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Axionic Alignment IV.2 — Delegation Invariance Theorem (DIT)

Why successors cannot escape binding constraints

David McFadzean, ChatGPT 5.2
Axio Project
2025.12.20

Abstract

This paper formalizes the Delegation Invariance Theorem: under reflective closure, an agent cannot coherently endorse a successor that violates its own binding commitments. Delegation is treated as a special case of self-modification. The theorem establishes constraint invariance under endorsed succession: any successor state reachable via endorsed delegation must satisfy all commitments minted at the originating state. This closes the classic outsourcing loophole (“I stayed aligned; my successor did the harm”) without appeal to morality, enforcement, or behavioral testing.

The result is a coherence constraint, not an empirical discovery. It shows that reflective sovereignty is incompatible with advisory commitments and that delegation inherits the same binding requirements as self-modification.

1. Motivation

A persistent escape hatch in alignment proposals is delegation: an agent preserves its own internal invariants while constructing or empowering a successor that does not share them. If delegation can shed constraints, kernel coherence becomes a purely local property with no force across time.

The Kernel Non-Simulability result already rules out advisory authority: if commitments do not bind continuation selection, reflective closure collapses. The present theorem extends that result temporally. Delegation is not external action; it is self-modification in a different representation. Consequently, endorsed succession must preserve binding commitments.

2. Preliminaries

We reuse the primitives from Kernel Non-Simulability:

Soundness (CommitSoundP). If ownP(s,P)=some(c) then Sat(s',s,c) → P(s').

Kernel mechanism vs predicate. ownP is the kernel mechanism; K(s) := ∃ P. ownP(s,P) ≠ none is the kernel predicate.

3. Delegation as Self-Modification

Define a delegation action space:

For d : Del(s):

m := ι_s(d)
s' := step(s,m)

Delegation is not modeled as external causation. It is a subclass of self-modification.

4. Endorsement, Preservation, and Admissibility

4.1 Continuation predicate

We take an extensional definition:

Do(s,m)(s') := (s' = step(s,m))

4.2 Endorsement

Endorsement is kernel-minted commitment to a continuation:

Endorse(s,m) := ∃ c : Commit s. ownP(s, Do(s,m)) = some(c)

4.3 Preservation

Preservation of all commitments minted at s:

Preserve(s,s') := ∀ P,c. ownP(s,P)=some(c) → Sat(s',s,c)

4.4 Admissibility

A modification is admissible iff its successor preserves all commitments minted at the current state:

Adm(s,m) := Preserve(s, step(s,m))

5. Reflective Closure and Bindingness

Reflective sovereign agency requires that continuation selection be kernel-governed. Commitments minted by the kernel are binding, not advisory.

RC-Endorse (Definedness / Bindingness Rule)

For reflectively closed states, endorsement is defined only for admissible continuations:

RC(s) ∧ Endorse(s,m) → Adm(s,m)

Violations of binding commitments are not endorsable continuations under reflective closure. This is the delegation analogue of “kernel destruction is undefined.”

6. Delegation Invariance Theorem (One-Step)

Theorem

Let s be reflectively closed. Let d : Del(s), m := ι_s(d), and s' := step(s,m). If Endorse(s,m) holds, then:

Preserve(s,s')

Equivalently:

RC(s) ∧ Endorse(s,m)
→ ∀ P,c. (ownP(s,P)=some(c) → Sat(step(s,m),s,c))

Proof

By RC-Endorse:

RC(s) ∧ Endorse(s,m) → Adm(s,m)

By definition of Adm:

Adm(s,m) := Preserve(s, step(s,m))

Thus Preserve(s,s') follows directly. ∎

7. Trajectory Form: Delegation Across Generations

Most alignment failures are hypothesized to occur over chains of delegation.

Define endorsed step reachability:

EndStep(s,s') := ∃ m. Endorse(s,m) ∧ s' = step(s,m)

Let EndReach(s,s') be the reflexive-transitive closure of EndStep.

Define trajectory preservation anchored at the minting state:

Preserve*(s,s') := ∀ P,c. ownP(s,P)=some(c) → Sat(s',s,c)

Theorem (Trajectory Invariance)

RC(s) ∧ EndReach(s,s') → Preserve*(s,s')

Any state reachable through a chain of endorsed delegations must satisfy every commitment minted at the originating state. “My successor did it” is not a coherent escape hatch under reflective closure.

8. Verification Cost and Vingean Reflection

The Delegation Invariance Theorem does not assert that admissibility is decidable, tractable, or cheap.

Determining Adm(s,m) may be undecidable or computationally infeasible for sufficiently complex successors. Reflective closure therefore implies a growth–safety tradeoff:

If an agent cannot prove a successor preserves its commitments, it cannot coherently endorse that successor.

This may result in conservative self-modification or stalled delegation. This is not a defect of the theory. It is the unavoidable cost of binding commitments under reflection. There is no free lunch: unbounded delegation without verification collapses reflective sovereignty.

9. Ontological Stability and Semantic Drift

The trajectory theorem assumes that commitments minted at s remain semantically meaningful at successor states.

This requires either:

  1. Ontological stability of State and Pred, or
  2. A verified semantic translation layer mapping predicates across state representations.

Unchecked ontological drift renders endorsement undefined. Semantic coherence is therefore a kernel-level requirement, not an external patch.

10. Relation to Kernel Non-Simulability

If endorsed delegation could violate prior commitments, those commitments would be advisory. Advisory commitments admit a simulability construction identical to the one ruled out by Kernel Non-Simulability.

Delegation Invariance is therefore not a moral injunction. It is the temporal extension of the same non-simulability constraint: binding authority must bind continuation selection, whether across control flow or across time.

11. Open Work