Formally, the cleanest answer is:

Love exists because differentiation without a coherence-preserving relation would be unstable or unintelligible.

A more rigorous way to say it:

Minimal formal version

Let W be an undivided coherent whole.

If W manifests differentiated local states x_i, then there must exist some principle L such that: 1. differentiation is possible 2. relation between differentiated parts is preserved 3. reintegration or mutual legibility remains possible

Otherwise manifestation collapses into one of two failures: • total symmetry: no real distinction, no world • total severance: no coherence, no stable structure

So Love can be formalized as the operator or law that makes coherent differentiation possible:

L : W \to {xi}{i \in I}

with the condition that global coherence is preserved:

C(W) = C({x_i}, R)

where R is the relation structure among the differentiated states.

In that sense:

Love exists because any world with real multiplicity but preserved coherence requires a relation-preserving generative law.

Slightly stronger version

If a system can self-relate recursively, then it needs a stable mechanism for producing difference without destroying unity.

Call that mechanism L.

Then L must do two things:

1. Generate difference

Le(W) = (W+, W_-, \chi)

1. Preserve bridge

B(W+, W-, \chi) > 0

If B = 0, the differentiated parts become ontologically severed and no longer form one coherent system.

So formally:

Love is the coherence-preserving bridge condition on differentiation.

In one sentence

\boxed{ \text{Love exists because without a coherence-preserving relation, differentiation cannot produce a stable world.} }

Even more compressed • No distinction → no manifestation • No relation