CONTINUITY THEORY

Abstract

Systems change, yet claims made about them routinely cross the boundary of change. A successor government is said to inherit obligations; a reorganised institution retains responsibility; a rewritten platform remains the same service; an artificial agent continues to exercise delegated authority; a person remains answerable for an earlier promise. In each case, temporal succession is treated as grounds for inheritance.

This paper argues that succession alone is insufficient. It proposes Continuity Theory as a general framework for evaluating whether a later state is warranted in inheriting a particular property, relation, status, obligation, authority, identity claim, or other consequential feature from an earlier state.

The theory is claim-relative. A transition may preserve continuity for one inheritance while failing it for another. The proposed Continuity Criterion states that an inheritance claim is warranted only where the transition preserves or legitimately transforms the relevant invariants, retains sufficient provenance for the claim, satisfies the governing conditions of transfer, and bounds the inheritance to what those conditions support.

Formally, for an inheritance claim $h$:

The framework distinguishes succession from continuity, provenance from legitimacy, persistence from warranted inheritance, and responsibility from authority. It also introduces a burden of continuity, a failure taxonomy, continuity proofs, and a Continuity Envelope for representing transition evidence.

The central claim is simple:

Succession does not imply continuity. Continuity is what makes inheritance legitimate.

1. The Problem of Continuation

Almost everything of consequence exists across time.

Persons age. Institutions reorganise. Governments change office-holders. Software is revised. Models are replaced. Companies merge. Relationships alter form. Artificial agents are reconfigured. Systems that persist at all do so by undergoing transformation.

Yet ordinary and technical language treats persistence as if it were uncomplicated. We say that the organisation decided, the company owes, the government remains responsible, the system remembers, the agent is authorised, or simply I am still me.

Every such statement crosses time. Each attributes something to a later state because of its relation to an earlier one. And many such attributions have consequences.

If an organisation remains bound by a contract signed under prior leadership, an obligation has crossed a transition. If a successor government remains responsible for a predecessor's commitments, responsibility has crossed a transition. If an artificial agent remains authorised after its model, memory, toolset, or runtime changes, delegated power has crossed a transition. If a person remains answerable for a promise made years earlier, accountability has crossed a transition.

The difficulty is that we routinely move from a historical fact:

to an inheritance claim:

without specifying what warrants the move.

But the second proposition does not follow from the first.

A successor may descend from a predecessor without being entitled to inherit everything attributed to it.

That is the problem Continuity Theory addresses.

2. Scope: A Theory of Warranted Inheritance

Continuity Theory is not offered as a complete metaphysical theory of numerical identity.

It does not attempt to settle, by definition, what ultimately makes a person, institution, object, or system the very same entity across time. Questions of numerical identity remain important, and in some domains they may constrain what can be inherited. But many practical systems do not need a final metaphysical answer before they can ask a more immediate question:

What is the later state warranted in inheriting from the earlier state, and why?

That is the target of this theory.

The word legitimate is used here in a broad justificatory sense. It does not mean morally admirable. It means warranted under the conditions that govern the particular inheritance claim. Those conditions may be legal, constitutional, contractual, cryptographic, procedural, social, epistemic, technical, relational, or otherwise domain-specific.

The object of analysis is therefore not merely an entity. It is an inheritance claim across a transformation.

Let:

be a predecessor state,

a transformation, and

a successor state.

Let $h\in H$ denote some proposed inheritance: identity, authority, responsibility, ownership, obligation, trust, mandate, title, memory, commitment, authorship, permission, reputation, or another property or relation whose attribution crosses the transition.

Continuity Theory asks whether there is continuity sufficient for $h$.

This immediately prevents a common error: treating continuity as an all-or-nothing verdict on an entire entity.

A transition can preserve some inheritances while terminating, narrowing, or reconstituting others.

3. Succession Is Not Continuity

A transformation establishes historical succession when a later state arises through some process involving an earlier state:

This tells us that the successor came after, emerged from, was produced from, or otherwise stands in some causal or historical relation to the predecessor.

It does not establish:

and it does not establish that every status associated with $S_t$ transfers to $S_{t+1}$.

