The quantum lifetime of a future-referential feedback loop: certified index, architecture floor, and thermal bonus

A quantum feedback loop that returns information from a forward simulation to an earlier internal time induces a completely positive trace-preserving map on a message register; iterating that map eventually destroys its ability to carry entanglement. The entanglement-breaking index N = n EB(Phi), the round at which this happens, is studied along two axes, interaction and bath. On the interaction axis, strict contraction onto a full-rank fixed point forces N finite in every dimension, via an explicit separable ball around the limiting Choi state, and across 3997 sampled channels index and stability gap are one clock, N [1 - rho(A)] in [0.60, 1.50]. On the bath axis, a thermal ancilla at polarisation p = tanh(hbar omega / 2 k B T) makes every channel quantity an exact quadratic in p, and one-sided certificates (no eigensolver) establish N = 3 at the reference circuit at every temperature. The infinite-temperature index is an architecture floor with closed form and exact measure (46.427% of circuits break entanglement in one round at infinite temperature). For exchange collisions (generalised amplitude damping) the index has a closed form and is monotone in p; for the loop the floor is not a bound: certified circuits dip below it in interior temperature windows, at a rate with Gaussian cutoff in epsilon = 1 - A 0 2 (marginal exponent 2.02 [1.90, 2.16], 4.1 million circuits), and shallow-floor valleys survive to epsilon = 0.125. On a certified coupling-temperature surface, temperature moves the index by at most 3/2, the interaction by 1213/3. Applied to quantum-cognition proposals, a per-bath polarisation table at 310 K shows nuclear spins maximally hot and intramolecular vibrations frozen, and a four-input checklist replaces decoherence times by round budgets; Fisher's nuclear-spin proposal specifies its bath and storage coherence, not its processing interaction or rate.