A Purely Model-Theoretic Analysis of Structural Collapse: Application of the Field-Theory Cultivation Framework

Abstract

This paper presents a dimensionless, field-theory-inspired coherence model for analysing regime stability. Structural collapse is defined strictly as the irreversible crossing of a self-consistency threshold, formalised by the governing equation $C=E+F+L-(S+X)$. The identical model is applied, without prediction or normative judgement, to the late-Soviet Union (1985–1991) and to contemporary China. The analysis isolates structural mechanisms through controlled counterfactual comparison.

1. Definition of the Collapse Field

The collapse field is reached when structural self-consistency declines below the minimum level required to sustain simultaneous fiscal solvency, coercive capacity, baseline societal compliance, and external control:

$$C(t)<C_{\text{crit}}$$

Normalised balance-sheet formulation:

$$C(t)=E(t)+F(t)+L(t)-(S(t)+X(t))$$

with the collapse condition (zero-threshold normalisation):

$$E(t)+F(t)+L(t)-(S(t)+X(t))<0$$

Irreversibility requires persistence:

$$C(t)<0\text{for}\mathrm{\Delta }t\ge T_{\text{crit}}$$

where $T_{\text{crit}}$ is the irreversibility time threshold at which repair elasticity is exhausted.

2. Core Variables and Directional Effects

Variable	Definition	Sign in $C$
$E$	Economic energy density (growth, industrial completeness, technological autonomy)	Positive
$F$	Fiscal capacity (tax base, borrowing space, reserves)	Positive
$L$	Institutional cohesion (policy execution, military loyalty, central–local control)	Positive
$S$	Social tension and internal friction (youth unemployment, inequality, repression costs)	Negative
$X$	External pressure (sanctions, technological blockade, war risk)	Negative

Figure 1 illustrates the illustrative 0–10 scores for each variable, enabling direct visual comparison between the two cases.

3. Necessary Conditions for Phase Transition

Collapse requires the simultaneous satisfaction of three independent conditions:

① Prolonged sub-critical growth and debt overhang $g<2\mathrm{\%}(\ge 5\text{ years})\text{and}\text{Debt/GDP}>300\mathrm{\%}$

② Entrenched high youth unemployment $\text{Youth Unemployment}>25\mathrm{\%}(\ge 3\text{ years})$

③ Abrupt external shock (comprehensive financial sanctions, major conflict, or closure of principal export markets)

The highest-risk pathway combines chronic internal dissipation with sudden external impulse, producing nonlinear exhaustion of repair capacity.

Figure 3 provides a schematic representation of the three-condition resonance required for phase transition.

4. Counterfactual Application: Soviet Union (1985–1991)

Illustrative 0–10 scaling under the identical equation yields $C=-5$, sustained over multiple years, precipitating irreversible phase transition. The dominant driver was rapid erosion of institutional cohesion $L$.

5. Application to Contemporary China (Conservative Parameter Ranges)

Variable	Estimate	Rationale
$E$	6–7	Positive growth, intact supply chains, rising technological autonomy
$F$	5–6	Central controllability despite local debt pressure
$L$	7–8	Strong military cohesion, absence of separatist trends
$S$	5–6	Youth pressure present, but social order intact
$X$	6	Technological containment short of full sanctions or warfare

Computation yields $C=+6>0$.

Figure 2 visualises the positive and negative aggregate contributions, confirming the positive coherence index for the contemporary case.

6. Structural Divergence

Factor	Soviet Union	Contemporary China
Ethnic separatism	High	Extremely low
Military loyalty	Eroding	High
Economic system	Rigid central planning	Hybrid market
Global integration	Low	High
Supply-chain resilience	Weak	Strong

7. Critical Observational Window and Conclusion

The decisive observation period is 2028–2033, when demographic pressure, local-debt maturity waves, and potential intensification of Sino-American technological rivalry converge.

Under the model, collapse-field entry is neither inevitable nor precluded; it requires simultaneous multi-variable resonance, particularly rapid decline in $L$ alongside the three necessary conditions. At present, sustained institutional cohesion $L$ places the system in a distinct stability class from the Soviet case.

Note on the Structural Self-Consistency Threshold Regime collapse occurs only when the state simultaneously loses the capacity to (1) collect sufficient revenue, (2) sustain and direct its coercive apparatus, (3) secure baseline compliance from core constituencies, and (4) project credible external control. At this threshold the system ceases to be structurally self-reproducing, irrespective of public discourse or episodic unrest.

This framework, augmented by the above visualisations, offers a transparent, replicable metric for comparative structural analysis across political regimes.