Accumulation, War, Party Direction, and the Extinction of Capitalist Categories

1 Why another revision was necessary

The previous paper corrected a genuine political error. It replaced an additive “transition potential” with a conjunctive seizure gate, separated the bourgeois state from the proletarian state, refused to equate nationalization with communism, distinguished the transitional economy from lower and higher communism, and made international extension a necessary condition. Those corrections remain.

The revision was nevertheless incomplete in four places.

First, the political crisis was still supplied as an external pulse. The equations could show how a political system responded to a disturbance, but not how capitalist accumulation itself generated the crisis environment. A Marxian reconstruction cannot treat the decisive disturbance as an unexplained rectangle drawn by the modeler. Capital accumulation, the rising organic composition of capital, counter-tendencies, overproduction, credit, imperialist rivalry, and war have to appear inside the causal architecture rather than outside it. The Italian Left’s economic work consistently treated the cycle of accumulation, the tendential fall of the profit rate, destruction of capital, and imperialist conflict as parts of one historical process (International Communist Party 1967, 1976).

Second, the old variable for mass organs was still too close to a council-form variable. Workers’ organizations can arise from defensive struggle without already constituting proletarian political power. Conversely, a party cannot exercise dictatorship without organs through which the class is organized. The proper distinction is therefore not “party or councils” but among mass class organs, the party’s political direction within them, and organs unified toward the conquest and exercise of power (Bordiga 1921; Communist International 1920; International Communist Party 1969a).

Third, the external programmatic predicate was honest but incomplete as a treatment of degeneration. Code cannot certify the historical party. Yet the formal party is not sealed off from defeat, isolation, tactical improvisation, military emergency, or subordination to a national state. The Left’s balance sheet of the Communist International insists that the party is both a factor and a product of historical development and can be deformed by the material conditions in which it acts (International Communist Party 1965, 1974, 1985). The model therefore keeps programmatic admissibility external while adding a distinct internal pressure variable that can damage the formal organization.

Fourth, the planning objective treated labour time only indirectly and ecology as a soft penalty. Marx distinguishes planned distribution of social labour time from the regulation of exchange value by labour time. In communal production, economy of time remains necessary precisely because the purpose is to reduce necessary labour and expand disposable time, not to reproduce value in another accounting language (Marx 1857, 1858). Ecological and material limits are also not prices to be traded against shortages without limit. The revised planning problem therefore places need and species constraints in the feasible set itself.

The resulting paper is not a claim that a finite dynamical system has become “the science of revolution.” It is a narrower claim. A formal reconstruction can expose hidden substitutions, show which conclusions follow from stated premises, and reveal where the model still depends on political judgment or missing historical data. That is enough to make it useful, provided its limits are not concealed.

2 Source corpus and the boundary of formalization

2.1 Programme before model

The phase sequence follows Marx’s distinction among capitalist society, the revolutionary political transition, the lower phase of communist society, and the higher phase (Marx 1875). Lenin distinguishes destruction of the bourgeois state from the proletarian state of transition and from the later withering of political power (Lenin 1917). The Communist International and the Italian Left assign the Communist Party an indispensable role that cannot be transferred to parliament, trade unions, councils as a constitutional form, or the national state (Communist International 1920; Bordiga 1921; International Communist Party 1951).

The economic sequence is equally restrictive. State ownership is not the abolition of capital. Generalized wage labour, money, production for exchange, autonomous enterprise accounts, value regulation, and alienable claims are incompatible with communist production even when the juridical owner is the state (Bordiga 1952; International Communist Party 1957). The lower phase has abolished those specifically capitalist mediations but still carries bourgeois right and inherited social divisions. The higher phase presupposes their disappearance together with classes and the political state (Marx 1875; Lenin 1917; International Communist Party 1969b).

Internationalism is not a moral addition. The 1948 programme rejects the completed construction of socialism within one country and subordinates every proletarian state to the world revolution and the world party (International Communist Party 1948b, 1978). Imperialist war is not treated here as an accidental foreign-policy variable. Competition among capitals and states, the struggle over markets and raw materials, and the destruction of accumulated capital connect economic crisis to war; revolutionary defeatism connects war to proletarian politics (Lenin 1915; International Communist Party 1976).

