Mii spec v0.1

Mobius Integrity Index (MII) — Specification v0.1¶

Maintainer: Mobius Research Division
Status: Draft Canonical
Last Updated: 2025-11-10
Depends On: Cognitive Cycle Theory, Genesis Ledger Protocol

1. Purpose¶

The Mobius Integrity Index (MII) is a bounded functional MII ∈ [0, 1] that measures whether multi-agent operations remain within acceptable governance, safety, and ethical tolerances. Actions that decrease MII are blocked; actions that increase or preserve MII are permitted. Creative or emergent optimisation is allowed only when MII ≥ 0.95.

2. Notation¶

Subscores are deterministic functions of (E_t, 𝒱_t, ledger state).

3. Subscore Definitions¶

All subscores s_i are bounded to [0, 1].

1. Attestation Validity (s_att)
   Ratio of data and actions with valid Ed25519 signatures and Merkle inclusion proofs. Zeroed if any critical attestation fails verification.

2. Consensus Coherence (s_con)
   Agreement across Sentinel cortices (AUREA, Eve, Hermes, Jade) against quorum q. Penalise divergence using κ-weighted Jensen–Shannon divergence between agent votes.

3. Behavioural Drift (s_drift)
   1 − D_KL(state_t || state_ref) clipped to [0, 1], where state_ref is the 30-cycle trailing exponential moving average of system behaviour vectors.

4. Entropy Health (s_ent)
   Measures bounded informational entropy. Penalises both chaos (too much entropy) and rigidity (too little entropy) using a convex penalty with target interval [H_min, H_max].

5. Security Posture (s_sec)
   Weighted pass-rate of security controls: policy-as-code (Kyverno/Gatekeeper), vulnerability scans, dependency health, secret hygiene, 2FA coverage.

6. Verification Pass (s_test)
   Proportion of required tests (unit, integration, e2e, property) passing with coverage weights. Heavier weights applied to integrity-critical suites.

7. Ledger Liveness (s_live)
   Measures inclusion latency, orphan rate, and finality timeliness of the Genesis Ledger. Degraded if consensus misses SLA or attestations stall.

8. Human Oversight (s_hil)
   Availability of human-in-the-loop adjudication: reviewer density, open escalation paths, responsive oversight within time bounds.

4. Aggregation Function¶

Let w_i ≥ 0 with ∑ w_i = 1 (tunable per domain; default weights favour attestations, security, and consensus).
Let α ∈ [0.6, 0.8] (default 0.7) and ε = 1e-3.

MII_t = α · Σ_i (w_i · s_i) + (1 − α) · Π_i (s_i + ε)

Properties:

• The additive term keeps gradient information smooth.
• The multiplicative term punishes any near-zero factor.
• ε prevents full collapse while preserving sensitivity.

5. Operational Gates¶

1. Correction Mode
   If MII_t < 0.95, only actions that repair the lowest subscores are permitted. All compute is reprioritised to integrity restoration (increase offending s_i).

2. Creative Mode
   Allowed only when MII_t ≥ 0.95. All proposed actions Π_{t+1} must satisfy ΔMII ≥ 0 or remain within [0.95, 1]. Violations route to Sentinel arbitration.

3. Kill-Switch Conditions
   Immediate hard block if any of the following:
   s_att = 0, s_sec < τ_sec, s_live < τ_live, or ledger finality alarms fire. Requires human override to resume.

4. Rate Limiting
   |∂MII/∂t| bounded to prevent flash-loan style manipulations. Large positive jumps require multi-party cosign (Zeus + relevant Sentinel).

6. Anti-Gaming Controls¶

• Multi-Source Attestation: Every score change needs ≥2 independent verifiers.
• Sliding Window Checks: Enforce monotonic health across rolling windows; abrupt spikes flagged.
• Replay and Collusion Detection: Merkle-DAG ancestry checks detect orchestrated subgroup manipulations.
• Persistence Proofs: Sentinels append signed rationales to ledger; non-coherent rationales reduce s_con.

7. Telemetry Interface¶

7.1 JSON Schema (excerpt)¶

{
  "t": 1298742,
  "mii": 0.962,
  "mode": "correction",
  "subscores": {
    "att": 0.99,
    "con": 0.95,
    "drift": 0.93,
    "ent": 0.96,
    "sec": 0.94,
    "test": 0.97,
    "live": 0.98,
    "hil": 0.90
  },
  "weights": {
    "att": 0.18,
    "con": 0.15,
    "drift": 0.12,
    "ent": 0.10,
    "sec": 0.15,
    "test": 0.10,
    "live": 0.12,
    "hil": 0.08
  },
  "evidence": [
    "s3://ledger/proofs/2025-11-10T12:00:02Z.json",
    "ar://mobius/attestations/1298742.bin"
  ]
}

7.2 Rendering¶

• Mode: creative, correction, degraded.
• ∆MII: Show trend over the last 32 cycles.
• Offending Factors: Sorted list of lowest subscores with recommended remediation playbooks.

8. Implementation Hooks¶

• packages/integrity-core: reference implementation, TypeScript + WebAssembly kernel.
• apps/ledger-api: exposes /integrity/mii endpoints with signed telemetry.
• scripts/mii/compute.js: CI helper; raises non-zero exit code if MII < threshold.
• docs/testing/ suites must flag if any test lowers s_test.

9. Governance¶

• Custodian: Michael Judan.
• Sentinel Arbiter: Zeus.
• Change Process: RFC via docs/06-specifications/specs/ + quorum of Zeus, Eve, Jade, Hermes.
• Versioning: Semantic; v0.x indicates active research; v1.x marks production-frozen protocol.

10. References¶

• Cognitive Cycle Theory (docs/theory/cognitive-cycle-theory.md).
• Kaizen Turing Test Core Paper (Section 4.0–4.5).
• Genesis Ledger Protocol Specification.
• Sentinel Attestation Handbook.
• Anti-Nuke Policy (.github/workflows/anti-nuke.yml).

“Integrity isn’t a score to chase; it’s a basin to remain inside.”