Open Problems: NEC, M-Hat, and the Lab

This is the open-problems paper after Synthesis III. It does not prove a new theorem. It lists what is closed, what is open, and what would falsify the arc. In 2026a (Ch. 124), we proved no unital map T → E for H = S^1. In 2026b (Ch. 125), we generalized to the triple (dim H^n, dim C^n, 1). In 2026c (Ch. 138), we defined the Bridge Conjecture. In 2026d (Ch. 139), we proved the eraser must be CPTP. In 2026e (Ch. 140), we proved all four follow from one Unifier Axiom: [x,y] = 1. In 2026f (Ch. 141), we categorified H. In 2026g (Ch. 142), we proved the Unifier survives in characteristic p. In 2026h (Ch. 143), we proved it survives for infinite H. In 2026i (Ch. 144), we gave the lab falsifier D^2 + V^2 ≤ 1. In 2026j (Ch. 145), we proved the nine papers are one theorem. In 2026k (Ch. 146), we proved the Unifier survives for any A with [x,y] = 1. In 2026l (Ch. 147), we constructed H(M) for M Lorentzian. In 2026m (Ch. 148), we defined causal homotopy, π1^causal, and H1^causal. In 2026n (Ch. 149), we defined H^n_causal(H(M)) for all n. In 2026o (Ch. 150), we proved the fourteen papers are one theorem. In 2026p (Ch. 151), we proved Einstein + NEC + Bridge ⇒ no CTC, and NEC violation still forces erasure. In 2026q (Ch. 152), we proved quantum M still forces erasure, branch + interference. In 2026r (Ch. 153), we gave the concrete lab protocol: Mach-Zehnder, W, E, D^2+V^2 ≤ 1, delayed-choice without retro-causation. In 2026s (Ch. 154), we proved the eighteen papers are one theorem. Closed in 2026s: the nineteen papers stand or fall together. Open here: (1) Is NEC true in nature? (2) Is M-Hat real, and if so, what is H(M-Hat) beyond block-sum? (3) Does the lab actually give D^2+V^2 ≤ 1 at >3σ with eraser restoring V? (4) Is [x,y] = 1 the right Unifier, or is there a weaker axiom that still forces erasure? (5) Can H^1_causal be computed for a concrete M with CTC, e.g. Misner, Gott, wormhole? Each problem is stated precisely, with what a solution would prove and what a counterexample would falsify. Tseglin 2026t = Ch. 155. Cites Tseglin 2026a DOI 10.5281/zenodo.23977165, 2026b DOI 10.5281/zenodo.23980498, 2026c DOI 10.5281/zenodo.23980738, 2026d DOI 10.5281/zenodo.23981860, 2026e DOI 10.5281/zenodo.23982063, 2026f DOI 10.5281/zenodo.23982359, 2026g DOI 10.5281/zenodo.23985216, 2026h DOI 10.5281/zenodo.23991367, 2026i DOI 10.5281/zenodo.23991442, 2026j DOI 10.5281/zenodo.23991535, 2026k DOI 10.5281/zenodo.23991603, 2026l DOI 10.5281/zenodo.23991665, 2026m DOI 10.5281/zenodo.23991998, 2026n DOI 10.5281/zenodo.23992083, 2026o DOI 10.5281/zenodo.23992187, 2026p DOI 10.5281/zenodo.23992267, 2026q DOI 10.5281/zenodo.23992317, 2026r DOI 10.5281/zenodo.23992397, 2026s DOI 10.5281/zenodo.23992535.