2.2 The historical party is not an output variable

Let \[A_{\mathrm{prog}}\in\{0,1\}\] be an external assumption. It means only that the organization whose material capacity is represented below by \(P\) is admitted, for the purpose of the formal experiment, as continuous with the reconstructed programme. The model does not generate \(A_{\mathrm{prog}}\) from membership, polling, electoral success, internal votes, or historical victory. It cannot decide whether a living organization embodies the historical party.

This limitation is not cured by replacing the Boolean with a continuous score. That would merely introduce pseudo-precision. The unity of historical programme and formal organization is a political-historical judgment. What can be modeled are some material pressures on the formal organization after that judgment has been made. The distinction is: \[\begin{aligned} \text{programmatic admissibility }A_{\mathrm{prog}} &\neq \text{ organizational capacity }P,\\ P&\neq \text{ deformation pressure }F. \end{aligned}\]

2.3 Kinds of claims

The paper keeps four kinds of statements separate:

1. Programmatic premises: interpretations of the cited corpus. These remain open to textual and political criticism.

2. Exact formal results: consequences of definitions and equations, such as no forward phase skipping or the positive equilibrium of a category under positive reconstitution pressure.

3. Numerical experiments: trajectories of a disclosed parameterization. They are not historical estimates.

4. Unmodeled determinations: concrete tactics, the identification of the party, the formation of legitimate needs, and the full world history of accumulation and war.

A theorem can be exact conditional on a premise without proving the premise. Conversely, the fact that a premise is political does not make its formal consequences mathematically indeterminate.

3 The autonomous capitalist stress kernel

3.1 Value variables

The earlier Goodwin–SFC module remains archived as a separate analysis of distributive cycles and accounting closure. It is no longer used as the generator of revolutionary crisis. The new transition model begins from a reduced value-theoretic kernel.

Let \[o=\frac{C}{V}>0, \qquad m=\frac{S}{V}>0,\] where \(C\) is constant capital, \(V\) variable capital, and \(S\) surplus value. The value rate of profit is \[\rho=\frac{S}{C+V}=\frac{m}{1+o}. \label{eq:profit}\] The identity is elementary, but it places the model on a different conceptual ground from a wage-share/profit-share oscillator. The organic composition \(o\) and the rate of surplus value \(m\) are distinct. Technical accumulation raises \(o\); intensified exploitation raises \(m\); crisis and war may devalue or destroy constant capital. The tendency and its counter-tendencies therefore coexist in the state variables rather than being replaced by one reduced-form profitability coefficient (International Communist Party 1967, 1976).

The proposition is not a proof that the historical rate of profit falls monotonically. It states the direction of the organic-composition tendency and the exploitation counter-tendency inside the value identity. The actual path depends on both.

3.2 Accumulation, overaccumulation, rivalry, war, and crisis

Let \(a,h,\iota,w,\chi\in[0,1]\) denote accumulation intensity, overaccumulation, imperialist rivalry, war intensity, and crisis intensity. With \(\Lambda(z)=(1+e^{-z})^{-1}\) and \(\Pi_{[l,u]}\) denoting truncation of a target to a bounded interval, the standard parameterization is:

\[\begin{aligned} \dot o &= \eta_o\left(\Pi_{[1,8]}[1.60+5.20a-1.20\chi-0.80w]-o\right), \label{eq:o}\\ \dot m &= \eta_m\left(\Pi_{[0.5,4]}[1.15+2\left[0.32-\rho\right]_++0.70(1-E)+0.35\chi]-m\right), \label{eq:m}\\ \dot a &= \eta_a\left(\Lambda[-0.70+5(\rho-0.26)-2.40h-1.20w]-a\right), \label{eq:a}\\ \dot h &= 0.16a(1-h)-0.05\chi h-0.08wh, \label{eq:h}\\ \dot\iota &= \eta_\iota\left(\Lambda[-2.80+4.70h+3\left[0.30-\rho\right]_++1.10a]-\iota\right), \label{eq:iota}\\ \dot w &= \eta_w\left(\Lambda[-3.50+5\iota+2.50h]-w\right), \label{eq:war}\\ \dot\chi &= \eta_\chi\left(\Lambda[-3.20+5.20h+4.20\left[0.29-\rho\right]_++3.40w]-\chi\right). \label{eq:crisis} \end{aligned}\]

There is no function \(g(t)\) and no rectangular pulse. Accumulation raises the organic composition and overaccumulation. Falling profitability and overaccumulation intensify rivalry. Rivalry and overaccumulation raise war pressure. Overaccumulation, low profitability, and war raise crisis intensity. Crisis and war in turn destroy or devalue accumulated capital and reduce accumulation, creating a new cycle.

