Human–Machine Convergence

Self-organisation, autopoiesis and operational closure

Rajesh Ranjan Mahapatra

A first-principles test for distinguishing systems that regenerate their own organisation from systems whose apparent autonomy is maintained by an outside caretaker.

© 2026 Rajesh Ranjan Mahapatra. 31 min read

Self-organisation, autopoiesis and operational closureAll Human–Machine Convergence

Computation, control and emergence

Self-organisation, autopoiesis and operational closure

A system maintains its own organisation only when the causal specificity needed to rebuild its constraints and boundary is generated within the system, rather than supplied by a hidden caretaker.

TLDR

  1. Order can arise spontaneously without the ordered thing producing the machinery that preserves it.
  2. Operational closure concerns mutually dependent constraints, not isolation from energy, matter or information.
  3. The decisive question is who supplies organised repair, not whether anything crosses the boundary.
  4. A system boundary is credible only when perturbations expose internal regeneration rather than external replacement.
  5. AI systems may automate maintenance while still borrowing their constitutive identity, infrastructure and authority from people.

Imagine two translucent droplets on a laboratory bench. Both absorb simple nutrients. Both keep the same diameter. Both replace damaged membrane and hold their internal chemistry within a narrow range. After a week, each still looks like the same tiny individual.

There is one concealed difference. Droplet A contains a reaction network that turns feedstock into its catalysts and boundary lipids. Droplet B sits above a microfluidic grid. Whenever one of its catalysts degrades, a technician’s controller injects a ready-made replacement. The membrane is patched in the same way. Through the microscope, their behaviour is indistinguishable.

Now disconnect the controller. B fades. A reorganises its flows and continues. The week-long observation did not reveal the cause of persistence because it recorded what stayed stable, not who regenerated the conditions of stability.

The difference between self-maintenance and maintenance-from-outside is a difference in the origin of causal specificity. Energy and raw material may arrive from the environment. The organisation that decides how those materials become a catalyst, a membrane or a repair must arise within the candidate system. That is the distinction this paper turns into a test.

The workshop behind the wall

A snowflake, a flame and a bacterium all display order. Only one continuously produces the structures that channel its own production.

Begin with the least mysterious case. Warm air rises above a radiator, cools, falls and forms a convection cell. No supervisor draws the circulating pattern. Local interactions plus a temperature gradient produce it. Remove the gradient and the pattern disappears. This is self-organisation: macroscopic order emerges from local dynamics without a central organiser.

A candle flame is more impressive. It draws wax upward, vaporises fuel and maintains a recognisable shape while its molecules change. Yet the flame does not manufacture the wick, replenish the wax block or rebuild the room’s oxygen supply. Its persistence depends on an organised support structure that it does not regenerate.

A bacterium also exchanges nearly all of its material over time. Unlike the flame, its enzymes help produce other enzymes; its membrane regulates flows that power membrane repair; its genome is copied using machinery encoded by that genome and maintained by the cell. This circularity motivated Varela, Maturana and Uribe’s original characterisation of living organisation as autopoietic, a network of production that continually realises its own components and boundary.[1]

Self-organisation explains how a pattern can arise; autopoiesis asks whether the pattern produces the organisation that keeps producing it. The words therefore answer different questions. A whirlpool is self-organised. A thermostat maintains a variable through feedback. An autopoietic candidate must do more: it must participate in producing the constraints and boundary that make those regulating operations possible.

This separates four claims that are often compressed into “it keeps itself going”. Stability means that an observable remains within a range. Homeostasis means that feedback counteracts a disturbance to a selected variable. Self-repair means that some damaged capacity is restored. Autopoiesis concerns the recursive production of the organisation that makes stability, regulation and repair possible. A device may satisfy the first three while failing the fourth. A redundant server can restore a process from an immutable image, yet neither server produces the image, the hypervisor or the authority that makes the restoration valid.

The distinction also changes what counts as identity. If identity meant retaining the same material, organisms would fail immediately. Their components turn over. If identity meant retaining exactly the same state, growth and adaptation would also count as death. Autopoietic identity is closer to an invariant organisation realised through changing material: a network continues to produce the relations that distinguish a unity from its surroundings. This is not a metaphysical proof of selfhood. It is a causal proposal about why the unity persists.

Reproduction is different again. A mule is alive despite being infertile. A fire can spread to a second log without producing a new organisation capable of maintaining itself. A photocopier makes copies while technicians maintain the copier. Reproduction concerns producing another system; autopoiesis concerns continuously producing this system. In evolutionary explanations they interact, but one should not be used as a shortcut for the other.

Evidence status

The original autopoiesis paper offers a general characterisation and a minimal computer model, not an experimental demonstration that autopoiesis is necessary and sufficient for all life. Later theories refine the causal vocabulary and disagree about sufficiency. The operational test in this paper is practitioner synthesis built from those theories, not a published consensus metric.

