A detailed reading of the existing ADL chain. Sections distinguish terms, transitions, formal representation and testable claims. Formulas clarify specific parts; they claim no universal proof.
Definition & modelling choice
Sets terms, boundaries and perspective. Checked for clarity and consistency, not proved as a measurement.
Assumption & hypothesis
An assumption holds within the chosen model. A hypothesis makes a testable claim and must allow possible failure.
Derivation & formal representation
A formula represents. A proof derives a conclusion from explicit assumptions using stated rules. Its scope remains tied to those assumptions.
Evidence & application
Measurements support bounded empirical claims. A working program shows technical feasibility. Neither automatically proves the entire metamodel.
Level 01 / 12
Element
Definition / Interpretation
An element is a unit identifiable within an explicitly chosen frame. It may be an object, a person, a statement, an event or an entire order. “Element” therefore claims neither indivisibility nor ultimate substance. What matters is that we can refer to the same unit, name its properties and track its identity through the changes under consideration.
What supports the transition
Choosing an element is a modelling decision tied to a question. A city may be one element in a transport question; street planning needs its parts. Changing resolution is allowed but must remain visible. “Anything can be an element” is permission to model, not empirical proof that everything has identical properties. Without an identity rule, different units could silently merge.
Formal representationE = {e₁, …, eₙ} xᵢ(t) ∈ Xᵢ
E is the set of chosen elements. xᵢ(t) denotes an element’s state at time t; Xᵢ its allowed states. This is a representation, not an existence proof.
Example
In a case file, party, claim, contract and review date are distinct elements. Two files of one contract may be versions of one element; different contracts remain distinct. Identifiers and version records make the choice testable.
Limits of the claim
An element without named identity is too flexible for substantive criticism. A name alone does not distinguish the object, its description and a data record. These levels must not be confused.
Test
Ask two people to identify the same units and identity rules independently. Differences must be explainable by the subject or question.
A relation describes an explicitly named connection between elements. Membership, dependency, exchange, proximity and contradiction are different types. Simply displaying two things next to each other does not establish a relation. Direction, meaning and basis must be stated. A directed relation from A to B does not automatically imply the reverse.
What supports the transition
Identifying elements does not logically entail a particular relation. That transition requires a definition, observation or extra assumption. A contract may be connected to a claim because its content is cited as a basis; whether that basis holds is another question. ADL adds structure by making relations themselves visible and criticisable rather than hiding them in prose.
Formal representationRₖ ⊆ E × E r = (eᵢ, eⱼ, k)
Rₖ is a relation of type k. The graph records source, target and label. Symmetry, transitivity or causation need separate justification.
Example
“Document proves payment” is stronger than “document mentions payment”. An evidence chain must not equate them. Distinct edge labels preserve the difference.
Limits of the claim
Arbitrarily labelled edges do not explain anything by themselves. An unsourced relation may be a legitimate hypothesis, but must remain identifiable as such.
Test
Remove a claimed relation or seek an independent source. Which conclusion disappears? Can other people interpret the edge consistently?
An effect is a distinguishable change attributed in the model to a relation. Separate two statements: a state changed; the relation caused or contributed to that change. The first may be an observation. The second is causal and requires extra grounds. A logical consequence, a legal consequence and a physical state change are different kinds of effect.
What supports the transition
A relation alone does not force measurable change. Numbers may stand in a static relation; an inactive channel carries nothing. Relation → effect is therefore a question about mechanism, not a universal proof. A causal claim needs checks for common causes, reverse direction, measurement error or chance. The graph records claim and source; it does not perform that verification automatically.
The difference describes change in measurable states. Without a comparison condition and mechanism it does not explain the cause. Qualitative states need named categories, not numerical subtraction.
Example
A post gains reactions after a reply. That records a sequence. Comparison with similar posts and reach is needed to support that the reply caused those extra reactions.
Limits of the claim
Correlation, graph representation and causal effect are distinct. A useful structural map does not prove an effect claim.
Test
Name a predicted result and an alternative before testing. Compare conditions with and without the suspected influence; record absent effects too.
Time makes states, events and changes comparable. ADL asks in which sequence things occur, how long they take and which relations change. Event time, recording time and planned date differ. A later record may describe an earlier event. A scheduled date records a plan, not an occurrence.
What supports the transition
A static connection does not entail dynamics. We need different state descriptions or an explicit update rule. Discrete time may suffice for dates; a continuous technical model needs other assumptions. Sequence alone does not prove cause. The timescale affects visibility: a weekly report can miss a brief failure entirely.