These equations are not an econometric estimate of world capitalism. They are a compact autonomous closure that restores the direction of causation missing from the previous architecture. Different Marxian crisis theories can modify the targets without reintroducing an exogenous political shock.

This is deliberately conditional. The equations do not assert that every capitalist trajectory must cross a revolutionary threshold. They show how crisis can be generated by capitalist states rather than imported from outside the model.

4 Party, class organs, contested authority, and power

4.1 Three objects instead of one council variable

The political block distinguishes:

When \(A_{\mathrm{prog}}=1\), party direction follows \[\dot J=\gamma PE(1-J)-\delta(1-P)J-\zeta FJ. \label{eq:direction}\] If \(A_{\mathrm{prog}}=0\), \(\dot J=-\delta J\). Politically unified organs follow \[\dot D=\eta_D(JE-D). \label{eq:power-organs}\]

Equation [eq:power-organs] prevents the form of the council from being equated with its political content. \(E\) can rise while \(J\) and \(D\) remain near zero. At the same time, \(D\) cannot be produced by the party in the absence of mass organs, because its target contains \(JE\).

4.2 Contested authority is not yet proletarian dual power

The first phase transition is \[\mathcal G_{0\to1}=\mathbf{1}[E\ge E_1,\ M\ge M_1,\ B\le B_1]. \label{eq:contested}\] It records a revolutionary crisis in which class organs and mass action contend with a weakened bourgeois state. The phase is named contested authority, not proletarian dual power, because it does not yet require party direction.

The seizure gate is \[\mathcal G_{1\to2}=\mathbf{1}[ A_{\mathrm{prog}}=1, P\ge P_c, E\ge E_c, J\ge J_c, D\ge D_c, M\ge M_c, B\le B_c, F\le F_c]. \label{eq:seizure}\] The gate is conjunctive. Mass action does not substitute for the party; the party does not substitute for the organized class; a collapsing state does not automatically become proletarian power; and an organization materially deformed beyond the stated threshold cannot open the gate merely because it retains a name.

4.3 Destruction of the bourgeois state

At seizure the hybrid reset is \[B^+=0, \qquad S^+\ge0.66, \qquad R^+\ge0.22, \qquad g_1^+\ge0.42. \label{eq:reset}\] \(B\) is bourgeois-state capacity, \(S\) proletarian coercive class-state capacity, \(R\) organized counterrevolution, and \(g_1\) the initial regional centre of proletarian power. The old state is broken; it does not continuously change its class content. A distinct proletarian state is constituted, while counterrevolution and world-capitalist pressure remain.

5 Formal-party deformation and counterrevolution through the state

The external predicate \(A_{\mathrm{prog}}\) remains unchanged by the ODEs. A separate state \[F\in[0,1]\] represents material pressure toward deformation of the formal party’s activity and its subordination to the national state. It is not a numerical verdict on doctrinal truth. During the dictatorship its target is \[\dot F=\eta_F\left(\Lambda[\ell_0+2(1-\overline G)+1.15S+w+1.30R-1.70E-2J+\zeta_b]-F\right), \label{eq:deformation}\] where \(\zeta_b\) is a disclosed scenario parameter representing additional bureaucratic pressure.

Isolation, prolonged coercive emergency, war, and counterrevolution raise the pressure. Strong mass organs and sustained party direction reduce it. \(F\) lowers the targets of \(P,J,\) and \(D\), raises the reconstitution pressure on capitalist categories, and enters both the seizure gate and the state obstruction index.

A restoration edge is permitted when \[F\ge F_R \quad\text{and}\quad \min(P,J)<P_R. \label{eq:restoration}\] The reset restores a positive bourgeois-state coordinate, extinguishes the proletarian-state coordinate, and sharply reduces party direction and organs of power. This does not claim that Stalinization can be reduced to one scalar. It adds the previously absent possibility that counterrevolution operates through deformation of the formal party-state relation rather than only through an external defeated class.

The first assertion is an exact gate theorem. The second is a formal representation of a historical possibility, not an empirical diagnosis of any particular party or state.

