This v8.1 update of Track A presents a threshold-free characterization of coexistence dynamics in the two-mode Jaynes-Cummings model with Lindblad dissipation, solved using BDF. It replaces the earlier versions v3, v4, v4.1, v5, and v6, and supersedes the intermediate versions v7, v7.1, and v7.3. Formal content includes: the model (Hilbert space, operators, Hamiltonian, Lindblad dissipator, master equation), the BDF numerical scheme, and the definitions of the intrinsic measures of the coexistence product P(t)=R(t)·I(t): A_coex, P_max, t_peak, W_1/2, tau_eff, eta, and the peak_reached flag. Informative content includes the numerical values used for reproducibility: N0=15, t_max=50, n_steps=3000, omega0=6 Hz, omega1=40 Hz, gamma_a=0.1 Hz, n_th=0.05, and four parameter points labeled Vigilance, Flow, Endogenous, and Sleep. The speculative content (labeling R as Reason and I as Instinct, and mapping the four points to consciousness states) is explicitly presented as a heuristic ontology, not as a validated neuroscience claim. Main results: with t_max=50 all peaks are reached, fixing the v8 artifact where the Vigilance bio peak was not reached. Vigilance is characterized as slow access (t_peak,bio=22.9, W_1/2,bio=45.9, tau_bio=42.5). Flow shows the highest P_max,math=0.318. Endogenous and Sleep have similar P_max,bio (~0.0155) but differ in tail width (W_1/2,bio=9.15 vs 8.18). In the 2D scan, the optima of A_coex and tau_eff do not coincide, showing a trade-off between integrated action and duration. This update contains only the v8.1 files plus this technical note: v8.1_summary.csv, v8.1_traj_.csv (4 files), v8.1_products.png, v8.1_bars.png, v8.1_scan2D_.csv (optional), track_A_v8.1_intrinsic.py, and this note. Versions v7, v7.1, and v7.3 are intentionally omitted to avoid confusion. DOI: 10.5281/zenodo.22904994