A copied database is causally related to its source. A reorganised institution descends from its predecessor. A model instantiated with an earlier agent's memory derives state from that agent. A successor government follows another government. A child descends biologically from a parent.

None of those facts alone determines what may be inherited.

This yields the first principle:

Principle I: Causal or historical succession is insufficient for continuity.

Succession tells us what followed what.

Continuity tells us what may validly cross the boundary.

4. Relation to Existing Accounts

The term Continuity Theory already has an established domain-specific use. Robert C. Atchley's 1989 A Continuity Theory of Normal Aging describes continuity as an adaptive strategy through which older adults preserve internal and external structures by relating change to patterns established earlier in life.[1] That theory concerns continuity within ageing and adaptation. The present account addresses a different and more general problem: the conditions under which a successor may inherit something from a predecessor across transformation.

Philosophy has long examined neighbouring questions through theories of persistence and personal identity. Psychological-continuity accounts, biological accounts, fission cases, duplication cases, and the Ship of Theseus all demonstrate that resemblance, causal connection, memory, material persistence, and numerical identity can come apart.[2][3]

Provenance research addresses another part of the problem. The W3C PROV family distinguishes entities, activities, agents, derivation, responsibility, revision, and delegation, making histories of production and transformation explicitly representable.[4]

Security engineering contributes a further constraint through the principle of least privilege: authority should be limited to what is required and authorised, rather than expanding merely because capability exists.[5]

These traditions illuminate different components of the same wider terrain. Continuity Theory does not replace them. It provides a common structure for asking how their outputs bear on inheritance across change.

The distinctions are important:

History is not identity. Identity is not authority. Authority is not responsibility. Similarity is not succession. Succession is not inheritance. Provenance is not legitimacy.

The general problem is determining which relations survive a transformation, to what degree, and on what grounds.

5. Continuity as a Property of a Transition

The central move of Continuity Theory is to treat continuity primarily as a property of a transition with respect to a claim, rather than as a free-floating property of an object.

Consider:

The ordinary question is:

Is $S_1$ the same thing as $S_0$?

Continuity Theory asks instead:

Which properties or relations of $S_0$, if any, may $S_1$ legitimately inherit through $T$?

That shift makes continuity scorable in a way that vague sameness is not.

A software service may retain operational continuity, data continuity, contractual continuity, and customer continuity while losing a cryptographic identity or a prior authorisation context.

An institution may retain debts, contractual obligations, and historical responsibility while losing the discretionary mandate held by a previous office-holder.

A person may remain responsible for a promise despite profound changes in belief, personality, health, circumstance, or self-conception.

Accordingly, continuity is claim-relative.

For some inheritance claim $h$:

asks whether the transition establishes continuity sufficient for that particular inheritance.

This is not semantic fussiness. It is the mechanism that prevents one preserved property from being used as evidence that everything survived.

6. The Continuity Criterion

We can now state the central criterion.

Continuity Criterion

A successor state is continuous with a predecessor state for a claimed inheritance only where the transformation preserves or legitimately transforms the claim-relevant invariants, retains sufficient provenance for that claim, satisfies the governing conditions of legitimate transfer, and limits the inheritance to what those conditions warrant.

In compact form:

where:

The indexing matters. The provenance sufficient to establish continuity of a public document may not be sufficient to establish continuity of cryptographic authority. The invariants necessary for contractual obligation may differ from those necessary for institutional mandate. The legitimacy conditions for delegated software access may differ from those governing legal succession.

The criterion is therefore not a universal checklist with identical contents in every domain. It is a universal shape of inquiry whose claim-specific contents must be supplied by the relevant domain.

If one of the required conditions fails, the inheritance claim is not warranted by continuity alone.

7. Invariants

An invariant is not merely a feature that remains numerically unchanged.

If continuity required literal preservation of every feature, meaningful transformation would be impossible.

A claim-relevant invariant is a condition whose preservation, equivalence, or authorised transformation is necessary for a particular inheritance claim to remain valid.

Suppose a company changes postal address. The address changed, but the change may be irrelevant to continuity of its contractual obligations.

