AIM Framework glossary
Dual-Locus Ignition Theorem
Canonical definition
Canonical Definition. The Dual-Locus Ignition Theorem is the formal result that ignition of the collective crisis transition admits exactly two position-indexed sufficient conditions, located at the two extremes of the distribution of provision and authority. The floor condition is sustained Appetite deficit at the worst-off segment at or beyond the unique critical depth at which Mimetic amplification first outruns correction across the guarded range of collective Belief (the Floor-Breach Ignition Corollary); it contains no leadership variable. The apex condition is an M-Captured leader whose Belief has crossed the action threshold and whose authority exceeds the imposition threshold (the ignition geometry of the Leadership Compression Principle); it contains no population variable. Either condition alone is sufficient, neither requires the other, and mid-distribution positions satisfy neither, because provision above the floor generates no fidelity forcing and authority below the imposition threshold provides no bypass. Formal statement: Appendix A, A.5.8.7. Prose derivation: Chapter 17, Section 17.7.8.
Explanation
A society's capacity to tip into crisis lives at its two ends, not in its middle. Deprive the bottom deeply enough and the transition ignites from below, whatever the leadership is doing — the mass-mobilised discharge whose historical face is revolutionary rupture. Concentrate authority in an M-Captured leader and the transition can be imposed from above, however well-provisioned the population is — war on executive decision. The two loci also differ in kind. The floor drive is extensive and slow: it takes deprivation at population scale to arm it, and it can be switched off entirely by provision, which is why universal Appetite-floor security is an entailment of Subcriticality Maintenance rather than a welfare preference appended to it. The apex drive is a point source: one Individual suffices, and it cannot be switched off, because no level of provision closes a Mimetic deficit; it can only be gated by authority design. A society can provision its way out of the floor locus but can only govern its way out of the apex locus. (The term is unrelated to Bipolar Convergence, where "bipolar" denotes two factions converging on each other as mutual scapegoats; here it denotes the two extremes of the provisioning-authority distribution.)
Epistemic status
Framework-Specific Named Result (Theorem; qualitative register, Appendix A).