From Identity to Dynamics: A State-Space Formulation of the Boundary Process Hypothesis

Pharmacological unconsciousness is not a single phenomenon. Propofol produces deep behavioral unresponsiveness with absent subjective reports; xenon produces comparable unresponsiveness through distinct molecular pathways; ketamine produces behavioral unresponsiveness in which rich internal experience nevertheless persists, as evidenced by post-emergence reports of dissociative phenomenology. Extending the earlier Boundary Process Hypothesis (BPH), which proposed that consciousness may be structurally related to the quantum-to-classical decoherence transition, we develop a minimal four-variable state-space formulation in which candidate consciousness states evolve along axes of global complexity (C), internal recurrence (R), external coupling (E), and a boundary-sensitive proxy (Q). The dynamics are specified as coupled nonlinear ordinary differential equations with drug-specific input terms. We define a dissociation index ΛD (t) = R (t) / (E (t) +ε) that captures the recurrence-coupling imbalance characteristic of ketamine-induced states. The central empirical signature distinguishing BPH from classical alternatives is stated as a residual prediction: when propofol and xenon are matched on C, R, and E through dose titration, any systematic difference in Q-proxy measurements would constitute evidence for a boundary-specific contribution that classical models do not naturally predict. This work does not resolve the ontological question of why boundary dynamics should correspond to phenomenal experience, nor does it specify the microscopic-to-macroscopic coupling mechanism in full. What it offers is a dynamical scaffold in which BPH's predictions become empirically constrained by pharmacological dissection. The framework should be read as a research program rather than a completed theory. This is a hypothesis paper / theoretical framework, not an empirical study. Update in v1. 6. 1: Manuscript revised in response to four-AI evaluator critiques (Perplexity, GPT, Gemini, internal review) across multiple rounds. Substantive changes from v1. 4: - §4. 3: explicit caveat that Q's deterministic ODE form is provisional, with underlying dynamics being noisy/quantum (mean-field summary). - §4. 5: Q explicitly positioned as "high-risk, high-information secondary contribution"; nested-model comparison promised and now delivered (Supplement S3). - §6. 4: R-proxy validity criterion stated; broad-band spectral exponent recommended; raw late-TEP magnitude excluded with explicit reasoning. - §7. 3: acknowledgment that the Q equation does not include an explicit external-magnetic-field term, with deliberate-omission rationale. - §10. 4: concrete BPH-vs-RPM discrimination protocol using controlled external magnetic fields (~µT to mT range). - §11. 2 Stage 1: cross-references to Supplements S2 and S3, with explicit recommendation to break the (aQG, aQD) structural degeneracy via G or D modulation. Two new supplements embedded in the main PDF: Supplement S2 — Stage 1 Preliminary Analysis (pages 42–48): A first-pass consistency check of the ΛD prediction against publicly reported aggregate statistics from Sarasso et al. (2015) and Colombo et al. (2019). The framework is consistent with the data when broad-band spectral exponent is used as the R proxy, but not when raw late-TEP magnitude is used—reinforcing the proxy-validity criterion in §6. 4. Supplement S3 — Identifiability and Parameter Recovery Analysis (pages 49–58): A synthetic-data exercise with four sub-analyses— (A) parameter recovery, (B) profile likelihood, (C) nested 3-variable vs 4-variable model comparison, (D) sensitivity analysis. Key findings: the C-R-E classical backbone is identifiable from public-style data; the Q-coupling parameters aQG and aQD are structurally non-identifiable from steady-state data without independent G or D modulation; the 3-variable reduction is statistically preferred for fitting (BIC) but cannot make the BPH-distinctive ΔQ residual prediction; ΔQ is robust to all parameters (<7% effect under ±20% perturbation).