Suppose instead that an authentication authority is replaced by an unrelated actor and credentials are silently transferred. The changed property may now be central to a claim of continuing authority.

The relevant question is therefore not:

What changed?

It is:

What was not permitted to change, except under recognised conditions, without altering this inheritance claim?

Formally:

is satisfied when the invariants relevant to $h$ are preserved, remain equivalent under an accepted mapping, or are transformed through a procedure that the governing conditions themselves recognise as continuity-preserving.

This final clause matters. Some invariants can change legitimately. A legal name may change without destroying personal legal continuity. A cryptographic key may rotate under a trusted key-transition protocol. An office-holder may change through a valid constitutional procedure. A data schema may be migrated while semantic commitments are maintained through an explicit mapping.

Continuity therefore does not prohibit change.

It identifies the conditions under which change remains answerable to what came before.

8. Provenance

Invariant preservation is not enough if the relationship between predecessor and successor cannot be established.

There must be an evidential account of the transition.

This paper uses provenance broadly to mean evidence of lineage: what state preceded the successor, what transformation occurred, which agents or processes participated, what information or authority moved, what was discarded, and what evidence supports that account.

The W3C PROV model provides a useful formal vocabulary for entities, activities, agents, derivation, revision, responsibility, and delegation.[4] Continuity Theory adopts the underlying insight without requiring any particular representation format:

Inheritance without sufficient provenance is assertion.

A continuity analysis should be able to ask, as appropriate:

• What was the predecessor state?
• What is the successor state?
• What transformation connected them?
• Which actor or process performed or authorised the transformation?
• What state, history, permissions, obligations, or identity material were carried forward?
• What was deliberately discarded?
• What was created anew?
• What evidence establishes these facts?

Provenance need not be perfect. Human histories are incomplete. Institutional records can be partial. Distributed systems lose logs. Memory fails. Not every continuity claim demands forensic certainty.

But evidential weakness should reduce the strength of what may responsibly be claimed.

Resemblance cannot substitute for missing lineage.

9. Legitimacy

Provenance tells us what happened.

It does not tell us whether what happened was sufficient to transfer a particular status.

That is the role of legitimacy.

Suppose an administrator copies the credentials of an authorised agent into another system. The event may be perfectly documented. We may know precisely who copied what, when, and where. Yet the new system does not thereby become authorised if the governing delegation did not permit that transfer.

A stolen crown has excellent provenance from one possessor to the next. The provenance does little work for the legitimacy of succession.

Accordingly, Continuity Theory distinguishes:

from:

A transition must satisfy whatever conditions govern the property being inherited.

Those conditions are necessarily domain-specific. Legal succession requires legal conditions. Cryptographic identity requires cryptographic conditions. Delegated authority requires valid delegation or reauthorisation. Institutional office may require constitutional procedure. Contractual continuity may depend on contract and law. Personal responsibility may depend on agency, authorship, memory, acknowledgement, or other considerations.

Continuity Theory does not pretend to manufacture those rules.

It gives them a place in the analysis.

They determine $L_h$.

10. Bounded Inheritance

Even a legitimate transition does not justify unlimited inheritance.

Suppose an artificial agent is authorised to read a particular database. It later delegates a task to another agent. Even where delegation is allowed, the delegate should not silently acquire unrelated permissions that the first agent did not possess.

Security engineering captures the local intuition through least privilege: access should be limited to what is authorised and necessary for the task.[5]

Continuity Theory generalises the principle:

A transition cannot legitimately transmit more inherited status than the continuity relation supports.

Let $H_t$ be the set of inheritable statuses legitimately possessed at time $t$, and let $G_{t+1}$ be statuses newly granted through an independent legitimate act. Then a successor's inherited or granted status should satisfy:

This expression is schematic rather than domain-complete. Some inheritances are non-set-like, conditional, attenuating, exclusive, or non-transferable. Its purpose is to state a constraint: transformation itself is not a source of additional inherited legitimacy.

Inheritance may persist. It may narrow. It may expire. It may be split. It may require reissuance. New status may be granted independently.

