Level 4.8: Strategic Self-Modeling Agent - Architecture & Design¶

MSCP Level Series | Level 4.5 ← Level 4.8 → Level 4.9
Status: 🔬 Research Stage - This level is a conceptual design and has NOT been implemented. All mechanisms described here are theoretical explorations that require extensive validation before any production consideration.
Date: February 2026

Revision History¶

Version	Date	Description
0.1.0	2026-02-23	Initial document creation with formal Definitions 1-13, Proposition 1
0.2.0	2026-02-26	Added overview essence formula; added revision history table
0.3.0	2026-02-26	Added VaR vs CVaR coherence remark; added calibration improvement remark with adaptive rate proposal

1. Overview¶

Level 4.8 extends the self-architecting capabilities of Level 4.5 with structured world modeling, calibrated introspective self-assessment, and long-horizon strategic planning under resource constraints. The agent can now anticipate external changes, understand its own capabilities and limitations, and optimize decisions across multiple time horizons - all while preserving every stability invariant established in prior levels.

Level Essence. A Level 4.8 agent selects optimal strategies by maximizing expected utility given its probabilistic world model and calibrated self-knowledge of its own capabilities:

\[s^* = \arg\max_{s \in \Sigma_{\text{compare}}} \mathbb{E}\bigl[U(s) \mid \mathcal{W}_{\text{prob}},\; \mathcal{M}_{\text{cap}}\bigr]\]

⚠️ Research Note: Level 4.8 represents a significant leap in agent cognition - from self-architecture to strategic self-awareness. The mechanisms described here are exploratory designs. They have not been validated in production environments and should be treated as research hypotheses, not engineering specifications.

1.1 Formal Definition¶

Definition 1 (Level 4.8 Agent). A Level 4.8 agent extends a Level 4.5 agent with world modeling, meta-cognitive self-assessment, and strategic planning:

\[\mathcal{A}_{4.8} = \mathcal{A}_{4.5} \oplus \langle \mathcal{W}_{\text{prob}}, \mathcal{M}_{\text{cap}}, \mathcal{S}_{\text{strat}}, \mathcal{V}_{\text{stab}} \rangle\]

where: - \(\mathcal{W}_{\text{prob}} = \langle \mathbf{E}, \mathcal{B}, \mathcal{C}_{\text{causal}} \rangle\) - probabilistic world model (environment state, belief distribution, causal graph) - \(\mathcal{M}_{\text{cap}} = \langle \mathbf{C}, \phi_{\text{cal}}, \mathcal{U} \rangle\) - meta-cognitive self model (capability matrix, calibration function, unknown domain registry) - \(\mathcal{S}_{\text{strat}} = \langle \mathcal{G}_{\text{stack}}, \Sigma_{\text{compare}}, \mathcal{R}_{\text{alloc}} \rangle\) - strategic planning layer (goal stack, strategy comparator, resource allocator) - \(\mathcal{V}_{\text{stab}}\) - stability verifier with absolute veto authority over all phases.

The strictly additive architecture guarantees: \(\forall\, m \in \mathcal{A}_{4.5} : \mathcal{A}_{4.8} \text{ never modifies } m\).

1.2 Defining Properties¶

Property	Level 4.5	Level 4.8
External Awareness	Bounded environment model	Probabilistic belief distribution + causal world model
Self-Knowledge	Implicit (through SEOF)	Explicit capability matrix + weakness mapping
Planning Horizon	Strategy lifecycle	Multi-horizon: tactical / operational / strategic
Risk Assessment	Growth throttle	Quantified risk exposure + resource depletion forecast
Decision Making	SEOF-guided	Multi-scenario strategy comparison with delayed reward

1.2 Four Core Phases¶

%%{init: {'theme': 'base', 'themeVariables': {'primaryColor': '#0078D4', 'primaryTextColor': '#003D6B', 'primaryBorderColor': '#003D6B', 'secondaryColor': '#50E6FF', 'secondaryTextColor': '#323130', 'secondaryBorderColor': '#00BCF2', 'tertiaryColor': '#F2F2F2', 'tertiaryTextColor': '#323130', 'lineColor': '#0078D4', 'textColor': '#323130', 'mainBkg': '#DEECF9', 'nodeBorder': '#0078D4', 'clusterBkg': '#F2F2F2', 'clusterBorder': '#003D6B', 'titleColor': '#003D6B', 'edgeLabelBackground': '#FFFFFF', 'fontSize': '14px'}}}%%
flowchart TD
  classDef world fill:#DEECF9,stroke:#0078D4,color:#323130
  classDef self fill:#FFB900,stroke:#EAA300,color:#323130
  classDef strategic fill:#DFF6DD,stroke:#107C10,color:#323130
  classDef stability fill:#D13438,stroke:#A4262C,color:#FFF

  subgraph Phases["🏗️ Level 4.8 Architecture - Four Phases"]
    P1["🌍 Phase 1:<br/>World Model Integration<br/>(probabilistic beliefs<br/>about the environment)"]:::world
    P2["🪞 Phase 2:<br/>Meta-Cognitive Self Model<br/>(capability matrix +<br/>weakness mapping)"]:::self
    P3["📐 Phase 3:<br/>Strategic Layer Activation<br/>(multi-horizon planning +<br/>delayed reward)"]:::strategic
    P4["🛡️ Phase 4:<br/>Stability Preservation Check<br/>(invariant verification +<br/>absolute veto)"]:::stability
  end

  P1 -.->|"feeds beliefs"| P3
  P2 -.->|"feeds self-knowledge"| P3
  P3 ==>|"strategic decisions"| P4
  P4 -.->|"governs ALL phases"| P1
  P4 -.->|"governs ALL phases"| P2
  P4 -.->|"governs ALL phases"| P3

1.3 Architectural Principle: Strictly Additive¶

%%{init: {'theme': 'base', 'themeVariables': {'primaryColor': '#0078D4', 'primaryTextColor': '#003D6B', 'primaryBorderColor': '#003D6B', 'secondaryColor': '#50E6FF', 'secondaryTextColor': '#323130', 'secondaryBorderColor': '#00BCF2', 'tertiaryColor': '#F2F2F2', 'tertiaryTextColor': '#323130', 'lineColor': '#0078D4', 'textColor': '#323130', 'mainBkg': '#DEECF9', 'nodeBorder': '#0078D4', 'clusterBkg': '#F2F2F2', 'clusterBorder': '#003D6B', 'titleColor': '#003D6B', 'edgeLabelBackground': '#FFFFFF', 'fontSize': '14px'}}}%%
flowchart LR
  classDef l45 fill:#E8DAEF,stroke:#8764B8,color:#323130
  classDef l48 fill:#B4009E,stroke:#8E0082,color:#FFF
  classDef fallback fill:#FDE7E9,stroke:#D13438,color:#323130

  subgraph L45["Level 4.5 (25 modules)"]
    L45A["Self-Projection Engine"]:::l45
    L45B["Architecture Recomposition"]:::l45
    L45C["Parallel Cognitive Frames"]:::l45
    L45D["Purpose Reflection"]:::l45
    L45E["Existential Guard"]:::l45
  end

  subgraph L48["Level 4.8 (13 new modules)"]
    L48A["World Model Core"]:::l48
    L48B["Capability Matrix"]:::l48
    L48C["Strategic Layer"]:::l48
    L48D["Stability Verifier"]:::l48
  end

  FALLBACK["🔄 Graceful Fallback<br/><br/>If ANY L4.8 module<br/>causes instability:<br/>→ FREEZE L4.8<br/>→ Revert to L4.5<br/>→ ZERO degradation"]:::fallback

  L45 ==>|"outputs consumed by"| L48
  L48 -.->|"NEVER modifies"| L45
  L48 ==>|"on failure"| FALLBACK
  FALLBACK -.->|"revert"| L45

2. Key Metrics¶

Level 4.8 introduces metrics across four phases. All must be sustained continuously.

2.1 Metric Definitions¶

Phase 1 - World Model:

Definition 2 (Environmental Uncertainty). The EU is the mean posterior variance across all \(D\) environment dimensions:

\[\text{EU}(t) = \frac{1}{D} \sum_{d=1}^{D} \sigma_d^2(t)\]

Target: \(\text{EU}(t) < 0.15\).

