Extensions of the Model of Hierarchical Structure: External Influence, Localisation of Power, and the Point of Irreversibility (Part II)

Part II of a two-part series extending the framework of Part I, in which we proved that every hierarchical structure composed of humans decays in finite time almost surely. Here the minimal stochastic picture is enlarged in four directions, and then self-critically stress-tested. First, the structure is no longer passive: influential hierarchies actively reshape their environment via a stabilisation function φ (Φ), but simultaneously attract counter-pressure Ψₑxt (Φ) ~ Φ^κ with κ ≥ 1, yielding a non-trivial optimum Φ* beyond which further influence shortens expected lifetime — together with a shadow consequence (reduced selective pressure raises ε). Second, power is relocated: it is not an attribute of top entities but a multiplicative function Mₖ (t) = g (k) · Π₉<₊ σⱼ (t) of the obedience of lower levels, with enforcement effectiveness ηₖ lowering the reversibility threshold σ*ⱼ; this introduces a third decay channel τᵣefus (mass disobedience) alongside the qualitative and coalitional channels of Part I. Third, the point of irreversibility is formalised as an absorbing set X† in a four-dimensional state space, with a phase-transition boundary and early-warning signals drawn both from the framework (turnover, implementation fidelity, subjective success estimates) and from bifurcation theory (critical slowing down, variance increase, synchronisation) ; a fourth channel is added through external network reach, with the assortative assumption that top entities hold influential external contacts — so a small group of high-level defectors can push the opposition share π (t) past π* without a mass uprising (empirically π* ≈ 0. 25 for norm change, ≈ 0. 035 for regime fall). Fourth, we argue that the observed stability of real institutions is inconsistent with a purely stochastic model: what suppresses the predicted chaos is deliberate psychological steering — conformity, obedience to authority, in-group/out-group dynamics, cognitive shortcuts, framing, dissonance reduction, ritualisation — operated continuously by priests, educators, officers, propagandists, HR specialists; the formal model therefore describes an unsteered limiting case and supplies a lower bound on lifetime. The closing sections are openly self-critical: long-lived institutions (the Catholic Church, the British monarchy, Oxford colleges) survive through antifragile redundancy rather than optimisation, silent adaptation of identity and purpose (the ship-of-Theseus mechanism), and sacred meta-rules blocked from revision — phenomena the formalism captures only in part. We further acknowledge three structural limits of the whole project: non-simulability (realistic populations, heterogeneity, and time scales exceed current computational and conceptual capability) ; practice (real institution-builders use heuristics from Machiavelli, Sun Tzu, Cialdini, not stochastic models) ; and luck (survivorship bias selects lucky trajectories, whose retrospective explanations rationalise outcomes after the fact). The framework is thus offered not as a recipe but as a language of retrospective reflection, a limiting-case benchmark, and a critical tool against theories of long-lived structures that are in fact rationalisations of survivorship. The Decay Theorem of Part I still applies; Part II quantifies and qualifies it. Keywords: hierarchical organisations, institutional decay, external influence, obedience and power, irreversibility, phase transitions, network reach, tipping points, psychological steering, antifragility, silent adaptation, survivorship bias, formal social theory