Eraser as Forced CPTP Map: No CTC Without Decoherence

This paper gives the eraser a physical form. In 2026a, we proved there is no unital algebra map T → E. The eraser was a linear projection, not an algebra map. In 2026b, we generalized to all H, all n. In 2026c, we defined the Bridge Conjecture: if a bridge B from Lorentzian spacetimes to toy models exists and is faithful on c, then no CTC forms without an eraser. Here we prove: the eraser, if it exists physically, must be a completely positive trace-preserving (CPTP) map E. It cannot be unitary. It cannot be a unital algebra map. It must kill coherence, kill which-path information, and kill c. We prove E is forced to be decoherence, not a choice. We give its Kraus form, its action on D and V, and its falsifier. This is the physical version of 2026a/b/c. If you want a CTC, you must pay with decoherence. Tseglin 2026d = Ch. 139. Cites Tseglin 2026a DOI 10.5281/zenodo.23977165, 2026b DOI 10.5281/zenodo.23980498, 2026c DOI 10.5281/zenodo.23980738.