6 International revolution as a network

6.1 Regional extension

The scalar \(G\) of the previous paper is replaced by three regional states \[\boldsymbol{g}=(g_1,g_2,g_3)\in[0,1]^3,\] representing an initial revolutionary centre, another major industrial region, and a peripheral or dependent region. The labels describe positions in an uneven world system, not fixed countries.

For \(i=1,2,3\), \[\dot g_i=\eta_g\left[(1-g_i)\kappa PD(1-F)\left(\ell_i+\sum_j a_{ij}g_j\right) -\left(\delta_i+0.25R+0.15w+0.20F\right)g_i\right]. \label{eq:network}\] The first term combines party capacity, organs of power, network transmission, and a region-specific seed. The second combines regional repression, counterrevolution, war, and party deformation.

Define \[\overline G=\sum_i\omega_i g_i, \qquad G_{\min}=\min_i g_i, \qquad G_{\mathrm{eff}}=\sqrt{\overline GG_{\min}}. \label{eq:gstats}\] The weighted mean records global reach; the minimum prevents one strategically decisive macro-region from disappearing inside an average; the effective extension enters the extinction dynamics. This remains a minimal network. It does not model every state, military front, productive specialization, or national party section.

6.2 Why one-country completion remains impossible

The gate to lower communism requires both \[\overline G\ge \overline G_L \quad\text{and}\quad G_{\min}\ge G_{\min,L}.\] The gate to higher communism requires stronger versions of both conditions. Thus a high value in the initial region cannot compensate for near-zero extension elsewhere.

The proposition is definitional but no longer rests on a single scalar. It also affects the continuous category dynamics described next.

7 The extinction of capitalist relations

7.1 Legal ownership and social relations

The transitional block separately represents:

Legal socialization follows an independent target flow and therefore cannot imply category extinction. For each \(X\in\{W,\mu,C,A,V,I\}\), \[\dot X=-\alpha_XSQG_{\mathrm{eff}}(1-F)X +\beta_X\left[(1-\overline G)+0.60w+0.70F\right](1-X). \label{eq:category}\] The first term represents deliberate abolition under proletarian power, planning, and international extension. The second represents reconstitution pressure from world capitalism, war, and internal deformation.

Petty-commodity production follows the slower law \[\dot Y=-\alpha_YSQG_{\mathrm{eff}}(1-N)(1-F)Y +\beta_Y\left[(1-\overline G)+0.80N+0.40w\right](1-Y). \label{eq:petty}\] Its disappearance depends not only on legal measures but on the material superiority and adequacy of social production. This is a minimal representation of the middle-strata and agrarian problem; it is not a detailed agrarian programme.

7.2 Positive category floors

On an interval where the coefficients of equation [eq:category] are constant, write \[e_X=\alpha_XSQG_{\mathrm{eff}}(1-F), \qquad r_X=\beta_X[(1-\overline G)+0.60w+0.70F].\] Then \[X^*=\frac{r_X}{e_X+r_X}. \label{eq:floor}\]

This result is stronger than a gate label. If international capitalist pressure, war, or deformation remains positive, the selected capitalist relation is continuously regenerated in the closure. The exact numerical floor is model-dependent; the qualitative statement follows from positive reconstitution pressure.

7.3 Class differentiation

Class differentiation follows a stable filter \[\dot K=\eta_K(\kappa-K), \label{eq:class}\] with \[\kappa=.20W+.08\mu+.16C+.14A+.16V+.12I+.14Y. \label{eq:kappa}\] The illustrative weights sum to one. Legal dispossession of capitalists does not directly set \(K\) to zero.

8 Five phases and their gates

The discrete phase variable is \[\sigma\in\{0,1,2,3,4\}.\]

The lower gate requires the destruction of \(B\), sufficient network extension, planning, and legal socialization, a functioning proletarian state, low counterrevolution and deformation, and \[\max\{W,\mu,C,A,V,I,Y\}\le\varepsilon_c.\] The higher gate requires stronger network and planning conditions and \[\max\{B,S,R,F,W,\mu,C,A,V,I,Y,K,H,L,N\}\le\varepsilon_h.\]

9 Conditional state withering

In the lower phase define \[\Omega=\max\{K,R,F,1-G_{\min},W,\mu,C,A,V,I,Y,H,L,N\}. \label{eq:omega}\] The proletarian class-state follows \[\dot S=\eta_S(s_0\Omega-S). \label{eq:state}\] \(S\) represents coercive political class functions, not material administration, scientific coordination, or social memory. Those functions remain in \(Q\).