Feedback occurs when an outcome returns through a path and changes the conditions of its further production. Sending a message back is insufficient. Returning information, energy or action must enter the next state or decision. The path may run through several elements and involve delay.
What supports the transition
A cycle in a graph is a possible structure, not proof of active feedback. Direction, transfer mechanism and timing are needed. Dampening feedback opposes a deviation; reinforcing feedback increases it under specified conditions. Either can help or harm. “Negative” and “positive” describe an effect relation, not morality. Even a dampening loop may become unstable with excessive delay.
y is the returned outcome, r a reference and K an explicit feedback rule. This control form is an example from control theory, not the definition of every social feedback process.
Example
A team reviews a result and changes the next step. If criticism is merely archived while work continues unchanged, a response is recorded but the claimed corrective loop is unproven.
Limits of the claim
Feedback does not necessarily yield balance or better knowledge. It can reinforce errors or trigger irreversible escalation.
Test
Interrupt the proposed return path conceptually or experimentally. Does the next action change? Check delay and alternative paths.
Here, order is a bounded arrangement of elements and relations whose cohesion or regularity can be described by a named criterion: a function, recurring interaction, institutional rule or observable connection. Order means neither moral goodness nor automatic stability. A conflict-ridden organisation can still form a connected arrangement.
What supports the transition
Many relations alone do not imply a viable order. Random edges may connect a graph without supplying meaningful coherence for the question. The explicit criterion is therefore essential. It must not be renamed after every observation so that all outcomes count as order. Mathematical order is narrower: a partial order requires reflexivity, antisymmetry and transitivity. ADL’s term does not automatically have that meaning.
Formal representationO = (E, R, T, B, C) C = explicit criterion
The tuple records elements, relations, timeframe, boundary and cohesion criterion. It is one possible formalisation of this reading, not a theorem proving every order exists.
Example
Trades, plans and dates form a project order relative to joint execution. Documents merely containing links are insufficient; dependencies must concern the actual process.
Limits of the claim
“Order” must not mean every arbitrary state. Without a distinguishing criterion, the claim would always be right by definition.
Test
Specify a case that fails your criterion in advance. Test whether independent readers distinguish it from a positive case.
A centre is a reference point or function around which certain relations gather. It may be a decision site, a goal, a common standard or a highly connected node. These meanings differ. A geometric midpoint is not decision authority; connectivity does not prove normative priority. The selected meaning must be named.
What supports the transition
An order need not possess one central node. Distributed networks, federated institutions and conflicting goals are possible. A claimed centre must be identified as an analytical choice or system observation. Selecting a goal may help, but does not prove all elements share it. Centrality measures a property of a specified graph, not a person’s worth.
Numerical centrality needs a definition, such as the number of specific connections. Different definitions produce different centres. A goal-centre is not automatically equivalent.
Example
A case’s main question may be its functional centre while the most linked document forms another graph centre. Both are valid if their roles remain distinct.
Limits of the claim
“Every order has exactly one centre” would be an additional universal claim. This reading does not assume it; distributed or multiple centres remain representable.
Test
Examine a decentralised network. Can the selected centre be named beforehand, or does its meaning change afterwards?
A boundary specifies which elements and processes belong to the order and which are treated as environment. It may be physical, legal, organisational, temporal or analytical. It does not imply absence of outward relations. Exchange across a boundary may be essential to persistence. Boundaries must therefore be described with their interfaces.
What supports the transition
A drawn circle does not establish a boundary. A cell may have a membrane, yet a study can choose cell plus medium. That analytical choice is viable only if excluded influences are named. Orders may overlap: one person can belong to a team and a family. The model needs explicit memberships rather than artificially disjoint worlds.
Formal representationE = Einside ∪ Eoutside I = {(a,b) ∈ R : a ∈ Einside, b ∈ Eoutside}
I records outgoing interfaces; incoming ones are recorded separately. This partition applies within one frame. Memberships of other orders may overlap.
Example
An external electricity supplier is outside a construction team but connected through supply. Removing it from the graph must not erase the open interface.
Limits of the claim
A convenient boundary can hide counterexamples. Boundary conditions belong to the claim, not to an after-the-fact exception.
Test
Extend the boundary to an excluded actor or process. Which explanation changes? Material changes require disclosing the dependency.
Balance is the maintenance of named conditions within a specified period and environment: a resource range, load threshold, functional viability or target corridor. It is not a universally present ideal state. A system may change continuously while staying within conditions; an unchanged state may already be unviable.