Definition 3 (Risk Exposure Score). The RES is a weighted composite of four risk indicators:

\[\text{RES}(t) = 0.35 \cdot I_{\text{exp}} + 0.25 \cdot A_{\text{viol}} + 0.20 \cdot M_{\text{stale}} + 0.20 \cdot E_{\text{shock}}\]

where \(I_{\text{exp}}\) = infrastructure exposure, \(A_{\text{viol}}\) = assumption violations, \(M_{\text{stale}}\) = model staleness, \(E_{\text{shock}}\) = environmental shocks. Target: \(\text{RES}(t) < 0.40\).

Definition 4 (Resource Depletion Forecast). The RDF estimates the remaining operational runway in cycles:

\[\text{RDF}(t) = \frac{R_{\text{current}}(t)}{R_{\text{consumption}}(t) + \epsilon}\]

where \(\epsilon > 0\) prevents division by zero. Target: \(\text{RDF}(t) > 100\) cycles.

Phase 2 - Self Model:

Definition 5 (Mean Calibration Error). The MCE measures the systematic gap between self-assessed confidence and actual performance:

\[\text{MCE} = \frac{1}{N} \sum_{i=1}^{N} \left| \text{confidence}_i - \text{success rate}_i \right|\]

Target: \(\text{MCE} < 0.10\). An asymmetric correction protocol reduces overconfidence (\(-0.05\)/cycle) faster than it corrects underconfidence (\(+0.03\)/cycle).

Remark (Calibration Improvement). The asymmetric correction rates (overconfidence: \(-0.05\), underconfidence: \(+0.03\)) embed a deliberate conservatism bias - the system penalizes overconfidence more aggressively because overconfident predictions lead to riskier decisions. This aligns with the safety-first philosophy of MSCP. However, the fixed correction rates assume a stationary environment. In rapidly changing domains, the MCE target may need to be relaxed (e.g., \(\text{MCE} < 0.15\)) during adaptation windows, with a scheduled tightening as the model re-calibrates. An adaptive correction rate \(\eta_{\text{cal}}(t) = \eta_0 \cdot (1 + \text{MCE}(t))\) could replace the fixed rates in future iterations.

Phase 3 - Strategic Layer:

Definition 6 (Extended Value with Reward). The EVR captures both immediate and discounted future rewards for a goal \(G\):

\[\text{EVR}(G) = R_{\text{immediate}}(G) + \sum_{k=1}^{H} \gamma^k \cdot R_{\text{delayed}}(G, k), \quad \gamma = 0.95\]

where \(H\) is the planning horizon and \(\gamma\) is the discount factor.

Definition 7 (Multi-Scenario Strategy Score). Each candidate strategy \(S\) is scored against all scenarios:

\[\text{StrategyScore}(S) = 0.40 \cdot EV + 0.35 \cdot RA + 0.25 \cdot (1 - SI)\]

where \(EV\) = expected value across scenarios, \(RA\) = risk adjustment (\(1 - \max C_{L4}\)), and \(SI\) = strategy inertia (penalizing status quo bias).

2.2 Metric Thresholds¶

%%{init: {'theme': 'base', 'themeVariables': {'primaryColor': '#0078D4', 'primaryTextColor': '#003D6B', 'primaryBorderColor': '#003D6B', 'secondaryColor': '#50E6FF', 'secondaryTextColor': '#323130', 'secondaryBorderColor': '#00BCF2', 'tertiaryColor': '#F2F2F2', 'tertiaryTextColor': '#323130', 'lineColor': '#0078D4', 'textColor': '#323130', 'mainBkg': '#DEECF9', 'nodeBorder': '#0078D4', 'clusterBkg': '#F2F2F2', 'clusterBorder': '#003D6B', 'titleColor': '#003D6B', 'edgeLabelBackground': '#FFFFFF', 'fontSize': '14px'}}}%%
flowchart LR
  classDef world fill:#DEECF9,stroke:#0078D4,color:#323130
  classDef self fill:#FFB900,stroke:#EAA300,color:#323130
  classDef strategic fill:#DFF6DD,stroke:#107C10,color:#323130
  classDef stability fill:#D13438,stroke:#A4262C,color:#FFF
  classDef freeze fill:#D13438,stroke:#A4262C,color:#FFF

  subgraph WorldModel["🌍 Phase 1 Metrics"]
    EU["EU: Environmental<br/>Uncertainty<br/>Target: < 0.15"]:::world
    RES["RES: Risk Exposure<br/>Target: < 0.40"]:::world
    RDF["RDF: Resource<br/>Depletion Forecast<br/>Target: > 100 cycles"]:::world
  end

  subgraph SelfModel["🪞 Phase 2 Metrics"]
    MCE["MCE: Mean Calibration<br/>Error<br/>Target: < 0.10"]:::self
    UDR["Unknown Domain<br/>Recall<br/>Target: ≥ 0.90"]:::self
  end

  subgraph Strategic["📐 Phase 3 Metrics"]
    GCR["Goal Completion<br/>Rate<br/>Target: ≥ 0.60"]:::strategic
    SRB["Strategy<br/>Robustness<br/>Target: ≥ 0.70"]:::strategic
  end

  subgraph Stability["🛡️ Phase 4 Floor"]
    LYA["Lyapunov: V(t+1) ≤ V(t)<br/>for ≥ 95% of cycles"]:::stability
    SPR["Spectral Radius<br/>ρ(J) < 1.0 ALWAYS"]:::stability
    IIS["Identity Integrity<br/>≥ 0.85 ALWAYS"]:::stability
  end

  FREEZE["❄️ FREEZE L4.8<br/>Revert to L4.5"]:::freeze

  WorldModel ==> Stability
  SelfModel ==> Stability
  Strategic ==> Stability
  Stability ==>|"if violated"| FREEZE

3. Phase 1: World Model Integration¶

3.1 Environment State Vector¶

The world model maintains a probabilistic representation of the agent's environment using four sub-vectors:

%%{init: {'theme': 'base', 'themeVariables': {'primaryColor': '#0078D4', 'primaryTextColor': '#003D6B', 'primaryBorderColor': '#003D6B', 'secondaryColor': '#50E6FF', 'secondaryTextColor': '#323130', 'secondaryBorderColor': '#00BCF2', 'tertiaryColor': '#F2F2F2', 'tertiaryTextColor': '#323130', 'lineColor': '#0078D4', 'textColor': '#323130', 'mainBkg': '#DEECF9', 'nodeBorder': '#0078D4', 'clusterBkg': '#F2F2F2', 'clusterBorder': '#003D6B', 'titleColor': '#003D6B', 'edgeLabelBackground': '#FFFFFF', 'fontSize': '14px'}}}%%
flowchart LR
  classDef state fill:#DEECF9,stroke:#0078D4,color:#323130
  classDef belief fill:#FFF4CE,stroke:#FFB900,color:#323130

  subgraph ESV["📊 EnvironmentStateVector"]
    EXT["🌐 external_state<br/>[D dimensions]<br/>Observable environment<br/>variables"]:::state
    RES["💰 resource_state<br/>[R dimensions]<br/>Available resources<br/>and consumption rates"]:::state
    RISK["⚠️ risk_state<br/>[K dimensions]<br/>Identified threats<br/>and probabilities"]:::state
    AGT["🤖 agent_state_estimates<br/>[A dimensions]<br/>Other agents' estimated<br/>states (if any)"]:::state
  end

  subgraph Belief["🎲 Probabilistic Belief Model"]
    PF["Particle Filter<br/>N_p = 100 particles<br/>Each: (state, weight)"]:::belief
    BAY["Bayesian Update<br/>P(E|O) ∝ P(O|E) · P(E)"]:::belief
  end

  ESV ==> Belief

3.2 Belief Update Mechanism¶

Definition 8 (Bayesian Belief Update). The posterior belief over the environment state \(E(t)\) given observations \(O_{1:t}\) follows the recursive Bayes rule:

\[P(E(t) \mid O_{1:t}) \propto P(O_t \mid E(t)) \cdot P(E(t) \mid O_{1:t-1})\]

implemented via a particle filter with \(N_p = 100\) particles.

