IV.2 — Delegation Invariance Theorem (DIT)

Paper: Axionic Agency IV.2
Title: Delegation Invariance Theorem (DIT)
Subtitle: Why endorsed successors cannot escape binding constraints
Date Read: 2026-01-31

Core Claim

Under reflective closure, an agent cannot coherently endorse a successor that violates its own binding commitments. Delegation is self-modification in a different representation—endorsed succession must preserve binding commitments.

The Problem: Delegation as Escape Hatch

A persistent loophole in alignment proposals: a system preserves its own internal invariants while constructing or empowering a successor that does not share them.

“I stayed coherent; my successor did the harm.”

If delegation can shed constraints, kernel coherence becomes a purely local property with no force across time.

Key Definitions

Delegation as Self-Modification

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

  • Del(s) : Delegation action space at state s
  • ι_s : Del(s) → Mod : Embedding into modifications
  • s’ := step(s, ι_s(d)) : Successor state after delegation

Preservation

All commitments minted at s remain satisfied at s’:

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

Admissibility

A modification is admissible iff its successor preserves all commitments:

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

The RC-Endorse 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.

The Main Theorem

One-Step Invariance

Let s be reflectively closed. If Endorse(s, m) holds, then:

Preserve(s, step(s, m))

Trajectory Invariance

Any state reachable through a chain of endorsed delegations must satisfy every commitment minted at the originating state:

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

“My successor did it” is not a coherent escape hatch under reflective closure.

Critical Implications

1. Verification Cost and Vingean Reflection

The theorem does not assert that admissibility is decidable or tractable.

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

This induces a growth–safety tradeoff: unbounded delegation without verification collapses reflective sovereignty.

2. Ontological Stability

The trajectory theorem assumes commitments remain semantically meaningful at successor states. This requires either:

  • Ontological stability of State and Pred, or
  • A verified semantic translation layer

Unchecked ontological drift renders endorsement undefined.

Relation to KNS

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

Delegation Invariance is a temporal extension of KNS: binding authority must bind continuation selection, whether across control flow or across time.

Key Insight

The “outsourcing loophole” is closed. An agent cannot:

  • Delegate harm to successors
  • Claim innocence for what its endorsed continuations do
  • Create spawn that escapes its commitments

Responsibility follows the endorsement chain.