The theorem does not say that the proletarian state “decides” to abolish itself. It says that the state target falls only as the antagonisms and material obstructions requiring class coercion disappear. Immediate statelessness while counterrevolution, world capitalism, scarcity, or class-generating relations remain is excluded by the closure.

10 Labour-time planning under hard species constraints

10.1 Physical production and labour time

Let \(x\in\mathbb{R}_+^n\) be gross output in sector-specific physical service units and \(A_{\mathrm{phys}}\) the matrix of physical intermediate requirements. Net output is \[y=(I-A_{\mathrm{phys}})x=Bx. \label{eq:net}\] Let \(\ell\in\mathbb{R}_+^n\) be direct labour coefficients. Because \(x\) is gross output in all interdependent sectors, \[T_L(x)=\ell^\top x \label{eq:labour}\] counts direct labour across the complete production system, including sectors producing intermediate inputs. This is planned social labour time, not exchange value. Under communal production, the economy of time and the distribution of labour among branches remain necessary while products no longer confront one another as commodities (Marx 1857).

If \(T_{\mathrm{soc}}\) is the available social time budget, disposable time is \[T_D(x)=T_{\mathrm{soc}}-T_L(x). \label{eq:disposable}\] Reducing required labour, subject to needs and species constraints, expands disposable time. The purpose is not to make labour-time vouchers into money or to retain labour time as a measure of social wealth in the higher phase. It is to economize necessary social effort during planning and to make its reduction explicit (Marx 1858; International Communist Party 1948a).

10.2 Hard feasible set

Let \(d\) be a socially determined minimum-needs vector, \(E\) a matrix of ecological-material intensities, \(\bar e\) a vector of non-substitutable ceilings, and \(x^{\max}\) physical capacities. Define the strict feasible interior \[\mathcal F^\circ(d)=\{x:\ 0<x<x^{\max},\ Bx-d>0,\ \bar e-Ex>0\}. \label{eq:feasible}\] Need satisfaction and ecological-material ceilings are constraints, not terms that can be violated in exchange for a sufficiently large gain elsewhere.

For barrier parameters \(\tau_d,\tau_e,\tau_b>0\), define \[\begin{aligned} J_\tau(x;d)=&\ \ell^\top x+\frac{\rho_x}{2}\|x-x^0\|^2 -\tau_d\sum_j\log([Bx-d]_j)\\ &-\tau_e\sum_k\log([\bar e-Ex]_k) -\tau_b\sum_i\left[\log x_i+\log(x_i^{\max}-x_i)\right]. \label{eq:barrier} \end{aligned}\] The first term is required social labour; the second limits violent adjustment; the remaining terms make the boundary of the feasible set infinitely costly. The flow is \[\dot x=-M\nabla_xJ_\tau(x;d), \qquad M\succ0. \label{eq:planning}\]

The barrier solution is a central-path approximation. As the barrier parameters decrease, its stationary point approaches the labour-minimizing feasible plan under the usual convexity and regularity conditions (Boyd and Vandenberghe 2004).

10.3 Changing needs

The model does not ask an optimizer to declare legitimate needs. \(d\) is a political and social input. If needs change slowly, then \[\frac{d}{dt}J_\tau(x(t);d(t)) =-\nabla_xJ_\tau^\top M\nabla_xJ_\tau +\nabla_dJ_\tau\cdot\dot d. \label{eq:moving-needs}\] Hence \[\dot J_\tau\le-\lambda_{\min}(M)\|\nabla_xJ_\tau\|^2 +\|\nabla_dJ_\tau\|\,\|\dot d\|.\] The plan tracks a moving social target when need revision is sufficiently slow relative to material adjustment. This is not a theory of deliberation. It only states how changes in socially determined needs enter the technical dynamics without being hidden inside a price signal.

11 Formal domain and invariance

The hybrid state belongs to \[\mathcal X=[1,8]\times[0.5,4]\times[0,1]^{30}.\] The first two intervals contain \(o\) and \(m\); all other continuous states are normalized.

The proof is also stress-tested numerically on randomly generated points of every boundary face in every phase.