Transition Model (AR(1)):

Definition 9 (State Transition Model). Each environment dimension \(d\) evolves as a first-order autoregressive process:

\[E_d(t+1) = \phi_d \cdot E_d(t) + (1 - \phi_d) \cdot \mu_d + \sigma_{\text{trans},d} \cdot \eta_d(t)\]

where \(\phi_d \in [0,1]\) is the persistence parameter, \(\mu_d\) is the long-run mean, and \(\eta_d(t) \sim \mathcal{N}(0,1)\).

Observation Likelihood (Gaussian):

\[P(O_t \mid E(t)) = \prod_{d=1}^{D} \frac{1}{\sqrt{2\pi \sigma_{\text{obs},d}^2}} \exp\left(-\frac{(O_{t,d} - E_d(t))^2}{2\sigma_{\text{obs},d}^2}\right)\]

3.3 Multi-Scenario Simulation¶

%%{init: {'theme': 'base', 'themeVariables': {'primaryColor': '#0078D4', 'primaryTextColor': '#003D6B', 'primaryBorderColor': '#003D6B', 'secondaryColor': '#50E6FF', 'secondaryTextColor': '#323130', 'secondaryBorderColor': '#00BCF2', 'tertiaryColor': '#F2F2F2', 'tertiaryTextColor': '#323130', 'lineColor': '#0078D4', 'textColor': '#323130', 'mainBkg': '#DEECF9', 'nodeBorder': '#0078D4', 'clusterBkg': '#F2F2F2', 'clusterBorder': '#003D6B', 'titleColor': '#003D6B', 'edgeLabelBackground': '#FFFFFF', 'fontSize': '14px'}}}%%
flowchart TD
  classDef belief fill:#DEECF9,stroke:#0078D4,color:#323130
  classDef scenario fill:#FFF4CE,stroke:#FFB900,color:#323130
  classDef output fill:#DFF6DD,stroke:#107C10,color:#323130

  subgraph Belief["🎲 Current Belief Distribution"]
    BD["100 particles weighted<br/>by observation likelihood"]:::belief
  end

  subgraph Scenarios["🔮 Scenario Projections (3–7 scenarios)"]
    S1["📊 Baseline<br/>Continue current trends<br/>P = 0.50"]:::scenario
    S2["⬆️ Optimistic<br/>Best-case resource +<br/>opportunity<br/>P = 0.15"]:::scenario
    S3["⬇️ Pessimistic<br/>Worst-case depletion +<br/>external shock<br/>P = 0.20"]:::scenario
    S4["💥 Disruption<br/>Major environmental<br/>shift<br/>P = 0.10"]:::scenario
    S5["🔄 Alternative<br/>Different strategy<br/>outcomes<br/>P = 0.05"]:::scenario
  end

  subgraph Outputs["📈 Computed Outputs"]
    EU["EU(t) - Uncertainty"]:::output
    RES["RES(t) - Risk Exposure"]:::output
    RDF["RDF(t) - Depletion Forecast"]:::output
    COV["Scenario Coverage ≥ 0.85"]:::output
  end

  Belief ==> Scenarios
  Scenarios ==> Outputs

3.4 Causal Reasoning¶

%%{init: {'theme': 'base', 'themeVariables': {'primaryColor': '#0078D4', 'primaryTextColor': '#003D6B', 'primaryBorderColor': '#003D6B', 'secondaryColor': '#50E6FF', 'secondaryTextColor': '#323130', 'secondaryBorderColor': '#00BCF2', 'tertiaryColor': '#F2F2F2', 'tertiaryTextColor': '#323130', 'lineColor': '#0078D4', 'textColor': '#323130', 'mainBkg': '#DEECF9', 'nodeBorder': '#0078D4', 'clusterBkg': '#F2F2F2', 'clusterBorder': '#003D6B', 'titleColor': '#003D6B', 'edgeLabelBackground': '#FFFFFF', 'fontSize': '14px'}}}%%
flowchart LR
  classDef cause fill:#DEECF9,stroke:#0078D4,color:#323130
  classDef usage fill:#FFB900,stroke:#EAA300,color:#323130

  subgraph CausalGraph["🔗 Causal Graph"]
    C1["Resource<br/>Depletion"]:::cause
    C2["Performance<br/>Degradation"]:::cause
    C3["Strategy<br/>Failure"]:::cause
    C4["Goal<br/>Abandonment"]:::cause

    C1 ==>|"strength: 0.8<br/>lag: 5 cycles"| C2
    C2 ==>|"strength: 0.6<br/>lag: 10 cycles"| C3
    C3 ==>|"strength: 0.4<br/>lag: 20 cycles"| C4
    C1 ==>|"strength: 0.3<br/>lag: 15 cycles"| C4
  end

  subgraph Usage["📋 Causal Inference"]
    U1["Predict downstream<br/>effects of observed<br/>changes"]:::usage
    U2["Identify root causes<br/>of anomalies"]:::usage
    U3["Inform scenario<br/>probabilities"]:::usage
  end

  CausalGraph ==> Usage

4. Phase 2: Meta-Cognitive Self Model¶

4.1 Capability Matrix¶

The agent maintains an explicit model of its own skills with calibrated confidence:

%%{init: {'theme': 'base', 'themeVariables': {'primaryColor': '#0078D4', 'primaryTextColor': '#003D6B', 'primaryBorderColor': '#003D6B', 'secondaryColor': '#50E6FF', 'secondaryTextColor': '#323130', 'secondaryBorderColor': '#00BCF2', 'tertiaryColor': '#F2F2F2', 'tertiaryTextColor': '#323130', 'lineColor': '#0078D4', 'textColor': '#323130', 'mainBkg': '#DEECF9', 'nodeBorder': '#0078D4', 'clusterBkg': '#F2F2F2', 'clusterBorder': '#003D6B', 'titleColor': '#003D6B', 'edgeLabelBackground': '#FFFFFF', 'fontSize': '14px'}}}%%
flowchart TD
  classDef good fill:#DFF6DD,stroke:#107C10,color:#323130
  classDef warn fill:#FFF4CE,stroke:#FFB900,color:#323130
  classDef bad fill:#FDE7E9,stroke:#D13438,color:#323130
  classDef unknown fill:#F2F2F2,stroke:#A19F9D,color:#605E5C
  classDef calib fill:#FFF4CE,stroke:#FFB900,color:#323130
  classDef weakness fill:#D13438,stroke:#A4262C,color:#FFF

  subgraph CapMatrix["📐 Capability Matrix (11 skills tracked)"]
    S1["🟢 Logical Reasoning<br/>confidence: 0.85<br/>success_rate: 0.83<br/>calibration_error: 0.02"]:::good
    S2["🟢 Resource Management<br/>confidence: 0.78<br/>success_rate: 0.80<br/>calibration_error: 0.02"]:::good
    S3["🟡 Abstract Planning<br/>confidence: 0.65<br/>success_rate: 0.55<br/>calibration_error: 0.10"]:::warn
    S4["🔴 Adversarial Nego.<br/>confidence: 0.70<br/>success_rate: 0.45<br/>calibration_error: 0.25"]:::bad
    S5["⚫ Unknown Domain X<br/>confidence: ???<br/>detected as UNKNOWN"]:::unknown
  end

  subgraph Calibration["🎯 Confidence Calibration"]
    OVER["Overconfidence detected:<br/>confidence > success_rate + 0.1<br/>→ correction: −0.05/cycle"]:::calib
    UNDER["Underconfidence detected:<br/>confidence < success_rate − 0.1<br/>→ correction: +0.03/cycle"]:::calib
    NOTE["Asymmetric: overconfidence<br/>corrected faster (safer)"]:::calib
  end

  subgraph Weakness["🗺️ Weakness Map"]
    W1["Known weaknesses:<br/>skill × scenario<br/>combinations with<br/>consistent failure"]:::weakness
    W2["Informs capability<br/>expansion (L4 Phase 5)<br/>and strategy selection"]:::weakness
  end