Figure 1. The membrane is a workshop, not a wallConceptual cutaway
Cutaway of an operationally closed cell-like system Raw materials and energy cross a selectively maintained membrane. Internal catalysts transform them into catalysts, transporters and new membrane. Dotted red arrows show organised replacement supplied by an external caretaker. Catalystshapes reactions Repairrebuilds catalyst new boundary lipid Energy + feedstocklow-specificity inputs Waste + heat Caretakerready-made repair disqualifying if constitutive
Matter and energy may cross continuously. The diagnostic red path is different: it imports a ready-made constraint that the system itself should regenerate. Alt: a cell cutaway separates ordinary feedstock flows from a dotted external repair path.
Thought experiment 1 · The invisible technician

Give Droplet B a larger reservoir so it survives every observation in a six-month experiment. Nothing in its visible trajectory changes. Does longevity make it self-maintaining? No. Reservoir size changes the delay before dependency becomes visible, not the source of repair. Next, replace ready-made catalysts with amino acids and energy. If B’s own network now constructs the catalysts, the causal relation changes even if the same molecules cross the membrane. The relevant intervention changes the specificity of the input, rather than only its quantity.

Worked example 1 · Four stable things
SystemSource of orderWhat it regulatesWho rebuilds constitutive machinery?
Convection cellTemperature-driven local dynamicsNo internal targetNo machinery is rebuilt
ThermostatDesigned feedback loopRoom temperatureInstaller replaces sensor and heater
Candle flameCombustion and flowDynamic flame shapeExternal wick, wax and atmosphere
BacteriumCoupled metabolic, genetic and boundary processesMany viability variablesCellular organisation repairs most constitutive machinery from environmental resources

“Most” matters. No organism makes atoms, sunlight or the whole ecology that supports it. Operational closure cannot mean causal independence from everything. It identifies a particular circular dependence among the structures that constrain internal processes. That requires a more exact model.

Notice what the comparison does not say. The bacterium is not independent of its environment, and the thermostat is not useless because it lacks autopoiesis. The categories reveal different causal organisations. This protects engineering language from becoming a status contest. A well-designed externally maintained controller may be safer than a system that can alter its own constitutive constraints. The point is to name what exists so that responsibility and failure boundaries remain visible.

The argument in one pass
Chart · flow
flowchart TD
  A["The workshop behind the wall"] --> B["The organisation must pay its<br/>own maintenance bill"]
  B --> C["Where artificial systems<br/>borrow their selves"]
  C --> D["The operational-closure audit"]
  D -. "re-test" .-> A
  classDef first fill:#0a1424,stroke:#5B5CF6,stroke-width:2px,color:#e6f3ff
  classDef step fill:#0a1424,stroke:#3f7da0,stroke-width:1px,color:#e6f3ff
  class A first
  class B,C,D step
A structural route through Self-organisation, autopoiesis and operational closure: from The workshop behind the wall to Test whether the boundary repairs itself. Reading use: follow the relation, then return to the surrounding argument for evidence and limits.

The organisation must pay its own maintenance bill

Closure is not a sealed container. It is a network in which each constitutive constraint helps sustain others and is sustained through the same organisation.

Consider an enzyme that channels a metabolic reaction. During the milliseconds in which it catalyses a reaction, its relevant shape is comparatively stable. On a longer timescale it degrades. Other cellular processes must replace it. Those processes depend on membranes, ribosomes, energy gradients and further enzymes, which are themselves maintained through the network.

Montévil and Mossio formalise this intuition by distinguishing processes, the changing flows of matter and energy, from constraints, structures that channel those flows while remaining sufficiently stable at the timescale of their action. In an organised biological system, constraints are mutually dependent: each contributes to maintaining at least one other and depends on at least one other.[2] Their later work treats organisation as a theoretical principle for making biological functions intelligible.[3]

Operational closure is closure of dependence, not closure to throughput. A cell remains thermodynamically open. It must import free energy and matter and export heat and waste. What closes is the circular organisation of constraints that harness those flows.

A river turbine makes the contrast clear. Water supplies energy; the shape of the blades channels it. If flowing water gradually fabricates and aligns replacement blades using structures maintained by the turbine system, blade production belongs to the candidate organisation. If a factory delivers machined blades, water is an energy input but the factory is a caretaker. Both cases are physically open. Only the origin of the blade-making constraint differs.

Specificity is not a mystical substance. It is a counterfactual property of an input. Replace glucose with another suitable carbon source and many cells reconfigure metabolism. Replace a required enzyme with a random protein of the same mass and the reaction fails. The enzyme therefore contributes organised structure beyond bulk matter and energy. To locate that contribution, vary the input’s chemical detail while holding energy and quantity as constant as possible. The point at which recovery fails locates an external dependency that the candidate cannot reconstruct.

Mechanism · The specificity transfer test

Ask what an input contributes. Glucose supplies matter and free energy, but cellular constraints determine how it becomes ATP, lipid or protein. A pre-folded replacement enzyme carries much more of the organisation required for its own function. The first is feedstock. The second is organised repair. The line is empirical: progressively simplify the input and observe whether the candidate system reconstructs the missing specificity.

Figure 2. The intervention that reveals the maintainerCounterfactual causality
Counterfactual comparison of feedstock and ready-made repair Two experimental branches remove an enzyme. In the first, raw materials are supplied and the system reconstructs it. In the second, the enzyme appears only after a caretaker injects a finished replacement. Interventiondisable constraint C₂ Forkchange one input Raw feedstocksystem rebuilds C₂ Finished C₂caretaker restores it Closure-supporting resultRecovery persists as inputs are simplifiedto matter, energy and non-specific precursors. Caretaker-dependent resultRecovery vanishes when the externallysupplied organisation is withheld.
A persistence observation becomes diagnostic only after the organised repair path is intervened upon. Alt: two branches compare recovery from raw feedstock with recovery after injection of a finished component.