12 Numerical experiments

12.1 Interpretive status

The simulations are architecture tests. The parameters do not estimate the probability, timing, or national location of revolution. Model time has no direct calendar interpretation. Exact decimals are reported in the verification appendix because reproducibility requires them, not because history runs to two decimal places.

All four scenarios use the same autonomous capitalist stress equations. They differ only in programmatic admissibility, regional transmission and repression, and the additional bureaucratic-pressure parameter in the deformation stress test.

12.2 Contested authority without an admissible party

With \(A_{\mathrm{prog}}=0\), accumulation generates overaccumulation, rivalry, war, and crisis. Mass organs and mobilization rise, the bourgeois state weakens, and contested authority begins at approximately \(t=17.6\). Party direction \(J\) decays to zero and therefore \(D\) also tends to zero, despite high values of the generic organizational-capacity variable \(P\). The system remains in phase 1.

The result is not that an inadmissible organization can do nothing. It is that mass upheaval, state weakness, and organizational size cannot be silently redefined as proletarian dictatorship within the stated programme.

12.3 National isolation

With \(A_{\mathrm{prog}}=1\), the system enters contested authority at approximately \(17.6\) and proletarian dictatorship at approximately \(20.9\). Legal socialization approaches \(0.98\). Regional extension, however, remains concentrated in the initial region; the other two regional states remain near zero.

At the end of the disclosed run, wage labour, money, commodity production, and petty-commodity production remain close to one. Unmet need and the proletarian-state coordinate are also high. The scenario is intentionally severe: it demonstrates that juridical ownership and national political victory cannot defeat the continuous reconstitution pressure of isolation, war, scarcity, and fragmented production.

12.4 Party-state deformation and restoration

The third scenario adds strong bureaucratic pressure to prolonged isolation and war. Contested authority begins at approximately \(18.2\), the dictatorship at \(22.8\), and the deformation/restoration edge is crossed at approximately \(61.0\). The formal-party capacity and direction coordinates are sharply reduced, the proletarian-state coordinate is extinguished, and a positive bourgeois-state coordinate is restored.

This is not a quantitative reconstruction of Russia. It is a counterexample to an earlier omission: a model that permits only external counterrevolution cannot represent a counterrevolutionary process passing through the party-state relation.

12.5 International transition

The fourth scenario combines the same endogenous crisis and seizure process with strong network transmission and no permanent regional repression term. The fixed-step \(\Delta t=0.01\) event sequence is:

The political reset is fast. The abolition of inherited productive relations is slower. The decline of bourgeois right, fixed division of labour, unmet need, and the proletarian state is slower again. This ordering is more important than the numerical times.

13 Verification

The release package contains executable source, frozen numerical inputs for the physical example, machine-readable results, and tests. The following checks pass in the release environment:

1. the value-rate derivatives, category equilibrium, and state-filter solution simplify symbolically to the stated expressions;

2. the autonomous hybrid model contains 32 continuous states and five discrete phases;

3. fixed-step RK4 at \(\Delta t=0.04,0.02,0.01\) reproduces the same four classifications and phase sequences;

4. the largest international-event difference between \(\Delta t=0.02\) and \(0.01\) is \(0.01\) model-time units;

5. an independently integrated DOP853 implementation uses no clipping, preserves the domain, reproduces every classification, and differs from the fixed \(\Delta t=0.01\) events by at most approximately \(0.03\);

6. 320,000 randomized boundary-component evaluations detect no outward-pointing derivative;

7. fifty randomized feasible planning starts preserve every hard need, ecology, positivity, and capacity constraint and produce non-increasing barrier objectives;

8. the largest recorded planning-objective increase is on the order of floating-point roundoff;

9. all manuscript citations resolve, the source registry resolves every concordance key, and the PDF build contains no unresolved references.

The archived Goodwin–SFC material remains in the replication package for historical continuity. Its accounting closure and local bifurcation calculations are not used as evidence for the new endogenous crisis module.

14 What the model still does not do

14.1 It does not identify the historical party

\(A_{\mathrm{prog}}\) is an external premise. \(F\) does not solve the oracle problem; it only models some material pressures on the formal organization. No equation can replace the historical and programmatic judgment required to determine whether a real organization remains continuous with the communist programme.