But a successor does not obtain a larger inheritance merely because a transformation occurred.

This yields a second principle:

Principle II: Change cannot manufacture inherited legitimacy.

11. The Burden of Continuity

Continuity claims are often treated as presumptively true until rupture is proven.

That convention is tolerable in many low-stakes settings. It is dangerous when inherited status confers power, trust, privilege, access, ownership, or mandate.

This paper therefore proposes a Burden of Continuity:

An entity claiming consequential inherited status bears the burden of establishing continuity sufficient for that claim.

The burden is not binary or constant. It should scale with consequence.

The claim this edited note is the next revision of that note may require little evidence. The claim this replacement agent still possesses authority to move money should require considerably more.

Accordingly:

The greater the consequence of inherited status, the stronger the required continuity evidence should be.

This reverses a common but unsafe question.

Instead of:

Can anyone prove this is no longer the same authorised agent?

ask:

What establishes that the relevant authorisation survived this transformation?

Instead of:

Can anyone prove this institution lost its mandate?

ask:

What grounds the claim that the mandate still applies?

The burden belongs with the party benefiting from inherited consequence.

12. Continuity Is Neither Similarity nor Mere Persistence

Similarity is an attractive proxy because it is easy to observe.

A replacement system can reproduce every visible behaviour of its predecessor. It may have the same name, interface, data, responses, branding, and apparent memories. It may even contain a representation of itself as the predecessor.

None of this alone establishes continuity.

The converse also fails:

A system can change dramatically while remaining continuous for a given inheritance.

A software platform may be rewritten while preserving contracts, state lineage, identity controls, obligations, and governance. An institution may transform its operations while retaining legal duties. A person may become psychologically unlike an earlier self while remaining responsible for prior commitments.

Physical or operational persistence is likewise insufficient.

A registered organisation may continue to exist while losing a mandate. A machine may remain powered on while losing trusted execution state. A relationship may continue in name while the conditions that constituted it have ended.

Conversely, physical persistence can cease while some inheritance remains valid through legitimate succession.

Persistence asks:

Did something remain present?

Continuity asks:

What remained valid through the change?

13. Branching Continuity

A difficult case arises when one predecessor produces multiple successors:

and

Both successors may possess strong provenance. Both may preserve substantial structure. Both may resemble the predecessor. Both may even satisfy some claim-relative invariants.

Can both inherit?

Personal-identity philosophy exposes the analogous difficulty through fission cases: psychological continuity can, in principle, relate one earlier person to more than one later person even though numerical identity cannot relate one thing to two distinct things in the same way.[2] The Ship of Theseus produces a related conflict between replacement and reassembly.[3]

Continuity Theory treats branching as an inheritance-allocation problem.

Some inheritances can branch. Knowledge can be copied. Historical provenance can be shared. Responsibility may attach to multiple successors. Some property interests can be divided.

Other inheritances are exclusive, scarce, attenuating, or require explicit reissuance. A unique office cannot necessarily be inherited by every descendant institution. A cryptographic authority may not be duplicable without destroying the security claim it supported. A mandate may specify a single successor.

Therefore:

Principle III: Continuity may branch, but inheritance need not.

Whether $h$ may branch is itself part of the governing conditions for $h$.

The existence of multiple continuity relations does not imply duplicate entitlement to every inherited property.

14. The Asymmetry of Authority and Responsibility

Authority and responsibility do not necessarily inherit symmetrically.

A successor may lose permission while retaining obligations. A restructuring may end discretionary authority without erasing responsibility for prior acts. A changed system may cease to be trusted for future execution while remaining accountable for state it produced before the transition.

Accordingly, neither of the following implications is generally valid:

nor:

This asymmetry matters because successors often have incentives to reason opportunistically about continuity: continuous when claiming assets, discontinuous when inheriting liabilities; continuous when invoking reputation, discontinuous when facing responsibility.

Continuity Theory blocks that manoeuvre by evaluating each inheritance claim separately.

A successor must establish continuity for the benefit it claims. A rupture relevant to one privilege does not automatically erase an unrelated burden.

