Journal — StormNet
The 0.71 question
A delay parameter near 0.71 kept turning up in the Lab's simulations. The ice storm gave a real signal to test it against. It is a hypothesis, and it is labeled as one.
Some entries in this journal report what was measured. This one reports what was suspected, so that the suspicion is on the record before any test of it.
The model
The Lab's physics work uses a phase-field equation to describe boundaries between two states. A phase field is a continuous variable that is one value inside one state, another value inside the other, and changes smoothly across the boundary. The Allen–Cahn equation is the standard form; it describes how such a boundary moves and sharpens over time. Rain becoming sleet becoming ice is, in this description, a boundary passing through a place.
The Lab's variant nests the equation in itself: the output of one pass is fed back as a delayed input to the next, scaled by a factor β (beta). In simulation, values of β near 0.71 produce a distinctive result. The system's energy rises, falls, and then locks onto a plateau instead of decaying to zero. The boundary persists. Values much lower let it die; values much higher make it unstable.
The number is close to 1/√2, which is roughly 0.707, and close to α* = φ/√5, roughly 0.7236, the constant used in the cavity model. Whether those coincidences mean anything is exactly the question.
Why the storm rig is the test
The two-device rig is a physical version of the nested delay. The outdoor unit is the raw signal. The indoor unit is the same signal after passing through walls, delayed and damped. If the nesting picture is right, the ratio between them during a phase transition should sit near β, and the differential should hold a lock while ice is forming rather than washing out.
What has been done
A cross-assistant analysis of the January data flagged what it called a clean phase lock in the outdoor signal during the late storm, and the Lab's own simulation reproduced a locked plateau at β = 0.71. Those are two observations, one on real data and one on synthetic data, made by people looking for the number.
That is not validation. Validation would require the ratio to be computed by a preregistered method on a held-out event, compared against a null model that does not know about β, with the threshold for "lock" fixed in advance. None of that has been done. Until it is, 0.71 is an interesting number, and this entry is filed under hypothesis.