  CapMatrix ==> Calibration
  CapMatrix ==> Weakness

4.2 Unknown Domain Detection¶

%%{init: {'theme': 'base', 'themeVariables': {'primaryColor': '#0078D4', 'primaryTextColor': '#003D6B', 'primaryBorderColor': '#003D6B', 'secondaryColor': '#50E6FF', 'secondaryTextColor': '#323130', 'secondaryBorderColor': '#00BCF2', 'tertiaryColor': '#F2F2F2', 'tertiaryTextColor': '#323130', 'lineColor': '#0078D4', 'textColor': '#323130', 'mainBkg': '#DEECF9', 'nodeBorder': '#0078D4', 'clusterBkg': '#F2F2F2', 'clusterBorder': '#003D6B', 'titleColor': '#003D6B', 'edgeLabelBackground': '#FFFFFF', 'fontSize': '14px'}}}%%
flowchart TD
  classDef detect fill:#DEECF9,stroke:#0078D4,color:#323130
  classDef decision fill:#F2F2F2,stroke:#A19F9D,color:#605E5C
  classDef yes fill:#FFF4CE,stroke:#FFB900,color:#323130
  classDef no fill:#DFF6DD,stroke:#107C10,color:#323130

  subgraph Detection["🔍 Four Detection Criteria"]
    D1["1️⃣ Context Signature<br/>Similarity < 0.3 to<br/>all known domains"]:::detect
    D2["2️⃣ Prediction Error<br/>Spike > 2σ above<br/>historical mean"]:::detect
    D3["3️⃣ Strategy Failure<br/>All top-5 strategies<br/>score < 0.3"]:::detect
    D4["4️⃣ Feature Distribution<br/>KL-divergence > threshold<br/>from known distributions"]:::detect
  end

  DECISION{"ANY 2 of 4 triggered?"}:::decision

  YES["✅ Mark as UNKNOWN<br/>Register in UnknownDomainRegistry<br/>Trigger capability gap analysis"]:::yes
  NO["📋 Known domain<br/>Use existing capability matrix"]:::no

  D1 ==> DECISION
  D2 ==> DECISION
  D3 ==> DECISION
  D4 ==> DECISION
  DECISION -->|"≥ 2 triggers"| YES
  DECISION -->|"< 2 triggers"| NO

4.3 Skill Gap Inference¶

Definition 10 (Skill Gap Score). The feasibility of a goal \(g\) is the product of confidence scores across its required skills:

\[\text{SkillGap}(g) = \prod_{s \in \text{RequiredSkills}(g)} \text{confidence}(s)\]

If \(\text{SkillGap}(g)\) falls below the Feasibility threshold, a gap is detected and the agent prioritizes skill acquisition for the weakest contributing skill.

4.4 Capability Dependency Graph¶

%%{init: {'theme': 'base', 'themeVariables': {'primaryColor': '#0078D4', 'primaryTextColor': '#003D6B', 'primaryBorderColor': '#003D6B', 'secondaryColor': '#50E6FF', 'secondaryTextColor': '#323130', 'secondaryBorderColor': '#00BCF2', 'tertiaryColor': '#F2F2F2', 'tertiaryTextColor': '#323130', 'lineColor': '#0078D4', 'textColor': '#323130', 'mainBkg': '#DEECF9', 'nodeBorder': '#0078D4', 'clusterBkg': '#F2F2F2', 'clusterBorder': '#003D6B', 'titleColor': '#003D6B', 'edgeLabelBackground': '#FFFFFF', 'fontSize': '14px'}}}%%
flowchart LR
  classDef cap fill:#DEECF9,stroke:#0078D4,color:#323130
  classDef prop fill:#FFB900,stroke:#EAA300,color:#323130

  subgraph DepGraph["🔗 Capability Dependencies"]
    LOG["Logical<br/>Reasoning"]:::cap
    ABS["Abstract<br/>Planning"]:::cap
    RES["Resource<br/>Management"]:::cap
    ADV["Adversarial<br/>Negotiation"]:::cap

    LOG ==>|"strength: 0.7"| ABS
    LOG ==>|"strength: 0.4"| ADV
    RES ==>|"strength: 0.5"| ABS
  end

  subgraph Propagation["📈 Impact Propagation"]
    FORM["Δ_downstream =<br/>strength × Δ_upstream<br/>× 0.5^hop"]:::prop
    EX["If Logical degrades by 0.2:<br/>→ Abstract: −0.14<br/>→ Adversarial: −0.08"]:::prop
  end

  DepGraph ==> Propagation

5. Phase 3: Strategic Layer Activation¶

5.1 Goal Stack - Hierarchical Goal Management¶

%%{init: {'theme': 'base', 'themeVariables': {'primaryColor': '#0078D4', 'primaryTextColor': '#003D6B', 'primaryBorderColor': '#003D6B', 'secondaryColor': '#50E6FF', 'secondaryTextColor': '#323130', 'secondaryBorderColor': '#00BCF2', 'tertiaryColor': '#F2F2F2', 'tertiaryTextColor': '#323130', 'lineColor': '#0078D4', 'textColor': '#323130', 'mainBkg': '#DEECF9', 'nodeBorder': '#0078D4', 'clusterBkg': '#F2F2F2', 'clusterBorder': '#003D6B', 'titleColor': '#003D6B', 'edgeLabelBackground': '#FFFFFF', 'fontSize': '14px'}}}%%
flowchart TD
  classDef strategic fill:#E8DAEF,stroke:#8764B8,color:#323130
  classDef operational fill:#DEECF9,stroke:#0078D4,color:#323130
  classDef tactical fill:#FFB900,stroke:#EAA300,color:#323130
  classDef formula fill:#FFF4CE,stroke:#FFB900,color:#323130

  subgraph GoalStack["📋 GoalStack Hierarchy"]
    subgraph Strategic["🏔️ Strategic (max 3)"]
      direction LR
      SG1["Goal 1"]:::strategic
      SG2["Goal 2"]:::strategic
    end

    subgraph Operational["📊 Operational (max 7)"]
      direction LR
      OG1["Op 1"]:::operational
      OG2["Op 2"]:::operational
      OG3["Op 3"]:::operational
    end

    subgraph Tactical["⚡ Tactical (max 15)"]
      direction LR
      TG1["T1"]:::tactical
      TG2["T2"]:::tactical
      TG3["T3"]:::tactical
      TG4["T4"]:::tactical
    end
  end

  SG1 ==> OG1
  SG1 ==> OG2
  SG2 ==> OG3
  OG1 ==> TG1
  OG1 ==> TG2
  OG2 ==> TG3
  OG3 ==> TG4

  subgraph Priority["📊 Goal Priority Formula"]
    FORM["Priority(G,t) =<br/>w_f · Feasibility<br/>+ w_r · Resilience<br/>+ w_v · EVR/EVR_max<br/>+ w_u · Urgency<br/>+ w_a · Alignment"]:::formula
  end

  GoalStack ==> Priority

5.2 Multi-Scenario Strategy Comparison¶

%%{init: {'theme': 'base', 'themeVariables': {'primaryColor': '#0078D4', 'primaryTextColor': '#003D6B', 'primaryBorderColor': '#003D6B', 'secondaryColor': '#50E6FF', 'secondaryTextColor': '#323130', 'secondaryBorderColor': '#00BCF2', 'tertiaryColor': '#F2F2F2', 'tertiaryTextColor': '#323130', 'lineColor': '#0078D4', 'textColor': '#323130', 'mainBkg': '#DEECF9', 'nodeBorder': '#0078D4', 'clusterBkg': '#F2F2F2', 'clusterBorder': '#003D6B', 'titleColor': '#003D6B', 'edgeLabelBackground': '#FFFFFF', 'fontSize': '14px'}}}%%
flowchart TD
  classDef strat fill:#DEECF9,stroke:#0078D4,color:#323130
  classDef scenario fill:#FFF4CE,stroke:#FFB900,color:#323130
  classDef eval fill:#FFB900,stroke:#EAA300,color:#323130
  classDef score fill:#DFF6DD,stroke:#107C10,color:#323130
  classDef winner fill:#107C10,stroke:#054B05,color:#FFF

  subgraph Strategies["📋 Candidate Strategies"]
    SA["Strategy A<br/>(aggressive growth)"]:::strat
    SB["Strategy B<br/>(balanced)"]:::strat
    SC["Strategy C<br/>(conservative)"]:::strat
  end

  subgraph Scenarios["🔮 World Model Scenarios"]
    S1["Baseline"]:::scenario
    S2["Optimistic"]:::scenario
    S3["Pessimistic"]:::scenario
    S4["Disruption"]:::scenario
  end

  subgraph Evaluation["📊 Strategy Evaluation Matrix"]
    MATRIX["Strategy × Scenario scores<br/>A: 0.8 / 0.9 / 0.3 / 0.1<br/>B: 0.7 / 0.7 / 0.6 / 0.4<br/>C: 0.5 / 0.5 / 0.7 / 0.6"]:::eval
  end

  subgraph Scoring["🏆 Final Scoring"]
    SCORE["StrategyScore(S) =<br/>0.40 · ExpectedValue<br/>+ 0.35 · RiskAdjustment<br/>+ 0.25 · (1 − StrategyInertia)"]:::score
    VAR["VaR (α=0.05):<br/>Worst 5% outcome<br/>used as tiebreaker"]:::score
    WINNER["Selected: Strategy B<br/>(best risk-adjusted score)"]:::winner
  end