We can compress the idea into a graph without pretending that the graph explains the chemistry. Let each node in a set C represent a constitutive constraint. Draw an arrow from Cᵢ to Cⱼ when the activity of Cᵢ contributes to regenerating Cⱼ within the selected timescale. A candidate is strongly closed under this audit when every constitutive node belongs to a mutually reachable internal network, the produced boundary is included, and no critical arrow is secretly an external caretaker action.

Candidate closure: SCC(C) = C  ∧  boundary ∈ C  ∧  caretaker-criticality = 0

SCC(C) = C is an audit heuristic, stronger than the minimal condition that every constraint has some incoming and outgoing dependence. It says that every constitutive constraint can participate, through some path, in the regeneration of every other. “Caretaker-criticality = 0” does not ban environmental inputs. It says that removing externally supplied organised replacements must not sever a necessary regeneration path.

Why use strong connectivity? Suppose A repairs B, B repairs A, and both happen to power C. If C never contributes to the continued existence of A or B, the graph contains a closed core plus a maintained appendage. Treating all three as one closed organisation would be misleading. Strong connectivity flags the appendage. The investigator can then decide whether C is truly constitutive, merely functional, or part of a second organisational level.

The edge itself needs evidence. Temporal correlation is not enough. If repair of B follows activation of A, both may be driven by an external controller. Useful evidence includes selective inhibition of A, tracing material from A-mediated processes into B, restoring A while holding the environment fixed, and showing that B’s recovery disappears specifically when the A→B mechanism is blocked. Each arrow is therefore a causal claim with a test, not decorative topology.

Timescale changes the graph. At one second, an enzyme constrains a reaction and appears stable. Across several cell cycles, the enzyme becomes a product requiring transcription, translation and folding. Across evolutionary time, the genetic organisation that supports those processes depends on populations and selection. An audit that mixes these scales may draw impossible simultaneous arrows. Declare a window long enough to include degradation and repair of every claimed constraint, then state which slower dependencies remain outside scope.

Worked example 2 · Three constraints

Suppose membrane M maintains the gradient that powers catalyst K. Catalyst K produces repair polymer R. Polymer R repairs M. The graph has three arrows: M→K, K→R and R→M. Remove R and supply monomers. If K reconstructs R, the loop recovers. If a robot must inject a finished polymer, the observed three-node cycle was only a diagram of function. The implemented system has a fourth, external node.

Give each constraint a ten-hour unassisted lifetime. Damage R at hour zero. In configuration A, K makes one functional unit of R per hour and the membrane loses viability after six hours without R. Recovery at hour one supports the K→R edge. In configuration B, a reservoir contains eight finished R units and releases one hourly. The system survives eight hours, longer than A, but produces none. Longevity would rank B higher; the causal audit correctly ranks its regeneration lower.

Figure 3. Recovery has a timescalePerturbation trajectory · illustrative
Illustrative viability trajectories after damageAn internally regenerating system dips after damage and recovers. A buffered system appears stable until its spare reservoir empties. An externally repaired system recovers only at technician intervention times. Time after damageViability proxy damage internal regenerationbuffer depletionperiodic caretaker
Long observation is insufficient if it is shorter than the depletion time of stored spares. Damage-and-recovery trials must span the degradation timescales of the constraints being claimed. Alt: three synthetic trajectories distinguish internal recovery, delayed collapse and periodic external repair.
Thought experiment 2 · The membrane swap

Take a candidate that makes every internal catalyst but receives a fresh membrane from a dispenser each hour. Move the dispenser inside the visible casing. Has closure been achieved? Merely relocating it changes topology, not organisation. Now let the dispenser’s parts be repaired by the internal catalysts and let it fabricate membrane from simple precursors. The causal graph has changed. Finally slow the trial so the dispenser never fails. Apparent closure returns, but only because the observation excludes its maintenance timescale. A boundary claim and a timescale claim must therefore be tested together.

Optional depth: why strong connectivity is not a definition of life

A strongly connected dependency graph can be engineered in a non-living chemical or computational system. It may also omit thermodynamic feasibility, spatial embodiment, reproduction, heredity, adaptation and open-ended evolution. Ruiz-Mirazo, Peretó and Moreno argue that individual autonomy must be joined to historical, open-ended evolution for a broader account of life.[4] Ruiz-Mirazo and Moreno likewise treat basic autonomy as necessary but not sufficient.[5] The graph is an assurance instrument for one property, not a universal life detector.

Where artificial systems borrow their selves

Synthetic cells and AI services become more autonomous by internalising dependencies. Their remaining external dependencies matter most when they supply the organisation being claimed.

