A CITY IS NOT A SUM OF VIRTUES: The Ontological Virtue Formula at Civic Scale

“A good city is not a city of good people; the difference lies in a form that belongs to no one” Abstract The Ontological Virtue Formula states that a virtue is Freedom restricted to a domain of human life and given durable form by the Discipline proper to that domain. The formula is stated for an agent. This article asks what it becomes for a community, and finds that the natural extension — collective virtue as the sum of individual virtues over a sum of domains — is false, and instructively so. Domains are restrictions, and restrictions do not add; a union of domains is a domain only if some Discipline is proper to the union. At personal scale one agent holds Freedom and Discipline together. At civic scale the domains are distributed across distinct bearers and the Discipline proper to their union is held by no individual: it is carried by institutions, streets, licensing regimes and custom. This article names that object the civic Discipline and derives its consequences. Four results follow. (1) The Interlock Threshold. Representing the conditioning relations among domains as a non-negative matrix and adopting a linear propagation postulate, effective resistance is the Neumann inverse of the interlock, finite for all admissible resistance profiles if and only if the interlock’s spectral radius is below unity; the amplification diverges at the threshold. This supplies, from the domain side, the critical value that the programme’s Problem V has sought from the agent side. (2) The Leverage–Fragility Identity. The sensitivity of civic strength to improvement in a domain and its sensitivity to damage in that domain are the same matrix entry; the highest-leverage domains for intervention are necessarily the highest-risk domains for shock. There is no interlock configuration in which they differ. (3) The Collective Inversion Theorem. Because the civic Discipline is borne by no individual, it admits deprivation that leaves every individual’s Freedom untouched. A city can therefore invert while each of its inhabitants remains personally free — inversion without external tyranny, the domain conserved and therefore the name conserved: it is still called safety, still called planning, still called community. (4) The Multiplicity and Observability Results. Social pressure, exogenous at agent scale, is endogenous at civic scale; closing that loop yields a self-consistent system whose fixed-point structure is multiple precisely when the conformity response is steeper than a stated bound. Two communities with identical law, identical distributions of autonomy, and identical external resistance may therefore rest at different stable levels. The condition is a threshold in social observability, from which follows the article’s head-to-head prediction against the collective-efficacy literature: observability raises not only the mean of civic outcomes but, discontinuously, their conditional variance. The article specifies a diagnostic instrument — the origination–coherence square, which reads the civic Discipline off the built fabric — six distinguishing predictions, a formal counter-model whose construction would collapse the theory to the aggregative account it displaces, and a pre-registerable protocol for a six-city pilot. Every quantity reported here is generated from author-assigned synthetic parameters and confirms nothing; the numbers exist to verify that the theorems are arithmetically what they claim and to fix the decision rules before data. The central claim is that a good city is not a city of good people, and a bad city is not a city of bad people; both are configurations of a Discipline that belongs to no one. Keywords: Ontological Virtue Formula · Dynamic Freedom Theorem · civic Discipline · domain interlock · Collective Inversion · equilibrium multiplicity · social observability · Capture Law · urban form · Holoviceosis · ALGUILAS-AI Highlights 1. Civic virtue is not aggregative: its Discipline has a bearer no individual holds. 2. A city can invert — safety into surveillance — while every inhabitant stays free. 3. Interlock spectral radius sets a collapse threshold; leverage and fragility coincide. 4. Observability raises not just the mean of civic outcomes but their variance. 5. Built fabric measures civic freedom: origination × coherence, no survey required. Significance Six decades of research on social capital, collective efficacy and the commons have measured the level of a community's collective good and treated its degraded state as a deficit. This article derives a different possibility and shows it is testable: because the Discipline that gives a community its form is deposited in institutions, procedure and stone rather than held by any inhabitant, it can be taken while everyone remains personally free. What follows is not less of the good but its domain-preserving opposite — the square fully provided as a corridor, the festival fully attended as spectacle, the name intact and the orientation reversed. The claim is made to lose. Seven predictions and six falsifiers are pre-registered, one of them in head-to-head contradiction with the collective-efficacy literature: observability should raise conditional variance discontinuously, not merely the mean. A diagnostic instrument reads civic freedom directly off open cadastral data, so the flagship test needs no survey and no proprietary database. Relevance in one line A good city is not a city of good people; the difference lies in a form that belongs to no one, and this article says how to measure it.