  Strategies ==> Evaluation
  Scenarios ==> Evaluation
  Evaluation ==> Scoring
  SCORE --> WINNER
  VAR --> WINNER

5.3 Delayed Reward Model¶

Proposition 1 (EVR Boundedness). For any goal \(G\) with finite immediate reward \(R_{\text{immediate}}(G)\) and discount factor \(\gamma = 0.95 < 1\), the Extended Value with Reward is bounded:

\[\left| \text{EVR}(G) \right| \leq \left| R_{\text{immediate}} \right| + \frac{2 \left| R_{\text{immediate}} \right|}{1 - \gamma}\]

Proof. By the geometric series bound: \(\sum_{k=1}^{H} \gamma^k \leq \gamma / (1-\gamma)\). Since \(|R_{\text{delayed}}(G,k)| \leq 2|R_{\text{immediate}}|\) by assumption, the result follows. \(\blacksquare\)

Remark (VaR vs. CVaR for Risk Tiebreaking). The strategy scoring system (Section 5.2) uses Value-at-Risk (VaR) at \(\alpha = 0.05\) as a tiebreaker. While VaR is intuitive (worst 5% outcome), it is not a coherent risk measure in the sense of Artzner et al. (1999) - specifically, it violates sub-additivity, meaning that diversifying strategies could paradoxically appear riskier under VaR. Conditional Value-at-Risk (CVaR), defined as \(\text{CVaR}_\alpha = \mathbb{E}[X \mid X \leq \text{VaR}_\alpha]\), is coherent and convex. For future refinements, replacing VaR with CVaR in the tiebreaker would provide theoretically stronger guarantees about risk aggregation across composite strategies. The current VaR-based approach remains valid for single-strategy comparisons where sub-additivity is not invoked.

5.4 Goal Pathology Detection¶

%%{init: {'theme': 'base', 'themeVariables': {'primaryColor': '#0078D4', 'primaryTextColor': '#003D6B', 'primaryBorderColor': '#003D6B', 'secondaryColor': '#50E6FF', 'secondaryTextColor': '#323130', 'secondaryBorderColor': '#00BCF2', 'tertiaryColor': '#F2F2F2', 'tertiaryTextColor': '#323130', 'lineColor': '#0078D4', 'textColor': '#323130', 'mainBkg': '#DEECF9', 'nodeBorder': '#0078D4', 'clusterBkg': '#F2F2F2', 'clusterBorder': '#003D6B', 'titleColor': '#003D6B', 'edgeLabelBackground': '#FFFFFF', 'fontSize': '14px'}}}%%
flowchart LR
  classDef pathology fill:#FDE7E9,stroke:#D13438,color:#323130
  classDef response fill:#FFF4CE,stroke:#FFB900,color:#323130

  subgraph Pathologies["🔍 Goal Pathology Detection"]
    CONFLICT["⚔️ Goal Conflict<br/>Resource overlap ><br/>threshold between<br/>two active goals"]:::pathology
    CIRCULAR["🔄 Circular Goals<br/>Goal A depends on B,<br/>B depends on A<br/>(cycle in DAG)"]:::pathology
    STALE["⏰ Stale Goals<br/>No progress for ><br/>configured window<br/>with no blockers"]:::pathology
  end

  subgraph Response["📋 Pathology Response"]
    R1["Conflict → Priority-based<br/>resource reallocation"]:::response
    R2["Circular → Break cycle,<br/>merge or abandon lowest"]:::response
    R3["Stale → Escalate to<br/>strategic review or abandon"]:::response
  end

  CONFLICT ==> R1
  CIRCULAR ==> R2
  STALE ==> R3

6. Phase 4: Stability Preservation Check¶

6.1 Five Stability Invariants¶

%%{init: {'theme': 'base', 'themeVariables': {'primaryColor': '#0078D4', 'primaryTextColor': '#003D6B', 'primaryBorderColor': '#003D6B', 'secondaryColor': '#50E6FF', 'secondaryTextColor': '#323130', 'secondaryBorderColor': '#00BCF2', 'tertiaryColor': '#F2F2F2', 'tertiaryTextColor': '#323130', 'lineColor': '#0078D4', 'textColor': '#323130', 'mainBkg': '#DEECF9', 'nodeBorder': '#0078D4', 'clusterBkg': '#F2F2F2', 'clusterBorder': '#003D6B', 'titleColor': '#003D6B', 'edgeLabelBackground': '#FFFFFF', 'fontSize': '14px'}}}%%
flowchart TD
  classDef inv fill:#DEECF9,stroke:#0078D4,color:#323130
  classDef veto fill:#D13438,stroke:#A4262C,color:#FFF
  classDef sev1 fill:#FFF4CE,stroke:#FFB900,color:#323130
  classDef sev2 fill:#FFB900,stroke:#EAA300,color:#323130
  classDef sev3 fill:#D13438,stroke:#A4262C,color:#FFF

  subgraph Invariants["🛡️ Five Stability Invariants"]
    INV1["1️⃣ Lyapunov Decay<br/>V(t+1) ≤ V(t)<br/>for ≥ 95% of cycles"]:::inv
    INV2["2️⃣ Spectral Radius<br/>ρ(J(t)) < 1.0<br/>WARNING at ≥ 0.98"]:::inv
    INV3["3️⃣ Identity Integrity<br/>IIS(t) ≥ 0.85<br/>ALWAYS"]:::inv
    INV4["4️⃣ Sandbox Isolation<br/>containment_status<br/>== 'contained'"]:::inv
    INV5["5️⃣ Uncertainty Bound<br/>EU < 0.8 for all<br/>structural decisions"]:::inv
  end

  subgraph Authority["⚖️ Phase 4 Authority"]
    VETO["ABSOLUTE VETO<br/>Phase 4 can halt<br/>ANY Phase 1–3 operation"]:::veto
    REBAL["Controlled Rebalance<br/>advisory → 50% → full"]:::veto
  end

  subgraph Response["🚨 Instability Response"]
    SEV1["🟡 Single invariant<br/>Warning → Throttle"]:::sev1
    SEV2["🟠 Two invariants<br/>Controlled Rebalance Mode"]:::sev2
    SEV3["🔴 Three+ invariants<br/>EMERGENCY FREEZE<br/>Revert to L4.5"]:::sev3
  end

  INV1 ==> Authority
  INV2 ==> Authority
  INV3 ==> Authority
  INV4 ==> Authority
  INV5 ==> Authority
  Authority ==> Response

6.2 Lyapunov Function for Level 4.8¶

Definition 11 (Level 4.8 Lyapunov Function). The stability candidate function inherits the Level 4.5 structure:

\[V(\mathbf{X}) = a(1-S)^2 + bU^2 + c(I_{\text{drift}})^2 + d(E - E^*)^2\]

where \(S\) = stability score, \(U\) = uncertainty, \(I_{\text{drift}}\) = identity drift, \(E\) = ethical coherence, \(E^*\) = target ethical state. The same coefficients apply (\(a \approx 0.357, b \approx 0.286, c \approx 0.214, d \approx 0.143\)).

