---
identifier: iit:result/feedforward-3node
title: A three-unit feedforward chain has φ_s = 0
vetted_by: "William G. P. Mayner"
formalism: iit-4.0-2026
summary: >-
  A feedforward chain A → B → C has φ_s = 0: the substrate is not strongly
  connected, so a partition cutting in the feedback direction, where there are
  no causal influences, makes no difference. Computed with PyPhi.
substrate: >-
  Three binary units in a feedforward chain A → B → C. A has no inputs and is
  maximally noisy (P(ON) = 1/2 regardless of the past); B copies A; C copies B.
state: "(0, 0, 0) — all units OFF"
phi: 0.0
mip: >-
  The substrate is not strongly connected, so φ_s = 0 by construction: a
  directional partition cutting in the feedback direction severs no causal
  connections and makes no difference. PyPhi reports the null cut over
  (A, B, C), zero connections severed.
pyphi_version: 2.1.dev1610+g0581dae8c.d20260807
script: feedforward-3node.py
see_also:
  - iit:measure/phi-s
sources:
  - ref: iit:ref/albantakis-2023b
    at: >-
      "Integration: Determining the irreducibility of a candidate system"
---

The result is structural, not numerical: integrated information is defined so
that φ_s = 0 whenever the system is not strongly connected in the
graph-theoretic sense, because there is then necessarily a system partition
that loses no information — cutting the connections that run in the feedback
direction, of which a feedforward system has none. No choice of units, state,
or noise changes this; the chain above is the smallest non-trivial witness.

Because φ_s = 0, the substrate does not exist as one whole for itself: it
supports no cause–effect structure and cannot be conscious, whatever function
it computes. This is the feedforward half of the dissociation that the
unfolding argument turns on (see the ledger).

To reproduce, run the script with any install of PyPhi 2.0+:

```
uv run python canon/feedforward-3node.py
```