without time to the structural non-invariance of temporal interpretation.
Aruna Reddy Katanguri (Fri,) studied this question.