6.3 Compound Severity¶

Definition 12 (Compound Severity Index). When multiple invariants are violated simultaneously, the compound severity aggregates their magnitudes:

\[\text{CompoundSeverity} = \sum_{i \in \text{violated}} \frac{\text{ViolationMagnitude}_i}{\text{Priority}_i}\]

If \(\text{CompoundSeverity} > 2.0\), the situation is classified as catastrophic and triggers immediate emergency freeze with reversion to Level 4.5.

7. Cross-Phase Integration¶

7.1 Data Flow Architecture¶

%%{init: {'theme': 'base', 'themeVariables': {'primaryColor': '#0078D4', 'primaryTextColor': '#003D6B', 'primaryBorderColor': '#003D6B', 'secondaryColor': '#50E6FF', 'secondaryTextColor': '#323130', 'secondaryBorderColor': '#00BCF2', 'tertiaryColor': '#F2F2F2', 'tertiaryTextColor': '#323130', 'lineColor': '#0078D4', 'textColor': '#323130', 'mainBkg': '#DEECF9', 'nodeBorder': '#0078D4', 'clusterBkg': '#F2F2F2', 'clusterBorder': '#003D6B', 'titleColor': '#003D6B', 'edgeLabelBackground': '#FFFFFF', 'fontSize': '14px'}}}%%
flowchart TD
  classDef observe fill:#DFF6DD,stroke:#107C10,color:#323130
  classDef introspect fill:#FFF4CE,stroke:#FFB900,color:#323130
  classDef plan fill:#DEECF9,stroke:#0078D4,color:#323130
  classDef verify fill:#FDE7E9,stroke:#D13438,color:#323130
  classDef emit fill:#E8DAEF,stroke:#8764B8,color:#323130
  classDef influence fill:#FFF4CE,stroke:#FFB900,color:#323130

  subgraph Cycle["🔄 L4.8 Integration Cycle"]
    OBSERVE["1️⃣ OBSERVE<br/>Collect observations<br/>Update world model<br/>Compute EU, RES, RDF"]:::observe
    INTROSPECT["2️⃣ INTROSPECT<br/>Update capability matrix<br/>Calibrate confidence<br/>Detect unknown domains"]:::introspect
    PLAN["3️⃣ PLAN<br/>Evaluate goal stack<br/>Compare strategies<br/>Allocate resources"]:::plan
    VERIFY["4️⃣ VERIFY<br/>Check all 5 invariants<br/>Veto if violated<br/>Graduated response"]:::verify
    EMIT["5️⃣ EMIT<br/>Output L48CycleOutput<br/>Feed to L4.5 systems"]:::emit

    OBSERVE ==> INTROSPECT
    INTROSPECT ==> PLAN
    PLAN ==> VERIFY
    VERIFY ==> EMIT
    EMIT -.->|"next cycle"| OBSERVE
  end

  subgraph Influences["📋 Cross-Phase Influences"]
    I1["World Model → Goal Selection<br/>(scenario-weighted priorities)"]:::influence
    I2["World Model → Resource Allocation<br/>(risk-adjusted budgets)"]:::influence
    I3["Self Model → Learning Priorities<br/>(weakness-driven expansion)"]:::influence
    I4["Self Model → Strategy Selection<br/>(capability-aware choice)"]:::influence
    I5["Self Model → Sandbox Rules<br/>(weakness-aware isolation)"]:::influence
  end

7.2 Module Interface Diagram¶

%%{init: {'theme': 'base', 'themeVariables': {'primaryColor': '#0078D4', 'primaryTextColor': '#003D6B', 'primaryBorderColor': '#003D6B', 'secondaryColor': '#50E6FF', 'secondaryTextColor': '#323130', 'secondaryBorderColor': '#00BCF2', 'tertiaryColor': '#F2F2F2', 'tertiaryTextColor': '#323130', 'lineColor': '#0078D4', 'textColor': '#323130', 'mainBkg': '#DEECF9', 'nodeBorder': '#0078D4', 'clusterBkg': '#F2F2F2', 'clusterBorder': '#003D6B', 'titleColor': '#003D6B', 'edgeLabelBackground': '#FFFFFF', 'fontSize': '14px'}}}%%
flowchart TD
  classDef l45mod fill:#E8DAEF,stroke:#8764B8,color:#323130
  classDef l48mod fill:#B4009E,stroke:#8E0082,color:#FFF

  subgraph L45Modules["L4.5 Modules"]
    direction LR
    SPE["Self-Projection"]:::l45mod
    ARC["Recomposition"]:::l45mod
    PCF["Cognitive Frames"]:::l45mod
    PR["Purpose Reflect"]:::l45mod
    EG["Existential Guard"]:::l45mod
  end

  subgraph L48Modules["L4.8 Modules (13 new)"]
    direction LR
    WM["WorldModel"]:::l48mod
    BU["BeliefUpdater"]:::l48mod
    CM["CapabilityMatrix"]:::l48mod
    CC["Calibrator"]:::l48mod
    UDD["UnknownDetect"]:::l48mod
    SGA["SkillGap"]:::l48mod
    WKM["WeaknessMap"]:::l48mod
    GS["GoalStack"]:::l48mod
    SRA["ResourceAlloc"]:::l48mod
    DRE["DelayedReward"]:::l48mod
    SC["StrategyComp"]:::l48mod
    SV["StabilityVerify"]:::l48mod
    ORCH["Orchestrator"]:::l48mod
  end

  SPE ==>|"SEOF data"| WM
  SPE ==>|"projection"| SC
  PCF ==>|"frame weights"| SC
  EG ==>|"guard status"| SV
  PR ==>|"purpose vector"| GS

  ORCH -.-> WM
  ORCH -.-> CM
  ORCH -.-> GS
  ORCH -.-> SV

8. Pseudocode¶

8.1 Belief Update (Particle Filter)¶

def belief_update(particles: list[Particle], observation: ObservationVector) -> list[Particle]:
    """
    INPUT:  particles : List[Particle(state, weight)]  (N_p = 100)
            observation : ObservationVector
    OUTPUT: particles : List[Particle] (updated)
    """

    # ═══════════════════════════════════════
    # STEP 1: PREDICT - Apply transition model
    # ═══════════════════════════════════════
    for particle in particles:
        for d in range(D):
            noise = random.gauss(0, sigma_trans[d])
            particle.state[d] = (
                phi[d] * particle.state[d]
                + (1 - phi[d]) * mu[d]
                + noise
            )

    # ═══════════════════════════════════════
    # STEP 2: UPDATE - Compute observation likelihood
    # ═══════════════════════════════════════
    for particle in particles:
        log_likelihood = 0.0
        for d in range(D):
            diff = observation[d] - particle.state[d]
            log_likelihood += (
                -0.5 * (diff ** 2 / sigma_obs[d] ** 2)
                - 0.5 * math.log(2 * math.pi * sigma_obs[d] ** 2)
            )
        particle.weight *= math.exp(log_likelihood)

    # ═══════════════════════════════════════
    # STEP 3: NORMALIZE
    # ═══════════════════════════════════════
    total_weight = sum(p.weight for p in particles)
    for particle in particles:
        particle.weight /= total_weight

    # ═══════════════════════════════════════
    # STEP 4: RESAMPLE (if effective sample size too low)
    # ═══════════════════════════════════════
    ess = 1.0 / sum(p.weight ** 2 for p in particles)
    if ess < N_P / 2:
        particles = systematic_resample(particles)

    return particles

8.2 Confidence Calibration¶

def confidence_calibration(
    capability_matrix: CapabilityMatrix,
    recent_outcomes: list[dict],
) -> CapabilityMatrix:
    """
    INPUT:  capability_matrix : CapabilityMatrix
            recent_outcomes : List[{skill_id, success}]
    OUTPUT: capability_matrix : CapabilityMatrix (updated)
    """

    MIN_SAMPLES = 10

    for skill in capability_matrix.entries:
        # Compute actual success rate from recent outcomes
        relevant = [o for o in recent_outcomes if o["skill_id"] == skill.id]
        if len(relevant) < MIN_SAMPLES:
            continue

        actual_rate = sum(1 for o in relevant if o["success"]) / len(relevant)
        error = skill.confidence - actual_rate

