The claim
In Das, Manikandan and Banerjee’s two optically trapped beads (THEORY-275), the hydrodynamic coupling is symmetric by construction, yet delayed mutual information and transfer entropy read the flow between the beads as two-way under moderate drive of one trap and as one-way under strong drive. What changed the reading was the drive, not the coupling. The record generalizes this: between reciprocally coupled units, a directional information measure locates where a one-sided drive enters and how strongly it dominates, and cannot alone distinguish a symmetric coupling with one-sided input from an asymmetric coupling. Telling them apart needs an intervention on a member.
The record’s earlier title for THEORY-275 asserted this as a general law. The source asserts it only for its system, which is why it is filed here as the record’s claim, with an interpretive warrant: it is untested beyond one linear Gaussian pair, and the strong-drive half rests on numerics.
What it does not say
- That information measures can tell a shared, unrecorded drive from coupling. That is QUESTION-063’s case and is untouched.
- That information moves from one unit to another. “Flow” is the direction of predictive improvement (CLAIM-335).
- That direction tests are useless. With the drive recorded, they locate where it enters.
It bears on CLAIM-172 and CLAIM-167, which read peer or hierarchical architecture from whether coupling runs both ways or one: an observational direction test would class the beads as hierarchical under strong drive. QUESTION-186 asks for the second system that would test the claim.
Note of 2026-10-30: the linear Gaussian pair, computed
The second branch of the defeated_if asks whether, in the linear Gaussian pair, delayed-MI asymmetry is fixed by the coupling and not by the drive. It is not. The eighteenth status review computed exact stationary moments for a pair with symmetric coupling 0.4, relaxation 1 and unit noise, and an unrecorded Ornstein–Uhlenbeck drive (rate 0.5) entering x₁ at strength d (p18/claim396_lgpair.py; controls: no drive gives zero asymmetry, no coupling gives zero MI and TE, the moments match a simulation).
- With no drive, delayed MI and transfer entropy are symmetric. Any d > 0 makes both favour x₁ → x₂, and moving the drive to x₂ reverses the sign.
- At d = 4 and lag 0.5 the symmetric pair reads ΔMI = 0.301, TE₁→₂ = 0.151 and TE₂→₁ = 0.022. A pair coupled one way, x₁ → x₂, with the same drive reads 0.292, 0.150 and 0.024 (p18/claim396_match.py). The two are close on all three measures, which is this claim’s second half for an unrecorded drive.
- One-way flow is not monotone in the drive here. TE₁→₂/TE₂→₁ rises to about 230 at d = 2 and falls back to between 4 and 8 for d from 4 to 64, because x₂ comes to carry information about the unrecorded drive. THEORY-275’s one-way reading under strong drive is for a recorded drive and the fitted bead model, which this model is not.
- With the drive recorded, transfer entropy conditioned on its past separates the two pairs without intervention: TE₂→₁ given the drive is 0.0067 for the symmetric pair and exactly 0 for the one-way pair (p18/claim396_conditioned.py). “Telling them apart needs an intervention on a member” holds at most where the drive is unrecorded.
This is THEORY-275’s model class, linear, Gaussian and two-body, so it is not QUESTION-186’s second system.
Note of 2026-10-30: what holds it back
It generalizes one linear Gaussian pair, and the test it names is a second system with a known reciprocal coupling driven at graded strengths (QUESTION-186), which has not been found. The computation of 2026-10-30 confirms that the drive sets the direction within that model class and reaches no further.