Włodarczyk, M. (2026). Addendum II to the Triptych: Resonant Dynamics of Consciousness, v0.2. Panel 1 computes O-information exactly from the distribution you build; panel 2 is a schematic of the model's logic, not measured data.
For three variables, Ω(Ri, Rj, Ct) = I(Ri; Rj) − I(Ri; Rj | Ct) (Section VI.4). Ω < 0: synergy dominates, information is carried by the variables jointly; Ω > 0: redundancy dominates. Condition C is met when −Ω > θΩ, a prior of 0.1 bits with a sensitivity range of 0.05–0.15. Build a joint distribution of three binary variables by mixing three textbook cases.
Ω is the dependence between Ri and Rj, minus the dependence that remains once the context is known.
v0.1 required H(Rij) > H(Ri) + H(Rj). With Rij determined by the participants’ states, H(Rij) ≤ H(Ri, Rj) (Section VI.4), and by subadditivity the joint entropy never exceeds the sum: for every distribution you build, the first bar stays at or below the second.
Checks against the source: the pure copy gives Ω = +1 bit and the pure xor Ω = −1 bit, the three-variable cases of Rosas et al. (2019, Proposition 2: Ω = n − 2 and 2 − n). In the xor preset the same distribution arises whether Rj is generated from an independent prior context (Rj = Ri ⊕ Ct) or Ct is computed from the participants (Ct = Ri ⊕ Rj). Ω cannot tell these apart, which is why Section VI.4 makes the definition of Ct (encoded before, and excluding, the samples of Ri and Rj) part of the criterion. A context that is constant within the window gives Ω = 0 whatever the participants do. Negative Ω establishes synergy dominance in the selected distribution, not causal irreducibility, and not consciousness.
| Ri, Rj, Ct | probability |
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C(t) = F(R, ρ(t), κ(t), θ): relational input at or above the sufficiency threshold θ is necessary but not sufficient for a coherent resonant field R. R stays coherent only while ρ(t) ≥ θ, temporal coupling κ(t) is stable, and input stays within the system's reconstructive capacity (Sections IV.1.4 and IV.6). Choose a route to see which condition fails: the routes differ in their cause, not in what follows.
Schematic: the curves illustrate the logic of the model, not measured data. No scales are yet defined for ρ(t) or κ(t) (Section IX, points 9 and 14) or for reconstructive capacity, and the duration of insufficiency that turns a change of phase into a crossing of the plasticity threshold is not yet specified (Section IX, point 10). Below θ consciousness changes phase; it is degraded, not switched off (Section II.2).
| route | condition that fails | what distinguishes it (Addendum II) |
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