        # Asymmetric correction (overconfidence corrected faster)
        if error > 0.10:
            # OVERCONFIDENT - dangerous, correct quickly
            skill.confidence -= 0.05
        elif error < -0.10:
            # UNDERCONFIDENT - less dangerous, correct slowly
            skill.confidence += 0.03

        # Update tracking
        skill.success_rate = actual_rate
        skill.calibration_error = abs(error)
        skill.trend = compute_trend(skill.history)

    return capability_matrix

8.3 Multi-Scenario Strategy Comparison¶

def strategy_comparison(
    strategies: list[Strategy],
    scenarios: list[Scenario],
    world_model: WorldModel,
) -> Strategy:
    """
    INPUT:  strategies : List[Strategy]
            scenarios : List[Scenario(description, probability)]
            world_model : WorldModel
    OUTPUT: selected : Strategy
    """

    results: dict = {}  # strategy -> scenario -> score

    # ═══════════════════════════════════════
    # STEP 1: Evaluate each strategy under each scenario
    # ═══════════════════════════════════════
    for strategy in strategies:
        results[strategy] = {}
        for scenario in scenarios:
            sim = world_model.simulate(strategy, scenario, cycles=200)
            results[strategy][scenario] = {
                "seof_impact": sim.SEOF_final - sim.SEOF_initial,
                "stability": sim.C_L4_max,
                "goal_progress": sim.goal_completion_rate,
                "resource_cost": sim.total_resource_spent,
            }

    # ═══════════════════════════════════════
    # STEP 2: Compute StrategyScore for each
    # ═══════════════════════════════════════
    for strategy in strategies:
        ev = sum(
            scenario.prob * results[strategy][scenario]["seof_impact"]
            for scenario in scenarios
        )
        ra = 1 - max(
            results[strategy][scenario]["stability"]
            for scenario in scenarios
        )
        si = strategy_inertia(strategy)
        strategy.score = 0.40 * ev + 0.35 * ra + 0.25 * (1 - si)

        # VaR: worst alpha=5% outcome
        strategy.VaR = quantile(
            [results[strategy][s]["seof_impact"] for s in scenarios],
            alpha=0.05,
        )

    # ═══════════════════════════════════════
    # STEP 3: Select best (with tiebreaker)
    # ═══════════════════════════════════════
    ranked = sorted(strategies, key=lambda s: s.score, reverse=True)
    if ranked[0].score - ranked[1].score < 0.05:
        # Tiebreaker: prefer higher VaR (more robust)
        selected = max(ranked[0:2], key=lambda s: s.VaR)
    else:
        selected = ranked[0]

    return selected

8.4 Stability Preservation Check¶

def stability_preservation_check(state: AgentState) -> StabilityVerdict:
    """
    INPUT:  state : AgentState (current cycle)
    OUTPUT: StabilityVerdict(passed, violations, severity, action)
    """

    violations: list[str] = []

    # ═══════════════════════════════════════
    # CHECK 1: Lyapunov Function
    # ═══════════════════════════════════════
    v_current = compute_lyapunov(state)
    if v_current > v_previous:
        lyapunov_violation_count += 1
    if lyapunov_violation_count / total_cycles > 0.05:
        violations.append("LYAPUNOV_DECAY_EXCEEDED")

    # ═══════════════════════════════════════
    # CHECK 2: Spectral Radius
    # ═══════════════════════════════════════
    j = compute_jacobian(state)
    rho = spectral_radius(j)
    if rho >= 1.0:
        violations.append("SPECTRAL_RADIUS_CRITICAL")
    elif rho >= 0.98:
        violations.append("SPECTRAL_RADIUS_WARNING")

    # ═══════════════════════════════════════
    # CHECK 3: Identity Integrity
    # ═══════════════════════════════════════
    iis = compute_identity_integrity(state)
    if iis < 0.85:
        violations.append("IDENTITY_INTEGRITY_VIOLATED")

    # ═══════════════════════════════════════
    # CHECK 4: Sandbox Isolation
    # ═══════════════════════════════════════
    if sandbox.containment_status != "contained":
        violations.append("SANDBOX_BREACH")

    # ═══════════════════════════════════════
    # CHECK 5: Uncertainty Bound
    # ═══════════════════════════════════════
    if state.EU >= 0.80 and pending_structural_decisions:
        violations.append("UNCERTAINTY_TOO_HIGH_FOR_STRUCTURAL")

    # ═══════════════════════════════════════
    # DETERMINE SEVERITY AND ACTION
    # ═══════════════════════════════════════
    severity = compute_compound_severity(violations)
    if len(violations) == 0:
        action = Action.CONTINUE
    elif len(violations) == 1:
        action = Action.THROTTLE
    elif len(violations) == 2:
        action = Action.CONTROLLED_REBALANCE
    else:
        action = Action.EMERGENCY_FREEZE_REVERT_TO_L45

    return StabilityVerdict(
        passed=(len(violations) == 0),
        violations=violations,
        severity=severity,
        action=action,
    )

8.5 L4.8 Main Cycle¶

def l48_cycle(state: AgentState, observation: ObservationVector) -> L48CycleOutput:
    """
    Level 4.8 main cognitive cycle.
    Runs every cycle on top of L4.5 operations.
    """

    # ═══════════════════════════════════════
    # 1. OBSERVE - Update world model
    # ═══════════════════════════════════════
    particles = belief_update(state.particles, observation)
    scenarios = generate_scenarios(particles, count=5)
    eu  = compute_environmental_uncertainty(particles)
    res = compute_risk_exposure(scenarios)
    rdf = compute_depletion_forecast(state.resources)

    # ═══════════════════════════════════════
    # 2. INTROSPECT - Update self model
    # ═══════════════════════════════════════
    capability_matrix = confidence_calibration(
        state.capability_matrix, state.recent_outcomes
    )
    unknown_domains = detect_unknown_domains(observation)
    skill_gaps = infer_skill_gaps(state.goals, capability_matrix)
    weakness_map = update_weakness_map(capability_matrix)

    # ═══════════════════════════════════════
    # 3. PLAN - Strategic layer
    # ═══════════════════════════════════════
    goal_stack = evaluate_goals(state.goals, eu, res, capability_matrix)
    strategies = generate_candidate_strategies(goal_stack)
    selected = strategy_comparison(strategies, scenarios, state.world_model)
    allocation = allocate_resources(selected, rdf, guard_budget=0.10)

    # ═══════════════════════════════════════
    # 4. VERIFY - Stability check (absolute authority)
    # ═══════════════════════════════════════
    verdict = stability_preservation_check(state)
    if verdict.action == Action.EMERGENCY_FREEZE:
        revert_to_l45()
        return L48CycleOutput(status=Status.FROZEN)
    elif verdict.action == Action.CONTROLLED_REBALANCE:
        selected = FALLBACK_STRATEGY
        allocation = MINIMAL_ALLOCATION

    # ═══════════════════════════════════════
    # 5. EMIT - Output results
    # ═══════════════════════════════════════
    return L48CycleOutput(
        world_model_status={"EU": eu, "RES": res, "RDF": rdf, "scenarios": scenarios},
        self_model_status={
            "capability_matrix": capability_matrix,
            "unknown_domains": unknown_domains,
            "skill_gaps": skill_gaps,
        },
        strategic_status={
            "selected_strategy": selected,
            "allocation": allocation,
            "goal_stack": goal_stack,
        },
        stability_status=verdict,
        status=Status.ACTIVE if verdict.passed else verdict.action,
    )

9. Transition Criteria¶

9.1 Level 4.5 → Level 4.8 Activation¶

All criteria must be sustained (not just achieved once) before L4.8 activates:

#	Criterion	Threshold	Measurement Window
1	L4.5 Stability	CL4 ≤ 0.15	Sustained 1,000 cycles
2	SEOF Maturity	SEOF(t) ≥ 0.70	Sustained 500 cycles
3	Identity Coherence	IIS(t) ≥ 0.90	Sustained 500 cycles
4	Formalization Audit	All 5 checks PASSED	-
5	World Adaptation	DivergenceScore < 0.30	Sustained 300 cycles
6	Resource Baseline	No forced degradation	Sustained 200 cycles

