τ-Identity and Nontrivial Return: A General Logical Primitive Schema — From Static Self-Sameness to Operational Re-Identifiability

This preprint proposes τ-identity as a candidate primitive schema for moving from static self-sameness to operational re-identifiability. Its lean Layer-0 form declares a domain, a distinguished identity, and a total operation such that the distinguished identity is first displaced and then recovered: τ ∈ Dτ, ρ : Dτ → Dτ, ρ(τ) ≠ τ, and ρ²(τ) = τ. The proposal supplements, rather than rejects, classical identity x = x. Complex, phase, signed, and two-coordinate τ notations are later representations of this operation-orbit role, not primitives already assumed at Layer 0.