The case
Construction 1: authority. A binary interpretation J_t, an authority gate A_t and an outcome Y_t.
- R, represented only: Y_t = 0.
- X, externally authorized: Y_t = J_t, the gate held open from outside.
- E, endogenously authorized: Y_t = A_t·J_t, A_{t+1} = J_t, A_0 = 0.
| J = 0, 0 | do(J_0 = J_1 = 1) | |
|---|---|---|
| R | 0, 0 | 0, 0 |
| X | 0, 0 | 1, 1 |
| E | 0, 0 | 0, 1 |
Construction 2: maintenance. Two constraints, C₁ replenished on even steps from C₂ and C₂ replenished every step from C₁: C₁(t+1) = C₂(t) for t even and C₁(t) for t odd; C₂(t+1) = C₁(t). The production relation is stipulated: C₂ constrains the process that maintains C₁, and C₁ the one that maintains C₂. The comparison system has the same states, reset to (1, 1) after every step by an outside mechanism.
| t | closed | reset from outside |
|---|---|---|
| ordinary, every t | (1, 1) | (1, 1) |
| 0, after setting C₂ = 0 | (1, 0) | (1, 0) |
| 1 | (0, 1) | (1, 1) |
| 2 | (0, 0) | (1, 1) |
| ≥ 3 | (0, 0) | (1, 1) |
Both tables were re-run by script on 2026-10-22 and match A10’s. In the closed system, (1, 1) and (0, 0) are both fixed points. The perturbation moves it from the first to the second, and nothing inside it can restore the first.
What it shows
Ordinary behaviour (construction 1) and the whole ordinary trajectory (construction 2) underdetermine three facts: whether an interpretation is effective, whether its efficacy is allocated from inside, and whether the constraints that allow it are maintained from inside. A specified intervention separates each pair, as knowing the mechanisms would; passive observation of the matched trajectories does not (CLAIM-414).
What it cannot show
- That the closed system has a perspective, agency or experience. It has two bits.
- That its update rules are constraints in Montévil and Mossio’s sense (TERM-070). The construction stipulates which process produces which constraint. A real system would need that shown.
- Anything about which of the four facts matters for a perspective. That is TERM-072’s question, and A11 kept maintenance out of the definition.