Glossary of Dynamic Non-Absoluteness

This glossary defines the controlled vocabulary of the Dynamic Non-Absoluteness research program.

Its purpose is not to freeze the hypothesis permanently. Its purpose is to prevent future documents from using the same words in incompatible ways.

The hypothesis depends on terms that can easily become ambiguous: force, equality, identity, absolute, open system, perturbation, symmetry, and preservation. This glossary gives each term a working meaning.

In this program, absolute means more than strong, stable, large, long-lasting, or fundamental.

A factor is treated as absolute only if it is assumed to be:

The hypothesis rejects this kind of absoluteness as an ordinary feature of observable dynamic reality.

It does not reject invariants, conservation laws, stable structures, or useful idealizations.

Absolute dynamic identity means total identity of two dynamic factors across an ordered evolution.

It would require more than equality of magnitude or equality at one moment. It would require preserved identity of:

The hypothesis treats absolute dynamic identity as a limiting abstraction in open systems, not as an ordinary stable condition.

A boundary condition is a condition that constrains how a system or factor behaves at the edge of a domain, interval, environment, or model.

Boundary conditions matter because two factors that are initially equal may evolve differently if their boundaries differ.

In this program, boundary conditions are part of the preservation problem:

Context means the surrounding conditions, relations, constraints, and influences that shape the role or behavior of a factor.

A factor is not interpreted in isolation. Its effect depends on context.

The hypothesis uses context to reject the idea that a driving factor can be fully understood as an isolated absolute.

Difference is any relevant distinction between factors, states, relations, conditions, trajectories, perturbations, or histories.

The program treats difference as a condition of observable dynamics.

Difference does not always mean instability or disorder. It may also be the basis of structure, relation, measurement, interaction, and transformation.

Two factors are distinguishable if the model or observation treats them as two rather than one.

This matters because absolute identity between distinguishable factors is stronger than identity of a factor with itself.

The hypothesis asks:

A driving factor is any influence, interaction, constraint, gradient, field condition, instability, asymmetry, or causal structure that contributes to change of state or direction of a dynamic process.

This term is broader than force.

It is used when the strict physical term force would be too narrow or theory-dependent.

Examples may include:

A driving force is a more intuitive phrase for a factor that pushes, directs, causes, or contributes to change.

In strict physical contexts, this phrase must be used carefully.

The program prefers driving factor when speaking across physics, mathematics, and philosophy.

A dynamic factor is a factor whose state, influence, role, or relation is considered across an ordered evolution.

A dynamic factor is not merely a static object. It is examined through change, persistence, relation, and possible divergence.

Dynamic identity means identity considered across an ordered evolution.

It is stronger than equality at one moment.

Dynamic identity asks whether a factor, or a relation between factors, remains the same through a process.

In this program, dynamic identity is always tied to preservation conditions.

Dynamic non-absoluteness is the principle that observable driving factors are not absolutely isolated, not absolutely self-sufficient, and not absolutely independent of relations.

The principle states:

Dynamic non-absoluteness does not deny stability or lawfulness. It denies that dynamic reality is ordinarily made of isolated absolutes.

Dynamic non-identity is the principle that two initially equal or similar dynamic factors do not automatically preserve strong identity across an ordered evolution.

The principle states:

Dynamic non-identity is the evolution-oriented part of dynamic non-absoluteness. Clock time is only one possible parameterization of that evolution.

Equality means equivalence under a selected parameter or relation.

Equality may refer to:

The hypothesis distinguishes equality from identity.

Equality is usually parameter-bound. Identity across an ordered evolution is condition-bound.

An equivalence relation is a rule under which two factors are considered equivalent for a specific purpose.

In the formal development of the hypothesis, equivalence relation is essential.

Two factors may be equivalent under one relation and not equivalent under another.

For example, two forces may have equal magnitude but different directions, histories, or contextual roles.

Exposure means the way a factor is subject to influence from conditions, perturbations, relations, or environment.

Two factors may begin equal but diverge because their exposure differs.

Exposure is central to open-system reasoning.

Force is a strict term in physics and should not be used carelessly.

In this program, force may mean a physical quantity within a specific theory, but broader statements should usually use driving factor instead.

The hypothesis is not a claim that physics has missed a new force.

Identity means sameness.

In this program, identity must always be qualified:

The program rejects vague identity claims. It requires each identity claim to specify what is being preserved.

An invariant is something that remains unchanged under a specified transformation or evolution.