Synthetic-cell research makes the distinction tangible. Murtas reported vesicle growth driven by an internally encapsulated enzyme that produced fatty acids incorporated into the boundary. This was explicitly a step towards self-reproduction, not a completed autonomous cell.[6] Blanken and colleagues later expressed phospholipid-producing enzymes from a synthetic minigenome inside liposomes. The experiment brought genetic control of boundary production inside, but supplied the transcription–translation system, precursors and other machinery; lipid production was insufficient for directly observed membrane growth or division.[7]

A newer system integrates transcription–translation of a partial genome, DNA self-replication and phospholipid biosynthesis in the same vesicles. It is a real advance in integration. Yet the vesicles begin with a preformed lipid mixture and an externally prepared PURE translation system, plus replication and lipid-synthesis substrates. Synthesised lipid remains below the amount needed for physical membrane expansion, and division is absent.[8] Calling the system “integrated” is supported. Calling it operationally closed would hide the organised machinery still supplied by the laboratory.

Progress towards closure is best measured by which constitutive dependencies have moved inside, not by how life-like the output appears. This avoids an all-or-nothing verdict. A system can internalise boundary synthesis while still borrowing translation. It can copy DNA while still borrowing energy regeneration. Each result closes a specific path.

This dependency view prevents two opposite mistakes. The first is dismissal: because a vesicle is not fully autonomous, one treats internally controlled membrane production as insignificant. The second is inflation: because several cellular functions coexist, one treats their enclosure as proof of a self-producing unity. Integration is necessary because isolated modules compete for energy and precursors, interfere with one another and must be coordinated. Closure asks the additional question of whether the integrated modules participate in regenerating the machinery that integrates them.

There is also a bootstrapping problem. Every present organism begins from an organised predecessor. A bacterium does not assemble its first ribosome from minerals. Operational closure therefore should not require spontaneous origin from raw chemistry. The relevant test begins after the candidate organisation is constituted and asks whether it can continue regenerating itself through ordinary turnover. For an engineered vesicle, supplying an initial membrane is compatible with a closure claim only if subsequent membrane maintenance and the machinery that enables it become internally regenerative over the declared cycle.

Figure 4. A dependency ledger for a synthetic vesicleAnnotated worked example
Dependency network for an illustrative synthetic vesicleDNA, translation and lipid synthesis form internal enabled paths, while preformed membrane, translation machinery, substrates and energy regeneration remain external inputs. Solid lines are demonstrated internal operations and dotted red lines are caretaker-supplied organisation. Partial genomeDNA replication Translationexpresses enzymes Lipid synthesismakes some DOPS boundary lipid PURE systempreassembled Precursorssubstrates + cofactors Energy systemexternally formulated Initial membranepreformed vesicle Solid: internal operation · Dotted: organised or configured external dependency
The experiment closes several internal paths while leaving others open. The figure is an analytical reconstruction of the cited system, not a claim that every listed external input has equal causal importance. Alt: a vesicle encloses three coupled functions while dotted paths connect it to four laboratory-supplied dependencies.

Autocatalytic-set theory supplies another useful boundary. A reflexively autocatalytic and food-generated set requires reactions catalysed from within the set and molecules constructible from a food set. Xavier and colleagues found such structures in reconstructed ancient metabolic networks.[9] But a RAF need not produce a membrane, distinguish itself spatially or repair every constraint that makes the network persist. Autocatalytic closure is evidence for one form of collective production, not automatically an autopoietic individual.

A cycle of production also need not be viable. Imagine two catalysts that make one another but consume a cofactor faster than it can be regenerated. The dependency graph closes while the chemistry runs down. This is why the structural test must be paired with a trajectory: fluxes must be thermodynamically possible, production must outrun degradation within the viability window, and side reactions must not destroy the boundary. Graph closure without kinetic adequacy is a promise that the dynamics may refuse to keep.

Figure 5. Internalisation changes by function, not by appearanceConfigured comparison · illustrative counts
Illustrative count of six constitutive functions internalised by four systemsA candle internally supports one of six selected functions, a 2020 liposome supports two, a configured 2026 synthetic vesicle supports three, and a bacterium supports all six at the analysed cellular level. Counts are illustrative audit classifications, not experimental measurements. 0123456 Functions internally regenerated in the configured audit Candle1 / 6 2020 liposome2 / 6 2026 vesicle3 / 6 Bacterium6 / 6 Selected functionscatalysis · energy couplinginformation copying · translationboundary production · repairClassification, not measurement
These counts illustrate the audit on six selected functions. They are not empirical autonomy scores and should change when the boundary, timescale or constitutive set changes. Alt: horizontal bars show increasing internalisation across four configured examples.

The AI case: automation is not autopoiesis

An AI Agent can monitor errors, rewrite code, restart workers, acquire new tools and verify outcomes. These are meaningful feedback and repair capabilities. Yet its model weights, execution runtime, identity, permissions, policy, network, energy and deployment pipeline usually come from an organisation that the Agent neither constitutes nor regenerates. If it corrupts its own policy store, a human-controlled backup restores it. If the cloud account disappears, the Agent cannot provision an authorised successor from raw resources.

The phrase “self-healing” often conceals this structure. A scheduler detects an unhealthy process and launches a container from a registry. Relative to process availability, recovery is automatic. Relative to the service’s constitutive software, the registry image is a ready-made replacement. Relative to the business system, identity and authority are issued by governance processes. All three descriptions can be true. Trouble begins when success at the narrow level is advertised as autonomy at the wider one.

