A5's Black Swan: Frankfurt, Oikeiôsis, and Hamilton's Rule: Searching for a Person Who Loves No One, and Finding That A5 Was Never One Variable

A5 — constitutive attachment to a specifically loved other — is this corpus's most load-bearing premise and its least stress-tested one. This paper goes looking for A5's black swan: a documented human case of someone who loves no one, which would falsify the universal claim every downstream formal result depends on. It does not find one, and argues the search itself, conducted properly, reveals something the corpus had not yet stated — that A5 was never a single variable. Harry Frankfurt's The Reasons of Love supplies the closest attempted counterexample — a person whose only object of love is themselves — and Frankfurt's own analysis, examined closely, shows self-love failing to be a counterexample by satisfying the same structural definition constitutive attachment requires, rather than by falling outside it. Stoic oikeiôsis, from Cicero and Diogenes Laertius through Hierocles's concentric circles, independently derives a specific ordering: self-preservation is the appetitive starting point from which other-directed concern for kin and community is a later, discounted extension, never a substitute. This corpus's own prior grounding of A5 in W. D. Hamilton's (1964) inclusive fitness mathematics, cited in the Sandbox Geometry for a different purpose, turns out to encode this exact ordering formally: Hamilton's Rule requires no discount for self-directed benefit, since relatedness to oneself is unity, while discounting other-directed benefit by a relatedness coefficient always below one — the equation the corpus had already cited, read for what it says about self versus other rather than only for why attachment exists at all. Buddhist non-attachment, examined against its own primary sources rather than its popular gloss, targets a different structure entirely: grasping, not attachment as such, with active compassion (karuṇā) toward specific suffering beings retained as a cultivated virtue throughout the tradition's ethical literature. Clinical psychopathy comes closest to a genuine null case, but even there the deficit is measured relative to a species-typical baseline the disorder is defined against, not evidence the baseline itself is optional. The paper's synthesis is that A5 decomposes into two structurally distinct components — self-directed and other-directed — that the corpus has, until now, treated as a single scalar. This sharpens rather than weakens two of this corpus's own prior findings: The Autoimmune Munus's mapping of A5 onto Esposito's communitas, shown here to describe only the other-directed half, with the self-directed half structurally closer to Esposito's own immunitas; and Grief-stage activation, for which the Antonine Plague case already inside this corpus's historical record supplies suggestive, previously unread evidence that political activation tracks non-clinging, actively caring attachment specifically, not attachment or non-attachment as undifferentiated wholes.