What supports the transition
Balance needs a standard derived from the question or supported by measurement, not merely from a system’s existence. Physical equilibrium, dynamic stability and normative fairness differ. A moral standard needs its own justification. “This state preserves the system” does not prove “this state is just”. Assessment must name whose conditions are preserved and which costs arise outside the boundary.
Formal representationx(t) ∈ K for t ∈ [t₀, t₁] K = stated viability region
K is the previously named viable region. Variables and duration belong to the claim. A stationary state additionally satisfies F(x*) = x*, but is not automatically stable.
Example
A team meets deadlines only because one person continually works overtime. The schedule looks stable while that person’s load condition fails. Different indicators yield different, explicitly bounded balance judgments.
Limits of the claim
A freely movable K could redefine every failure as balance. Criteria and duration must not be chosen after the outcome.
Test
Fix K and the test period beforehand. Add a small disturbance. Do the relevant conditions persist, and who bears the costs?
Drift is directional or accumulating deviation from a named reference region. It may affect states, rules, relations or the boundary itself. Not every change is drift. The claim requires a baseline, direction, period and indicator. Without them, development, measurement noise and loss of viability are hard to distinguish.
What supports the transition
Balance and drift are not an exhaustive division of reality. A state may lie outside a region without moving further away; a system may switch between regions. A drift indicator is a bounded measurement choice. Distance from a goal has no moral meaning without a justified goal. Measurement changes must be distinguished from system changes; changing definitions makes values incomparable.
dist needs a named metric. This formula captures one possible indicator, not every drift. Non-numerical states may use a justified category change.
Example
Missing evidence increases across review cycles despite constant case volume. This may indicate process drift. A one-off rise after adding old cases is different: the population changed.
Limits of the claim
Drift is not automatically diagnosed in the betas. Programs display entered states and open points; the indicator needs domain definition and testing.
Test
Use an unchanged measurement rule and a control history. Different case composition must not be presented as change in the same system.
Development describes a traceable change in structure or possibilities. Correction is change relative to a named error or target criterion. Splitting creates distinguishable suborders. Decay loses previously named cohesion conditions. These are different readings of histories, not an automatically complete or mutually exclusive list of all states.
What supports the transition
Drift does not necessarily entail decay. A system may correct itself, create new conditions, move its boundary or persist problematically. Description depends on criteria fixed beforehand. Splitting can be loss for the original order and development for new ones. Judgments must retain scale, boundary and time rather than changing perspective arbitrarily. ADL organises these questions; prediction needs an additional dynamic model.
Formal representationO(t₁) → O(t₂) classify by stated criteria, not by label alone
The arrow denotes an observed or assumed sequence. Without a transition rule it is neither a mathematical proof nor a prediction.
Example
A team splits into two groups with independent responsibilities. Original authority ends while some relations remain. This is not complete disconnection but a new boundary and role structure testable against concrete tasks.
Limits of the claim
Calling every retrospective story “development” is unfalsifiable. An explanation needs an outcome distinguishable in advance.
Test
Define distinct observable criteria for correction, splitting and decay. Classify an unseen history without changing them.
An order previously studied as a whole may be treated as an element at a higher level. A cell becomes an element of tissue, a team of an organisation, a case of an overview. Initially this changes representation and resolution. The inner order does not disappear; details must remain accessible through a reference or traceable substructure.
What supports the transition
The additional structure is the ability to ask the same questions at multiple scales and document transitions. This does not imply identical laws at every scale. Aggregation may lose information. Higher-level dynamics require that relevant internal differences do not change predictions, or remain as extra state variables. If equal summaries later react differently, the higher element is insufficient for that prediction.
q is an aggregation. The right condition is one possible requirement for closed aggregated dynamics, not an automatically satisfied ADL theorem. A purely structural map does not need it; the corresponding predictions do.
Example
Two teams produce equally today. One depends on a single person; the other distributes work. Aggregated as equal output they look identical, but a person’s absence affects them differently. Robustness analysis must retain the internal dependency.
Limits of the claim
Reusable syntax is not proof of universal dynamics. Describing something as an element proves neither complete explanation nor lossless predictability.
Test
Find two different detailed states with the same summary. Apply the same disturbance. Divergent higher states refute the claimed closure.
The mathematics case gives a real, bounded proof for graph aggregation. The technical case derives disturbance decay in an explicitly simplified control model. Both remain distinct from empirical validation of the entire ADL model.