A computational implementation can still instantiate operational dependence. There is no rule that only carbon chemistry can form a mutually regenerative network. But simulation and realisation must be separated. A program that calculates a model of membrane repair does not thereby repair the computer that executes it. A service that rewrites parts of its code moves closer only if those changes can become operative, preserve identity and policy, and regenerate the mechanisms that perform future repair. Whether a purely computational network counts as autopoietic remains contested because the relation between symbolic operations and material self-production is precisely what must be argued, not assumed.

The relevant system may be larger than the model. Include schedulers, monitors, repositories and automated deployment, and more maintenance paths move inside. Include the operations team and perhaps the socio-technical service repairs itself across staff shifts. Expand further to chip fabrication and the electricity grid, and new dependencies appear. There is no trick boundary that makes everything closed. The audit asks for a boundary that is explanatory for the question at hand and then exposes what crosses it.

For engineering, that answer may be enough. If the question is whether a service can recover during a two-hour network partition, the power grid need not be modelled. If the claim is that the service independently preserves its organisational identity for years, staff succession, key rotation, model replacement and hardware renewal become relevant. A boundary is justified by the failure decision it supports, not by the prestige of the autonomy claim it produces.

Thought experiment 3 · The fork with borrowed authority

An Agent notices memory corruption, creates a clean fork, copies validated world state and redirects traffic. It looks self-repairing. Now revoke the signing key that authorises deployment. The Agent can still propose a fork but cannot make it operative. Give it the key, then revoke the cloud account. Give it provisioning authority, then remove the prebuilt model checkpoint. Each intervention moves the constitutive dependency outward. The exercise does not prove that machine closure is impossible. It shows that ability to propose repair, authority to enact repair and capacity to regenerate the repairing substrate are different claims.

Figure 6. Closure moves when the candidate system movesNested boundary view
Nested boundaries around an AI model, service, organisation and industrial ecologyFour nested shapes show how including more maintenance machinery internalises some dependencies while exposing others. No level is labelled absolutely closed. Industrial ecologygrid · fabrication · logistics Operating organisationpeople · governance · budgets · recovery AI serviceruntime · monitor · repository · deployment Model processproposal + local state runtime repair authority hardware Expanding the boundary internalises some repair and reveals a new exterior.
Boundary expansion is informative only if the newly included processes actually regenerate one another. Drawing a larger box does not create closure. Alt: four nested levels place the model inside a service, organisation and industrial ecology, with an external dependency at each level.
Boundary condition · What closure does not buy

Operational closure does not establish consciousness, sentience, intelligence, moral standing or even life. Autopoiesis has been criticised and reformulated precisely because its relation to cognition and the necessary or sufficient conditions for life remains contested.[10] Physicalism, functionalism, biological naturalism, process philosophy and other metaphysical positions can agree on the dependency evidence while disagreeing about its significance for mind.

How the claim changes under pressure
Chart · state
stateDiagram-v2
  [*] --> Claim
  state "The AI case, automation is not<br/>autopoiesis" as Claim
  state "Run the graph test" as Test
  state "Operational-closure lab" as Revision
  Claim --> Test: expose mechanism
  Test --> Decision: evidence survives
  Test --> Revision: rival survives
  Revision --> Claim: narrow or rebuild
  Decision --> [*]
The revision loop begins with The AI case, automation is not autopoiesis and keeps counterexamples inside the reasoning path. Reading use: follow the relation, then return to the surrounding argument for evidence and limits.

The operational-closure audit

The audit turns a vague autonomy claim into a dependency model, a perturbation plan and a bounded verdict.

The proposed instrument has six moves. It is deliberately stricter than an uptime test and narrower than a definition of life.

  1. Fix the candidate boundary and timescale. Name what is inside, what is outside and how long every constitutive constraint must persist.
  2. Declare the constitutive set. List the constraints without which the system would cease to be the kind of system under discussion, rather than merely perform worse.
  3. Trace regeneration edges. For each constraint, identify which internal operation produces, repairs or re-establishes it.
  4. Classify external inputs by specificity. Separate energy and feedstock from configured modules, finished replacements, authority grants and scheduled caretaker actions.
  5. Intervene on critical edges. Damage a constraint, simplify the input and observe whether internal operations reconstruct it before viability is lost.
  6. Report a profile, not a mystical score. State closed paths, open paths, untested paths, boundary production and the timescale over which the result holds.

Start the constitutive list with a deletion question. If this element disappeared permanently while every other capacity remained, would the candidate cease to exist as the same organised kind, or would it merely lose a performance feature? A cell may live without a particular motility protein, so that protein is not constitutive for cellular identity in the current audit. A membrane that creates the cell’s controlled interior usually is. For an AI service, a recommendation module may be optional while the identity, policy and effect ledger that distinguish valid operations are constitutive.

Then make every edge typed. “Produces” means constructing a component. “Repairs” means restoring function in the existing component. “Enables” means maintaining a condition without which production cannot occur. “Authorises” means making an action institutionally valid. These relations should not be blended. An Agent may generate deployment code but lack authority to execute it. A membrane may enable metabolism without producing an enzyme. Typed edges reveal which causal contribution the evidence actually supports.