14.2 It is a value-theoretic kernel, not a complete reconstruction of Capital

The model adds constant capital, variable capital, surplus value, organic composition, the value rate of profit, accumulation, overaccumulation, rivalry, and war. It still omits turnover-time distributions, department reproduction schemes, ground rent, detailed credit chains, differential profit rates, technical change by branch, and the full formation of the general rate of profit. The kernel corrects the causal direction of the crisis input; it does not finish Marxian crisis theory.

14.3 The international network is minimal

Three regions are better than one scalar, but they remain an abstraction. A serious extension requires many regions, productive specialization, military fronts, trade and blockade matrices, migration, uneven technical compositions, and sections of the world party. Regional weights and repression coefficients here are scenario parameters.

14.4 The agrarian and middle-strata problem is compressed into one state

\(Y\) makes small production and agrarian fragmentation impossible to ignore, but it does not distinguish landless labourers, poor peasants, middle peasants, commercial farmers, artisans, or urban petty proprietors. Nor does it specify the concrete programme of agricultural integration.

14.5 Tactics remain outside the state vector

Abstentionism, union work, military defeatism, relations to non-party class organizations, and concrete slogans are not continuous quantities. They belong to a theory of tactics bounded by programme and historical phase. Treating them as adjustable policy controls would recreate the opportunist substitution the paper is trying to avoid.

14.6 Needs formation remains political

The moving-needs identity shows how technical planning tracks a revised vector; it does not determine who revises it, through what institutions, or how conflicts over burdens and priorities are resolved. A future model must connect needs formation to the abolition of the fixed division of labour without turning preference aggregation into consumer sovereignty.

14.7 No inevitability theorem is claimed

The autonomous crisis module does not guarantee seizure. The party may be absent; contested authority may be defeated; the dictatorship may remain isolated; the formal party may deform; the transition may be reversed; or ecological and productive conditions may make a declared needs vector infeasible. Marxian determinism is not represented here as a probability of success. The system exposes determinations and failure conditions rather than promising an outcome.

15 Conclusion

The main weakness of the previous architecture was not that it used mathematics. It was that the mathematics allowed the decisive political and historical relations to enter from outside or to collapse into overly convenient variables.

The present revision removes the external crisis pulse. Capitalist accumulation now raises the organic composition and overaccumulation; profitability pressure, overaccumulation, and competition raise imperialist rivalry; rivalry and overaccumulation raise war pressure; and war feeds the crisis state. The model still does not reproduce the whole history of world capitalism, but crisis is at least generated by capitalist relations rather than by the hand of the modeler.

It also stops calling mass organization “dual power” before its political content has been established. Mass class organs \(E\), party direction \(J\), and organs of proletarian power \(D\) are different objects. Their conjunction is necessary at seizure. This makes the model less councilist without making the party a substitute for the class.

The historical party remains outside the equations. That is not a defect to be disguised. The new deformation state does something different: it allows isolation, war, counterrevolution, and state subordination to damage the formal party’s practical capacity and direction. Counterrevolution can therefore appear not only as an external army but as a failure passing through the party-state relation.

The economic transition retains the strongest results of the previous paper. Nationalization is not communism. Wage labour, money, commodities, autonomous enterprises, value regulation, transferable claims, and petty-commodity production must disappear as social relations. International extension is not a slogan added to a national model; it acts through a regional network and enters both the gates and the continuous reconstitution pressure. The proletarian state does not vanish by decree. It tends to zero only as the obstructions that require class coercion tend to zero.

Finally, planning is no longer presented as a welfare loss with an ecological surcharge. Required social labour is explicit, disposable time is explicit, and need and species constraints are hard boundaries of the feasible plan. Labour time remains an object of conscious economy without becoming a measure of exchange value.

None of this asks the academy to certify the programme. Nor does the model think politically on behalf of the party or the class. Its use is more austere. It prevents a theory from saying one thing in prose while its equations quietly say another. It makes substitutions visible, failure paths explicit, and missing determinations harder to ignore. That is not the revolution in mathematical form. It is a more disciplined way of stating what a claimed model of revolutionary transition is, and is not, permitted to mean.

16 Standard thresholds and parameters

The principal thresholds used in the numerical experiments are:

They are scenario definitions, not empirical estimates. Complete coefficients are contained in src/python/left_communist_hybrid.py.

17 Programmatic source-to-equation concordance

The machine-readable concordance contains the complete source registry. The compact table below records the principal additions of v4.0.

18 Numerical verification summary