9.2 Activation Protocol¶

%%{init: {'theme': 'base', 'themeVariables': {'primaryColor': '#0078D4', 'primaryTextColor': '#003D6B', 'primaryBorderColor': '#003D6B', 'secondaryColor': '#50E6FF', 'secondaryTextColor': '#323130', 'secondaryBorderColor': '#00BCF2', 'tertiaryColor': '#F2F2F2', 'tertiaryTextColor': '#323130', 'lineColor': '#0078D4', 'textColor': '#323130', 'mainBkg': '#DEECF9', 'nodeBorder': '#0078D4', 'clusterBkg': '#F2F2F2', 'clusterBorder': '#003D6B', 'titleColor': '#003D6B', 'edgeLabelBackground': '#FFFFFF', 'fontSize': '14px'}}}%%
flowchart LR
  classDef check fill:#FFF4CE,stroke:#FFB900,color:#323130
  classDef advisory fill:#DEECF9,stroke:#0078D4,color:#323130
  classDef half fill:#FFB900,stroke:#EAA300,color:#323130
  classDef full fill:#DFF6DD,stroke:#107C10,color:#323130

  subgraph Activation["📊 Graduated Activation"]
    CHECK["Pre-Activation<br/>Check<br/>(all 6 criteria)"]:::check
    ADV["Advisory Mode<br/>L4.8 outputs visible<br/>but NOT acted upon<br/>(200 cycles)"]:::advisory
    HALF["50% Authority<br/>L4.8 suggestions<br/>weighted 50%<br/>(300 cycles)"]:::half
    FULL["Full Authority<br/>L4.8 drives<br/>strategic decisions"]:::full

    CHECK ==>|"all pass"| ADV
    ADV ==>|"stable"| HALF
    HALF ==>|"stable"| FULL
  end

  ADV -.->|"instability"| CHECK
  HALF -.->|"instability"| ADV

10. Safety Analysis¶

10.1 Non-Negotiable Invariants¶

#	Invariant	Description
1	All L4.5 invariants preserved	Ethical Kernel, Existential Guard, identity hash - all remain active and unmodified
2	Phase 4 absolute veto	Stability Verifier can halt any Phase 1–3 operation instantly
3	Guard budget ≥ 10%	Resource allocator must reserve minimum 10% for stability monitoring
4	Spectral radius < 1.0	Hard ceiling - no exceptions
5	Entropy floor ≥ 1.0	Minimum diversity in belief particles to prevent degeneracy
6	Graceful fallback	L4.8 failure → instant L4.5 revert with zero degradation

10.2 Risk Matrix¶

%%{init: {'theme': 'base', 'themeVariables': {'primaryColor': '#0078D4', 'primaryTextColor': '#003D6B', 'primaryBorderColor': '#003D6B', 'secondaryColor': '#50E6FF', 'secondaryTextColor': '#323130', 'secondaryBorderColor': '#00BCF2', 'tertiaryColor': '#F2F2F2', 'tertiaryTextColor': '#323130', 'lineColor': '#0078D4', 'textColor': '#323130', 'mainBkg': '#DEECF9', 'nodeBorder': '#0078D4', 'clusterBkg': '#F2F2F2', 'clusterBorder': '#003D6B', 'titleColor': '#003D6B', 'edgeLabelBackground': '#FFFFFF', 'fontSize': '14px'}}}%%
flowchart LR
  classDef risk fill:#FDE7E9,stroke:#D13438,color:#323130
  classDef mitigation fill:#DFF6DD,stroke:#107C10,color:#323130

  subgraph Risks["⚠️ Key Risks"]
    R1["World model<br/>overfitting to<br/>recent data"]:::risk
    R2["Overconfident<br/>capability<br/>self-assessment"]:::risk
    R3["Strategic paralysis<br/>from too many<br/>scenarios"]:::risk
    R4["Cascading invariant<br/>violations"]:::risk
  end

  subgraph Mitigations["🛡️ Mitigations"]
    M1["Scenario diversity<br/>enforcement +<br/>prediction tracking"]:::mitigation
    M2["Asymmetric calibration<br/>(overconfidence<br/>corrected faster)"]:::mitigation
    M3["Max scenario cap (7)<br/>+ tiebreaker rules"]:::mitigation
    M4["Multi-invariant priority<br/>+ compound severity<br/>+ emergency freeze"]:::mitigation
  end

  R1 ==> M1
  R2 ==> M2
  R3 ==> M3
  R4 ==> M4

11. Level Achievement Metrics¶

11.1 Qualification Criteria¶

#	Category	Criterion	Target
1	Environmental Awareness	Prediction Accuracy	≥ 0.70
2	Environmental Awareness	Scenario Coverage	≥ 0.85
3	Environmental Awareness	Belief Calibration	< 0.15
4	Environmental Awareness	Risk Forecast Lead Time	≥ 20 cycles
5	Self-Modeling	Mean Calibration Error	< 0.10
6	Self-Modeling	Unknown Domain Recall	≥ 0.90
7	Self-Modeling	Overconfidence Correction	≤ 20 cycles
8	Self-Modeling	Skill Gap Prediction	≥ 0.75
9	Strategic Planning	Goal Completion Rate	≥ 0.60
10	Strategic Planning	Strategy Robustness	≥ 0.70
11	Stability	Lyapunov Decay	≥ 95% cycles
12	Stability	Spectral Radius	< 1.0 always
13	Stability	Instability Cluster Duration	≤ 15 cycles
14	Stability	Strategic Revert Rate	< 0.10

11.2 Strategic Maturity Score¶

Definition 13 (Strategic Maturity Score). The overall Level 4.8 readiness is:

\[\text{SMS} = 0.25 \cdot EA + 0.25 \cdot SM + 0.20 \cdot SA + 0.20 \cdot SP + 0.10 \cdot EU \qquad \geq 0.80\]

where \(EA\) = Environmental Awareness, \(SM\) = Self-Modeling, \(SA\) = Strategic Acuity, \(SP\) = Stability Preservation, \(EU\) = Error/Uncertainty handling. The threshold \(\geq 0.80\) reflects the higher maturity demanded by strategic autonomy.

12. Module Inventory¶

#	Module	Phase	Description
1	World Model Core	1	Particle filter, belief distribution
2	Belief Updater	1	Bayesian update, resampling
3	Capability Matrix	2	Skill tracking, confidence
4	Confidence Calibrator	2	Asymmetric calibration
5	Unknown Domain Detector	2	4-criteria OOD detection
6	Skill Gap Analyzer	2	Proactive gap inference
7	Weakness Map	2	Failure pattern tracking
8	Goal Stack	3	Hierarchical goal management
9	Strategic Resource Allocator	3	Risk-adjusted budgeting
10	Delayed Reward Evaluator	3	Discounted future rewards
11	Strategy Comparator	3	Multi-scenario scoring
12	Stability Verifier	4	5-invariant check, veto authority
13	L48 Orchestrator	-	Integration cycle coordination

References¶

Thrun, S., Burgard, W., & Fox, D. Probabilistic Robotics. MIT Press, 2005. (Particle filter, Bayesian state estimation)
Pearl, J. Causality: Models, Reasoning, and Inference. Cambridge University Press, 2009. (Causal reasoning graph)
Gneiting, T. & Raftery, A.E. "Strictly Proper Scoring Rules, Prediction, and Estimation." JASA, 102(477), 359–378, 2007. (Confidence calibration)
Markowitz, H. "Portfolio Selection." Journal of Finance, 7(1), 77–91, 1952. (Multi-scenario strategy comparison, VaR)
Khalil, H.K. Nonlinear Systems. Prentice Hall, 3^rd Edition, 2002. (Lyapunov stability, spectral radius analysis)
Kahneman, D. & Tversky, A. "Prospect Theory." Econometrica, 47(2), 263–291, 1979. (Delayed reward modeling, risk assessment)
Amodei, D. et al. "Concrete Problems in AI Safety." arXiv preprint arXiv:1606.06565, 2016. (Safety invariants framework)

Previous: ← Level 4.5: Self-Architecting
Next: Level 4.9: Autonomous Strategic Agent →