External inputs need the same care. Energy and feedstock are expected in an open system. A template can be ambiguous: DNA inside a cell is both a constraint and a material sequence copied by the organisation. A signed container image entering a service carries executable organisation and usually counts as a caretaker input. Human instructions can be ordinary environmental perturbations or constitutive purpose-setting, depending on whether the system’s identity and norms collapse without them. Record the classification and the intervention that could overturn it.

Figure 7. Evidence matrix for a closure claimDecision instrument
QuestionWeak evidenceUseful evidenceBreak condition
Does it persist?Long uptimeRepeated recovery after targeted damageStored spares merely delay collapse
Does it self-repair?Restarts from an imageReconstructs the damaged constraint from feedstockImage or repair module is caretaker-supplied
Does it make its boundary?Boundary growsInternal network produces and regulates boundary componentsPreformed boundary is periodically replaced
Is the network closed?Every node has an arrowInternal mutual reachability plus perturbation supportCritical edge resolves to an external actor
Is the result general?One favourable environmentSpecified viability range and multiple perturbationsSmall environmental change exposes hidden control
A positive claim requires both structural evidence and perturbation evidence. The strongest break condition is a critical organised input masquerading as ordinary resource flow. Alt: a matrix maps five audit questions to weak evidence, useful evidence and failure triggers.

Run the graph test

The lab below accepts a typed JSON description. Each constraint has an identifier, a boundary flag and the identifiers of constraints it regenerates. External dependencies are classified as feedstock, energy, organised-repair or authority. The algorithm finds strongly connected components, checks boundary production and identifies critical caretaker dependencies.

The three presets demonstrate why a single output score would mislead. The toy cell passes because its three declared constraints form one internal cycle, its boundary both receives and supplies regeneration, and its external dependencies are classified as resources. The vesicle fails boundary participation and retains organised external machinery. The AI service contains a closed restart graph, yet critical image and authority dependencies prevent the broader closure verdict. Edit those declarations and the result changes, which is a feature: the model makes assumptions contestable.

Operational-closure lab

Choose a synthetic preset or edit the JSON. Press “Run audit” to produce a bounded verdict.

Set critical to true only when removing that external input breaks a constitutive regeneration path within the audit timescale.
Choose a preset and run the audit.
JavaScript · core graph test used by the lab
function auditClosure(model) {
  const ids = new Set(model.constraints.map(c => c.id));
  const graph = Object.fromEntries(model.constraints.map(c => [c.id,
    c.regenerates.filter(id => ids.has(id))]));

  // Kosaraju: one internal SCC means every constraint is mutually reachable.
  const seen = new Set(), order = [];
  const visit = n => { if (seen.has(n)) return; seen.add(n);
    graph[n].forEach(visit); order.push(n); };
  Object.keys(graph).forEach(visit);
  const reverse = Object.fromEntries([...ids].map(id => [id, []]));
  for (const [a, targets] of Object.entries(graph))
    targets.forEach(b => reverse[b].push(a));
  seen.clear(); const groups = [];
  const collect = (n, group) => { if (seen.has(n)) return; seen.add(n);
    group.push(n); reverse[n].forEach(x => collect(x, group)); };
  order.reverse().forEach(n => { if (!seen.has(n)) {
    const group = []; collect(n, group); groups.push(group); }});

  const boundaryProduced = model.constraints
    .filter(c => c.boundary).every(c => c.regenerates.length > 0 &&
      Object.values(graph).some(targets => targets.includes(c.id)));
  const caretakers = model.external.filter(x =>
    x.critical && ["organised-repair", "authority"].includes(x.kind));
  const closed = groups.length === 1 && boundaryProduced && !caretakers.length;
  return {closed, groups, boundaryProduced, caretakers};
}

What does the code test? It tests the explicit graph for mutual internal reachability, internally participating boundary nodes and acknowledged critical caretaker inputs. Its assumptions are visible: the modeller has chosen the right constraints, edges, boundary and timescale. A positive result permits the phrase “operational-closure candidate under this model and timescale”. A negative result locates open dependencies; it does not show that the system lacks every form of autonomy. The test cannot establish thermodynamic feasibility, life, cognition or consciousness.

A practical assurance record should attach evidence to every edge: experiment identifier, intervention, observed recovery time, reserve-depletion estimate, confidence and known rival cause. Structural edges without operating evidence remain hypotheses. Conversely, a successful recovery without a dependency model may show resilience while leaving the maintainer unidentified. The combination is the contribution: topology specifies what must be tested, and perturbation determines whether the topology is causal.

Worked example 3 · A configured AI service

Model three internal constraints: runtime monitor, deployment worker and state verifier. The monitor regenerates the worker by restarting it; the worker regenerates the verifier from a signed image; the verifier repairs monitor configuration. The graph is strongly connected. Add one external dependency: the signed image is produced and authorised by a human-controlled pipeline. If corrupting the image defeats every internal recovery path, the pipeline is critical organised repair. The service has a closed operational loop for process restart, but not for constitutive software regeneration.