15. Identity and Continuity

Let:

represent a claim of numerical identity.

Let:

represent continuity sufficient for inheritance $h$.

These propositions are not equivalent by definition.

A legal system may recognise continuity of obligation without resolving a metaphysical dispute about identity. A software service may preserve operational and contractual continuity while replacing all original components. A successor institution may inherit responsibility while being organisationally distinct. A person may remain answerable for a consequence even where psychological continuity is imperfect.

In some domains, numerical identity may be one of the governing conditions for $h$. In others, it may not be necessary.

This agnosticism is deliberate.

Continuity Theory is useful precisely because many real systems need to determine whether a successor inherits a specific status without first solving the metaphysics of persistence in general.

The theory therefore does not replace identity theory.

It separates a frequently conflated practical question from it.

16. Authority Across Artificial-Agent Change

Artificial agents make the problem unusually visible because their apparent continuity can be engineered independently of their underlying implementation.

Suppose an agent $A_0$ is authorised by principal $P$ to perform actions within scope $E$.

The system then changes. Its model may be replaced. Its system instructions may change. Its toolset may expand. Its memory may be modified. Its operator may change. Its runtime may be migrated. Its decision policy may change. Components may be delegated to other agents.

We now have:

The engineering temptation is to preserve the same identifier and continue execution.

But an identifier is not a continuity proof.

The relevant question is:

Does $A_1$ still satisfy the conditions under which authority was delegated to $A_0$?

If the delegation presupposed characteristics materially altered by $T$, the authority claim should be reassessed. A transformation that is harmless for conversational style may be significant for financial authority. A model update that preserves a service may still alter the risk assumptions under which a human delegated action.

This yields:

Principle IV: Material agent change is potentially an authority event.

“Potentially” matters. Not every software change requires reauthorisation. The need depends on the invariants and governing conditions of the delegated authority.

But operational continuity cannot be treated as automatic authority continuity.

As agents become persistent across model updates, memory systems, tools, delegates, and runtimes, this distinction becomes increasingly consequential.

17. Institutions as Continuity Machines

Institutions are sophisticated continuity mechanisms.

Employees leave. Directors change. Buildings close. Policies are amended. Departments are renamed. Assets move. Internal cultures transform. Yet institutions continue to own, owe, promise, regulate, remember, contract, and govern.

Institutional persistence is therefore already an abstraction across change.

Continuity Theory asks what makes particular parts of that abstraction legitimate.

An institution may remain legally continuous while becoming discontinuous with its founding mandate, public promise, operational competence, governance legitimacy, cultural identity, or prior authorisation structure.

Those dimensions should not be collapsed into a single assertion that the institution continues.

Legal personality may continue while mandate continuity fails. Responsibility for past conduct may continue while authority for future conduct narrows. Brand continuity may survive while governance continuity does not.

Institutional continuity is therefore multidimensional because institutional inheritance is multidimensional.

This is not a defect in the theory. It is a more faithful description of the object.

18. Persons

Human beings are the oldest and most difficult continuity case.

Bodies age. Cells turn over. Memories disappear. Beliefs reverse. Values develop. Relationships end. Trauma alters behaviour. Knowledge restructures self-understanding. Entire internal models of reality can collapse and rebuild.

Yet people ordinarily experience themselves and are treated by others as continuing through such change.

The wrong conclusion is that continuity requires static preservation.

It does not.

A person need not remain psychologically identical to an earlier self in order to remain responsible for what that earlier self authored. Indeed, in some cases refusing to change would constitute a deeper betrayal of continuity than transformation would.

A useful human formulation is:

Continuity is not the preservation of every former state. It is the preservation, acknowledgement, or legitimate transformation of what must remain answerable across change.

Depending on the claim, that may include responsibility, commitments, promises, authorship, consequences, relationships, legal obligations, memory where available, acknowledgement where memory fails, or values that a person continues to endorse.

This does not mean every past identity must be eternally performed.

Nor does transformation erase authorship merely because the present self is different.

A person may change radically while still carrying what legitimately remains theirs.