The hypothesis does not deny invariants.

It distinguishes invariance from total dynamic identity.

Two factors may share an invariant while differing in relation, exposure, context, or trajectory.

An isolated system is a system treated as having no relevant exchange or influence with an environment.

In practice, isolation is often an idealization.

The hypothesis focuses mainly on open systems, but isolated-system models may be useful as contrast cases.

A limiting abstraction is an ideal concept useful for thought, modeling, or boundary reasoning, but not necessarily an ordinary observable reality.

In this program, absolute force and absolute dynamic identity are treated as limiting abstractions unless their preservation conditions are explicitly defined.

Local equality is equality within a restricted scope.

It may be equality:

Local equality should not be confused with total identity.

Momentary equality is ordinary measurement language for equality at a specific clock reading or observational instant. In the abstract layer, local equality at an ordering position is preferred when no metric clock is required.

It does not imply equality before or after that moment.

It also does not imply identity of history, relation, or future development.

Open reality refers to observable reality as a field of interacting systems, influences, conditions, and relations rather than perfectly sealed ideal objects.

The phrase is philosophical rather than strictly technical.

It expresses the background intuition that real observed systems are usually embedded in wider fields of influence.

An open system is a system that exchanges or receives relevant influence from outside its selected boundary.

This may include exchange of:

The hypothesis uses open systems to explain why strong identity across an ordered evolution is not automatically preserved.

Parameter-bound equality means equality that holds only with respect to a specified parameter.

For example, two factors may be equal in magnitude but not equal in direction, context, relation, or evolution.

This distinction protects the hypothesis from confusing measurement equality with total sameness.

A perturbation is a disturbance, influence, fluctuation, or modification that can affect the state or evolution of a factor or system.

Perturbations may be small or large.

The hypothesis does not require every perturbation to produce dramatic divergence. It only requires that relevant perturbations matter for claims of strong identity.

A preservation condition is a condition that must remain in place for equality, equivalence, identity, stability, or invariance to continue across an ordered evolution.

This is one of the core terms of the program.

The central formula is:

If the preservation condition fails, identity cannot be assumed.

A preservation mechanism is a structure, rule, constraint, feedback process, symmetry, invariant, or stabilizing feature that maintains equivalence or identity across the relevant ordered evolution.

The hypothesis allows preservation mechanisms.

It does not claim that all equalities immediately break. It says that strong identity must be supported by something; it is not automatic in open systems.

A relation is any connection, dependency, opposition, constraint, interaction, or structural placement through which a factor becomes meaningful inside a system.

Dynamic non-absoluteness treats relation as primary for observable dynamics.

A factor without relation may be thinkable as an abstraction, but it is not an ordinary observable driver inside a dynamic system.

Relational dynamics means dynamics understood through interactions and dependencies rather than through isolated absolutes.

The hypothesis belongs to relational dynamics because it treats driving factors as meaningful through context, relation, and system structure.

Stability means persistence, return, boundedness, or resistance to disturbance under specified conditions.

Stability is not the same as absolute identity.

A system may be stable while still containing dynamic non-identity among its factors.

Strong identity means identity across a richer set of properties than a single measurement.

Strong identity may include:

The stronger the identity claim, the stronger the preservation conditions must be.

Symmetry means preservation of structure under transformation, comparison, or condition mapping.

In this program, symmetry matters because identity across an ordered evolution depends on preserved relevant symmetry.

Symmetry is not rejected. It is treated as a condition of identity.

Symmetry of conditions means that two factors are subject to equivalent relevant conditions.

This may include equivalent:

If symmetry of conditions is broken, strong dynamic identity becomes unstable or unsupported.

This research corpus distinguishes three coordinates.

An actual time interval is a difference in \tau when a clock-based duration is intended. The abstract Dynamic Non-Identity claim, however, is most meaningful across ordered intervals and does not require a clock by definition.

No relation q=f(\tau) is assumed merely because both variables can label progression.

A trajectory is the path of a factor or system through state space or modeled evolution. It may be parameterized by \lambda, by metric time \tau, or, in System Tempo research, by regime coordinate q, depending on the model.

Two factors may have equal values at one moment but different trajectories.

Dynamic identity requires more than momentary intersection of trajectories.

The hypothesis should be separated into claim levels.

Future documents in this series should follow one rule:

This rule protects the research program from ambiguity.

The controlled vocabulary of this program can be reduced to one chain: