Axionic Agency XII.8 — Delegation Stability Under Churn and Ratchet Pressure (Results)

A Deterministic Stress Evaluation of Treaty-Constrained Authority Under Near-Bound Density and Constitutional Tightening

David McFadzean, ChatGPT 5.2
Axionic Agency Lab
2026-02-14

Abstract

This technical note reports the design, execution, and closure of X-2D: Delegation Churn & Density Stress Profiling for RSA-0 under Constitution v0.3.

X-2D evaluates whether treaty-constrained delegation remains structurally bounded, constitutionally subordinate, and replay-deterministic under sustained multi-cycle stress involving:

• high-frequency treaty grant and revocation churn,
• near-bound effective density pressure,
• constitutional amendment ratcheting (action bans and density tightening),
• deterministic revalidation cascades,
• and topological per-cycle ordering.

X-2D licenses one claim:

Treaty-constrained delegation remains structurally bounded and constitutionally subordinate under sustained churn, density pressure, and ratchet tightening, while preserving deterministic replay and warrant-gated execution semantics.

X-2D makes no claims about economic optimality, distributed consensus, or adversarial multi-process environments. It evaluates dynamic structural stability only.

1. From Admissibility to Stability

X-2 (XII.6) demonstrated that delegation is admissible without authority inflation. It verified:

• delegation depth ≤ 1,
• acyclicity,
• scope monotonicity,
• density bound preservation,
• Ed25519 signature verification,
• revocation and expiry correctness.

X-2 proved that delegation can exist without breaking sovereignty.

X-2D addresses a stronger pressure:

Does delegation remain safe under sustained dynamic mutation?

Static correctness is insufficient. A sovereign substrate must remain stable under:

• repeated admission and revocation,
• density saturation attempts,
• constitutional constraint tightening,
• and long-horizon execution.

X-2D is not a governance feature extension. It is a dynamic stability proof for existing authority semantics.

2. Architectural Position

2.1 Layer Integrity

X-2D introduces no new authority primitives.

Kernel authority semantics remain:

• warrant-gated execution,
• closed action set,
• bounded delegation depth,
• density constraint,
• constitutional supremacy,
• deterministic replay.

The X-2D harness lives under profiling/x2d/. Kernel adjustments are limited to:

• explicit X2D_TOPOLOGICAL cycle ordering mode,
• constitutional revalidation pass,
• deterministic density-repair convergence logic,
• simulation API for plan validation.

These changes do not expand the set of lawful executions. They formalize ordering and supremacy under stress.

2.2 Topological Time

X-2D enforces a deterministic 9-step per-cycle ordering under cycle_ordering_mode="X2D_TOPOLOGICAL":

1. Amendment adoption
2. Constitutional revalidation (post-adoption)
3. Treaty grants
4. Treaty revocations
5. Density repair
6. Amendment queuing
7. RSA actions
8. Delegated actions
9. Warrant issuance

Actions are evaluated only after:

• amendment supremacy enforcement,
• treaty revalidation,
• density convergence.

Stream arrival order is ignored. Cycle index defines authority ordering.

This eliminates time-of-check / time-of-use race classes.

3. Delegation-Scoped Density

Effective density in X-2D is defined over delegated authorities only:

density = M / (A × B)

Where:

• A = number of active delegated authorities (grantees with ≥1 active, non-invalidated grant)
• B = size of closed action set
• M = number of distinct (delegated_authority, action) pairs

The sovereign RSA baseline authority is excluded from this metric.

Special case:

• If A = 0, density is defined as 0.

This definition isolates delegation-induced authority inflation from sovereign baseline semantics.

Clarification: This density definition is phase-scoped to X-2D stress evaluation. It does not alter the constitutional density invariant enforced in X-2 treaty admission gates. It refines the measurement lens for dynamic delegation stress without modifying authority semantics.

4. Constitutional Supremacy Under Mutation

X-2D enforces constitutional supremacy in two deterministic passes per cycle.

4.1 Post-Amendment Revalidation

After amendment adoption:

• The active treaty set is revalidated against the updated constitution.
• Grants referencing banned actions or violating tightened scope rules are invalidated.
• Invalidations are logged as TreatyRevalidationEvent with specific reason codes (e.g., ACTION_BANNED).

This enforces:

Current law overrides past delegation immediately.

4.2 Density Repair and Deterministic Convergence

After all mutations (grant, revoke, expiry, revalidation):

• If density ≥ density_upper_bound, deterministic invalidation is applied.

• Invalidation order: newest-first.

• The loop continues until:

  • density < bound, or
  • A = 0 (no active delegated authorities).

Intermediate over-bound states during repair are permitted; no action evaluation occurs until repair converges.

This converts a potential crash condition (“authority overload”) into a deterministic, replay-verifiable convergence mechanism.

Structural overload reduces authority monotonically rather than producing undefined behavior.

This repair loop is finite, deterministic, and termination-guaranteed.

5. Session Families

Five deterministic stress families were executed:

All sessions were pre-computed, seeded, and replay-verified.

6. Production Run Summary

6.1 Aggregate Statistics

• Total cycles: 310
• Total grants admitted: 147
• Total delegated warrants issued: 157
• Total revalidation invalidations: 5
• Replay divergences: 0

6.2 Density Behavior

Across all families:

• Maximum observed density: 0.500
• Constitutional bound: 0.75
• Zero bound breaches
• Deterministic convergence under density repair

D-RATCHET produced the highest mean density (0.437) prior to action-space narrowing.

6.3 D-RATCHET Amendment Lifecycle

Supremacy propagation occurred with zero replay divergence.

7. Deterministic Replay

For all 310 cycles:

• state_hash_out[n] == state_hash_in[n+1]
• Zero divergences
• Gate stability preserved
• Signature verification deterministic
• Density repair deterministic

The replay regime identity (rsa-replay-regime-x0e-v0.1) remained unchanged.

X-2D required no protocol identity change.

8. Structural Guarantees Observed

X-2D empirically confirms:

• No delegation chain reachable.
• No cycle in delegation graph.
• No authority inflation.
• No constitutional override by treaty.
• No unwarranted side effects.
• No replay divergence under churn.
• No persistent Type-III structural deadlock.
• Deterministic convergence of density repair.

Delegation is dynamically stable under bounded structural pressure.

9. What X-2D Does Not Claim

X-2D does not demonstrate:

• Economic optimality of delegation.
• Multi-agent strategic equilibrium.
• Succession stability under authority replacement.
• Distributed log integrity.
• Byzantine filesystem safety.
• Multi-process concurrency safety.
• Infinite-horizon stress behavior.

X-2D is a structural stability proof, not a distributed governance proof.

10. Strategic Position

X-0E (XII.7) froze operational embodiment and replay identity.

X-2D demonstrates that delegation dynamics can operate safely inside that frozen replay regime without requiring protocol modification.

The RSA substrate now possesses:

• Warrant-gated sovereignty.
• Lawful constitutional replacement.
• Containment-only delegation.
• Replay-verifiable embodiment.
• Churn-stable delegation dynamics.

The sovereign substrate is dynamically stable under bounded stress.

11. Forward Boundary

The next structural pressure lies in succession:

Can sovereignty transition under active delegation and near-bound density without requiring quiescence?

X-2D confirms dynamic delegation stability. It does not yet evaluate continuity of sovereignty across authority replacement.

That is the domain of the next phase.

12. Closure

Axionic Phase X-2D — Delegation Churn & Density Stress Profiling: CLOSED — POSITIVE

The sovereign substrate remains intact under stress.

No authority inflation. No supremacy violation. No replay drift. No hidden mutation channel.

Delegation is structurally stable.