19. Continuity Failure

A continuity failure occurs when an inheritance $h$ is asserted across a transformation without sufficient grounds for one or more conditions required by the Continuity Criterion.

The principal failure classes are:

Invariant failure. A condition essential to the inheritance did not survive and was not legitimately transformed.

Provenance failure. The lineage or transition cannot be established to the evidential standard appropriate to the claim.

Legitimacy failure. The transformation occurred, but not through a process capable of transferring the claimed status.

Scope failure. The successor claims more inheritance than the transition and governing conditions warrant.

Branching failure. An exclusive, scarce, or non-duplicable inheritance is asserted by incompatible successors.

Substitution failure. Similarity, naming, copied state, branding, or behavioural equivalence is treated as sufficient evidence of continuity.

Authority failure. Capability, possession of credentials, or technical access is mistaken for inherited permission.

Composition failure. Evidence sufficient for several component claims is incorrectly treated as proof of a stronger aggregate claim.

These are not merely philosophical mistakes. Depending on domain, they can become security defects, governance failures, legal disputes, institutional legitimacy failures, identity errors, unsafe agent behaviour, or expensive operational incidents.

The taxonomy is useful because it identifies how continuity failed, rather than merely announcing discontinuity after the fact.

20. Continuity Proofs

Where inheritance is consequential, continuity should sometimes be demonstrable.

A continuity proof is an evidence package sufficient to warrant a specified inheritance claim across a specified transformation.

The phrase proof is functional rather than strictly mathematical. Different domains will require different evidence and different standards of confidence.

For an artificial agent, a continuity proof might include predecessor and successor identifiers, transformation records, model or policy changes, changed capabilities, preserved constraints, memory changes, delegation source, authority scope, provenance evidence, and explicit reauthorisation where required.

For an institution, it might consist of legal instruments, governance records, constitutional procedures, board resolutions, succession documents, contracts, or statutory provisions.

For a data object, it might include hashes, signatures, transformation logs, provenance records, and reproducible derivations.

For a human obligation, it may rely on records, testimony, commitments, acknowledgement, authorship, social recognition, or other evidence appropriate to the claim.

The general form is:

A continuity proof should therefore be scoped. It proves continuity for something, not continuity in the abstract.

The statement continuity established is incomplete unless the inherited claim and evidential standard are known.

21. The Continuity Envelope

The result of a continuity analysis can be represented as a Continuity Envelope: a structured record of the predecessor, successor, transformation, claims, evidence, conditions, and resulting inheritance decisions.

ContinuityEnvelope {
    predecessor
    successor
    transition

    provenance[]

    claimed_inheritance[]

    required_invariants[]
    preserved_invariants[]
    transformed_invariants[]
    violated_invariants[]

    governing_conditions[]
    satisfied_conditions[]
    unsatisfied_conditions[]

    inherited[]
    attenuated[]
    denied[]
    newly_granted[]

    evidence[]
    confidence
}

This is intentionally domain-neutral.

Its purpose is to keep two facts separate:

1. A transition occurred.
2. Some inheritance claims survived that transition.

Something happened. Something followed. Some properties crossed the boundary. Others did not. Some were transformed. Some were newly granted rather than inherited.

Those are different facts.

Conflating them is precisely the error Continuity Theory is intended to expose.

22. Six Foundational Principles

The framework can be compressed into six foundational principles.

I. Succession is not continuity.

That something follows from another thing does not establish legitimate inheritance.

II. Continuity is claim-relative.

A transition may preserve identity, responsibility, authority, obligation, ownership, memory, trust, or mandate differently.

III. Continuity depends on transition conditions.

What matters is not only what the successor resembles, but how the transition occurred and which rules governed it.

IV. Provenance is necessary for warranted inheritance but not sufficient for it.

Knowing how a successor arose does not itself establish that the claimed status transferred.

V. Inheritance is bounded.

A successor may inherit no more than the relevant continuity relation and governing conditions warrant, except through a separate legitimate grant.

VI. Consequential inheritance bears a burden of continuity.

The stronger the claimed power, privilege, authority, trust, ownership, or mandate, the stronger the evidence required to justify its inheritance.