Worked example 4 · The backup orchard

A greenhouse robot carries ten replacement sensors, selects a spare after failure and recalibrates it using an internal reference. A thirty-day trial destroys one sensor each day. The robot recovers ten times, then fails on day eleven. The initial conclusion, “self-repairing sensor system”, confuses replacement with regeneration. Repeat the trial after adding a fabrication unit. If the unit prints sensor housings but receives finished sensing chips, one caretaker edge remains. If it constructs functional sensors from feedstock yet its calibration reference drifts without an external standard, another remains. The audit does not erase real progress. It specifies exactly which repair dependencies have closed.

Figure 8. Maintenance launderingAdversarial failure path
Failure path in which external maintenance is relabelled as internal autonomyA vertical audit path begins with an autonomy claim, checks for an automatic repair, traces its source, and rejects claims where a configured image, authority grant or human procedure remains external. “The system repairs itself” Where did the repairspecificity originate? internal production external package Test internal closuredamage · simplify input · recoverwithin declared timescale Expose caretaker edgeimage · authority · replacementmust remain in the model do not erase by redrawing boundary
Automation launders maintenance when a system executes a repair plan whose operative specificity, authority or substrate remains external. Trace every repair to its source. Alt: a decision path separates internally produced repair from external packages and preserves the caretaker edge.
Thought experiment 4 · The hundred-year greenhouse

A sealed greenhouse contains plants, microbes, robots, spare parts and a learning controller. It maintains atmosphere and repairs pumps for a century. At year 101 a specialised bearing fails; the only replacement requires a factory outside. Was the greenhouse closed for a century? Under a one-year operational timescale, perhaps its selected constraints formed a closed candidate. Under the bearing’s lifetime, no. Add a machine shop, then ask who maintains its tools. Closure is scale-relative as a test result, but not arbitrary: every widened boundary incurs new regeneration obligations.

What would strengthen or weaken the proposal?

The specificity-transfer test would be strengthened if independent auditors classify inputs similarly and if systems predicted to be more closed survive progressive input simplification through internal reconstruction. It would be weakened if “specificity” cannot be operationalised consistently, or if systems regenerate constraints despite receiving inputs the audit classifies as organised repair. A rival explanation is simple redundancy: recovery may use stored copies rather than produce new organisation. Isotope tracing, component lineage and trials longer than reserve depletion can separate production from substitution.

Do not apply the audit as a single numerical leaderboard across unrelated systems. Constraint choice depends on the explanatory question. A bacterium, a hospital and a software service operate across different materials and timescales. The smallest useful implementation is a dependency ledger with one targeted failure injection. The open research programme is to calibrate specificity by measuring how much environmental structure can be removed before internal reconstruction fails.

Several rivals can imitate closure. Redundancy imitates production. A hidden operator imitates internal control. Environmental regularity imitates regulation because disturbances never arrive. Selection across a population imitates individual repair when failed units disappear and observers track only survivors. A generous boundary imitates mutual dependence by including every supplier but never testing whether suppliers are regenerated. The audit should name the strongest live rival before choosing an intervention.

There is also a normative temptation. Because organisms are operationally organised, readers may treat closure as inherently desirable. In safety-critical engineering, increasing constitutive autonomy can reduce operator control and make failure recovery harder. A system able to rewrite its own policy machinery may close a dependency that ought to remain external. The audit describes where maintenance resides. Governance must decide where it should reside.

Open hypothesis · Closure gradient

As synthetic systems internalise organised dependencies, successful recovery should become less sensitive to the detailed structure of environmental inputs and more sensitive to the availability of low-specificity matter and energy. This predicts a measurable gradient rather than an abrupt life/non-life boundary. A system that only survives when given precisely folded proteins would rank below one that reconstructs them from amino acids under the same perturbation.

The evidence conversation
Chart · sequence
sequenceDiagram
  participant Q as Question
  participant M as Mechanism
  participant E as Evidence
  participant D as Decision
  Q->>M: The workshop behind the wall
  M->>E: The AI case, automation is not autopoiesis
  E-->>M: compare rival explanations
  E->>D: Test whether the boundary repairs itself
  D-->>Q: revise scope or act
Question, mechanism, evidence and decision exchange the burdens developed in Self-organisation, autopoiesis and operational closure. Reading use: follow the relation, then return to the surrounding argument for evidence and limits.

Test whether the boundary repairs itself

Stop awarding autonomy for stable output. Require evidence about the origin and recovery of the organisation that makes the output possible.

For synthetic-life research, report exactly which production and boundary-maintenance paths have been internalised. “Makes membrane lipid” is more informative than “life-like”. “Copies a partial genome using externally supplied translation machinery” is more informative than “self-replicating”. This language preserves genuine progress while keeping the next dependency visible.

For AI engineering, separate service resilience from constitutive autonomy. Automatic restart, self-critique and code generation are valuable controls. They do not show that an Agent regenerates its runtime, model, authority or organisational purpose. Treat those as explicit external constraints. Doing so improves architecture: backups, permission boundaries, effect receipts, independent verification and human escalation become designed dependencies rather than embarrassing exceptions.

For public claims, ask one counterfactual question: When a constitutive constraint is damaged, can the system reconstruct it from low-specificity resources before the relevant viability limit, or does an outside actor supply the missing organisation? If the answer is unknown, say “self-organising”, “adaptive” or “automatically maintained” as appropriate. Do not upgrade the claim to autopoietic.