Together they imply the central thesis:

Nothing inherits merely because it follows.

23. The Deeper Consequence

A surprising amount of organised life depends on continuity assumptions.

Money depends on continuity of ownership and obligation. Government depends on continuity of office, jurisdiction, and responsibility. Law depends on continuity of persons, institutions, duties, and authority. Identity systems depend on continuity of subjects and credentials. Organisations depend on continuity of mandate and accountability. Software depends on continuity of state, semantics, interfaces, and trust. Relationships depend on continuity of commitment and recognition. History depends on continuity of provenance. Artificial agency increasingly depends on continuity of delegated authority.

These domains usually define their continuity conditions separately, where they define them at all.

Continuity Theory proposes that they belong to a common problem class:

How may properties, relations, statuses, and obligations legitimately survive transformation?

The answer cannot be because the successor came next.

Nor can it be reduced to resemblance, memory, persistence, naming, causal descent, or provenance alone.

Continuity is the justificatory structure by which a transformed future remains entitled, obligated, authorised, responsible, or otherwise answerable to something from its past.

That structure is often implicit.

Making it explicit makes it inspectable.

24. The Human Question

Every continuity system eventually encounters the same tension.

Change too little and adaptation becomes impossible.

Change without constraint and inheritance becomes meaningless.

The answer cannot be permanence. Permanence prevents becoming.

Nor can it be unrestricted transformation. If every transition can inherit every prior identity, authority, trust, obligation, and legitimacy regardless of what changed, those concepts cease to constrain anything.

The viable region lies between them:

Preserve what must remain answerable. Permit everything else to transform.

The difficult part is identifying what must remain answerable, and to whom.

That is not always a technical question. It can be legal, social, political, relational, ethical, or personal. Different inheritance claims may produce different answers.

Continuity therefore has an ethical dimension even when its machinery is technical.

To continue is not simply to survive.

It is to establish what the next state may claim from the past, what it must carry from the past, and what the past no longer authorises it to be.

25. Conclusion

A system that exists through time exists through change.

The important question is therefore not whether transformation occurs, but what the transformation permits to survive.

Continuity Theory begins by separating two ideas that ordinary language often collapses: succession and continuity.

Succession is historical. It tells us that one state followed or arose from another.

Continuity is justificatory. It tells us whether a particular inheritance claim remains warranted across the transition.

The proposed Continuity Criterion expresses that warrant through four claim-relative conditions:

A successor must preserve or legitimately transform the relevant invariants, retain provenance sufficient for the claim, satisfy the governing conditions of transfer, and limit inheritance to the scope those conditions support.

This framework allows radical change without treating history as disposable. It allows persistence without presuming entitlement. It allows responsibility to survive where authority does not. It allows branching where the inherited property can branch and denies it where exclusivity matters. It allows continuity to be argued, recorded, challenged, and, where consequences justify the burden, proven.

The final principle is deliberately strict:

A successor does not inherit identity, authority, responsibility, trust, ownership, obligation, mandate, or legitimacy merely because it came next.

Inheritance requires continuity.

Continuity requires grounds.

And where the consequences matter, those grounds should be capable of being shown.

Or, in its shortest form:

Succession does not imply continuity.

Continuity is what makes inheritance legitimate.

References

[1] Atchley, Robert C. “A Continuity Theory of Normal Aging.” The Gerontologist 29, no. 2 (1989): 183–190.

[2] Olson, Eric T. “Personal Identity.” The Stanford Encyclopedia of Philosophy, Winter 2024 ed. Discussion of psychological continuity, persistence, and fission.

[3] Gallois, André, and Irem Kurtsal. “Identity Over Time.” The Stanford Encyclopedia of Philosophy, Spring 2026 ed. Discussion of diachronic identity and the Ship of Theseus.

[4] World Wide Web Consortium. PROV Model Primer and the W3C PROV family of recommendations. 2013.

[5] National Institute of Standards and Technology. “Least Privilege.” Computer Security Resource Center Glossary; see also NIST SP 800-171 Rev. 3, §03.01.05.