This changes procurement and assurance too. A vendor’s “autonomous recovery” claim should arrive with a boundary diagram, a typed dependency ledger and failure-injection results. Ask which images, keys, knowledge bases, operators and infrastructure services are assumed healthy. Ask how long reserves last and what happens after they are exhausted. The answers will often reveal a capable but externally maintained system. That may be exactly what the buyer needs, provided the caretaker path is staffed, observable and tested.

It also changes the research roadmap. Instead of pursuing a vague leap from machine to life, teams can choose one open dependency at a time: energy regeneration, catalyst production, boundary growth, translation renewal, damage sensing or division. The target experiment is not “make it look more alive”. It is “remove this organised external input and demonstrate recovery from simpler resources”. Negative results remain informative because they locate the present boundary of autonomy.

Finally, the distinction clarifies responsibility. An AI service that depends on external identity, policy and deployment authority remains part of a human institution’s operational closure, not an independent bearer of organisational purpose. Designers should not cite automated maintenance to dissolve accountability. If people supply the norms and restore the constitutive machinery, people still own the decisions attached to those functions.

Figure 9. Choose the claim the evidence earnsDecision surface
Decision surface comparing internal regeneration with caretaker specificityA two-dimensional surface places externally maintained systems at low internal regeneration, self-organising systems at low regeneration and low caretaker specificity, partially closed systems in the middle, and operational-closure candidates at high internal regeneration with low caretaker specificity. Fraction of constitutive regeneration performed internally →Caretaker specificity required → Externally maintainedavoid autonomy claim Self-organising patternorder without self-production Partial closurename the open paths Closure candidateafter perturbation evidence internalise repair dependencies
A claim becomes stronger as constitutive regeneration moves inside and dependence on organised caretaker inputs falls. Position requires declared boundaries and interventions, not visual resemblance. Alt: a two-axis surface distinguishes externally maintained, self-organising, partially closed and closure-candidate systems.
Decision rule

Call a system an operational-closure candidate only when its constitutive constraints, including its boundary, form an internally regenerative network that recovers from targeted damage without critical organised repair from outside, over the declared timescale.

The word “candidate” is intellectual discipline, not timidity. Every audit is model-relative. New failure injections can expose an omitted caretaker. Yet this is still a decisive improvement over judging autonomy from persistence, complexity or fluent behaviour. It turns an impression into a causal question and a causal question into an experiment.

Glossary

Autopoiesis
Self-production of a network of components that continually realises the network and its boundary.
Constraint
A structure that channels a process while remaining sufficiently stable at the timescale of its action.
Operational closure
Mutual dependence among constitutive operations or constraints, despite material and energetic openness.
Self-organisation
Emergence of macroscopic order from local interactions without a central organiser.
Causal specificity
The organised detail that determines how resources become a particular functional constraint.
Caretaker edge
An external action that supplies, repairs or authorises a constitutive constraint in an organised form.
Viability
The range of states within which the system can continue its constitutive organisation.
RAF set
A reflexively autocatalytic and food-generated reaction set whose catalysts and products can arise from a food set.

References

  1. Primary formulation
    Varela, F. G., Maturana, H. R. & Uribe, R. (1974). Autopoiesis: the organization of living systems, its characterization and a model. Biosystems, 5(4), 187–196.
  2. Primary theory
    Montévil, M. & Mossio, M. (2015). Biological organisation as closure of constraints. Journal of Theoretical Biology, 372, 179–191.
  3. Primary theory
    Mossio, M., Montévil, M. & Longo, G. (2016). Theoretical principles for biology: Organization. Progress in Biophysics and Molecular Biology, 122(1), 24–35.
  4. Conceptual synthesis
    Ruiz-Mirazo, K., Peretó, J. & Moreno, A. (2004). A universal definition of life: autonomy and open-ended evolution. Origins of Life and Evolution of the Biosphere, 34, 323–346.
  5. Primary theory
    Ruiz-Mirazo, K. & Moreno, A. (2004). Basic autonomy as a fundamental step in the synthesis of life. Artificial Life, 10(3), 235–259.
  6. Experimental study
    Murtas, G. (2010). Internal lipid synthesis and vesicle growth as a step toward self-reproduction of the minimal cell. Systems and Synthetic Biology, 4, 85–93.
  7. Experimental study
    Blanken, D., Foschepoth, D., Calaça Serrão, A. & Danelon, C. (2020). Genetically controlled membrane synthesis in liposomes. Nature Communications, 11, 4317.
  8. Experimental study
    Restrepo Sierra, A. M., Ramirez Gomez, F., van Tongeren, M., Sierra Heras, L. & Danelon, C. (2026). A synthetic cell with integrated DNA self-replication and lipid biosynthesis. Nature Communications, 17, 2727.
  9. Computational reconstruction
    Xavier, J. C., Hordijk, W., Kauffman, S., Steel, M. & Martin, W. F. (2020). Autocatalytic chemical networks at the origin of metabolism. Proceedings of the Royal Society B, 287, 20192377.
  10. Critical review
    Luisi, P. L. (2003). Autopoiesis: a review and a reappraisal. Naturwissenschaften, 90, 49–59.