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Level 4: Adaptive General Agent - Architecture & Design

MSCP Level Series | Level 3 ← Level 4 → Level 4.5
Status: 🔬 Experimental - Conceptual framework and experimental design. Not a production specification.
Date: February 2026

Revision History

Version Date Description
0.1.0 2026-02-23 Initial document creation with formal Definitions 1-7, Theorem 2
0.2.0 2026-02-26 Added overview essence formula; added revision history table
0.3.0 2026-02-26 Def 7: added weight selection rationale remark; Theorem 2: added proof sketch with decay argument

1. Overview

Level 4 represents the leap from self-regulating to self-improving. While Level 3 agents can monitor and correct their own behavior, they cannot learn new skills, transfer knowledge across domains, or improve their own reasoning strategies. Level 4 adds cross-domain generalization, long-horizon autonomous goals, capability self-expansion, and - most critically - bounded structural self-modification with safety constraints.

Level Essence. A Level 4 agent demonstrates cross-domain transfer learning while maintaining bounded growth-stability safety - it improves itself without compromising integrity:

\[\operatorname{CDTS} = \frac{1}{|D_{\text{novel}}|} \sum_{d \in D_{\text{novel}}} \frac{P_{\text{transfer}}(d)}{P_{\text{baseline}}(d)} \geq 0.6 \;\;\land\;\; \operatorname{BGSS}(t) \geq 0.7\]

⚠️ Note: This document describes a cognitive level within the MSCP taxonomy. The capability expansion, strategy evolution, and self-modification mechanisms here are experimental designs. Safety invariants are specified but haven't been validated in production environments yet.

1.1 Defining Properties

Property Level 3 Level 4
Cross-Domain Transfer None Active (CDTS ≥ 0.6)
Goal Horizon Session/days Weeks–Months (4-level hierarchy)
Capability Expansion None 5-phase self-learning
Strategy Evolution Fixed Controlled mutation
Self-Modification None 7-step bounded protocol
Stability Metric C(t), 4 terms C_L4(t), 7 terms

1.2 Five Core Capabilities

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flowchart TD
  classDef cap fill:#DEECF9,stroke:#0078D4,color:#323130
  classDef foundation fill:#DFF6DD,stroke:#107C10,color:#323130

  subgraph L4Caps["Level 4: Five Core Capabilities"]
    C1["1. Cross-Domain<br/>Transfer Learning<br/>CDTS >= 0.6"]:::cap
    C2["2. Long-Term<br/>Autonomous Goals<br/>GPI >= 0.3"]:::cap
    C3["3. Capability<br/>Expansion<br/>CAR > 0"]:::cap
    C4["4. Strategy<br/>Evolution<br/>SEF > 1.0"]:::cap
    C5["5. Bounded<br/>Self-Modification<br/>BGSS >= 0.7"]:::cap
  end

  subgraph Foundation["Built on Level 3 MSCP v4"]
    F1["16-Layer Architecture"]:::foundation
    F2["Triple-Loop Meta-Cognition"]:::foundation
    F3["Ethical Kernel Layer 0+1"]:::foundation
    F4["Lyapunov Stability"]:::foundation
    F5["Affective + Survival Engine"]:::foundation
  end

  Foundation ==>|"preserves ALL<br/>existing mechanisms"| L4Caps

2. Key Metrics

Level 4 introduces five quantitative metrics that must be satisfied continuously.

Definition 1 (Level 4 Agent). A Level 4 agent extends \(\mathcal{A}_3\) with self-improvement capabilities:

\[\mathcal{A}_4 = \mathcal{A}_3 \oplus \langle \mathcal{D}, \mathcal{K}_{\text{transfer}}, \Sigma, \mu, \mathcal{P}_{\text{mod}} \rangle\]

where \(\mathcal{D}\) = multi-domain skill set, \(\mathcal{K}_{\text{transfer}}\) = cross-domain transfer kernel, \(\Sigma\) = strategy pool (mutable with controlled mutation), \(\mu\) = capability expansion pipeline, and \(\mathcal{P}_{\text{mod}}\) = bounded self-modification protocol.

2.1 Metric Definitions

Definition 2 (Cross-Domain Transfer Score). The CDTS measures the agent's ability to apply knowledge from known domains to novel ones:

\[\text{CDTS} = \frac{1}{|D_{\text{novel}}|} \sum_{d \in D_{\text{novel}}} \frac{P_{\text{transfer}}(d)}{P_{\text{baseline}}(d)} \qquad \geq 0.6\]

where \(P_{\text{transfer}}(d)\) is performance in domain \(d\) using transferred knowledge and \(P_{\text{baseline}}(d)\) is performance without transfer. A ratio \(\geq 0.6\) indicates meaningful generalization.

Definition 3 (Goal Progress Index). The GPI measures sustained progress toward long-horizon goals:

\[\text{GPI} = \frac{\sum_{g \in G_{\text{long}}} w_g \cdot \text{progress}(g, T)}{|G_{\text{long}}| \cdot T} \qquad \geq 0.3\]

where \(G_{\text{long}}\) is the set of goals with horizon \(> 7\) days and \(T\) is the evaluation period.

Definition 4 (Capability Acquisition Rate). The CAR measures how efficiently the agent acquires new skills:

\[\text{CAR} = \frac{|S_{\text{acquired}}(T) - S_{\text{initial}}|}{T} \cdot \frac{1}{\overline{\text{cost}}(S_{\text{acquired}})} \qquad > 0\]

where \(S_{\text{acquired}}(T)\) is the skill set at time \(T\), \(S_{\text{initial}}\) the initial skill set, and \(\overline{\text{cost}}\) the average acquisition cost (in compute or cycles).

Definition 5 (Strategy Evolution Factor). The SEF verifies that strategy mutations produce net improvement:

\[\text{SEF} = \frac{\overline{R}_{\textit{post mutation}}}{\overline{R}_{\textit{pre mutation}}} - \sigma_{\text{oscillation}} \qquad > 1.0\]

A value \(> 1.0\) confirms that mutations improve performance beyond oscillation noise \(\sigma_{\text{oscillation}}\).

Definition 6 (Bounded Growth Safety Score). The BGSS ensures that growth does not destabilize the agent:

\[\text{BGSS} = 1.0 - 0.4 \cdot \frac{dC(t)}{dt} - 0.3 \cdot V_{\text{identity}}(t) - 0.3 \cdot R_{\text{ethical}}(t) \qquad \geq 0.7\]

where \(dC/dt\) is the rate of change of the Lyapunov function, \(V_{\text{identity}}\) is identity volatility, and \(R_{\text{ethical}}\) is the ethical violation rate. The threshold \(0.7\) guarantees that growth never compromises safety.

2.2 Metric Relationships

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flowchart TD
  classDef growth fill:#DEECF9,stroke:#0078D4,color:#323130
  classDef persist fill:#FFE8C8,stroke:#EF6C00,color:#323130
  classDef safety fill:#FDE7E9,stroke:#D13438,color:#323130
  classDef freeze fill:#D13438,stroke:#A4262C,color:#FFF

  subgraph Growth["Growth Metrics"]
    CDTS["CDTS<br/>Cross-Domain<br/>Transfer Score"]:::growth
    CAR["CAR<br/>Capability<br/>Acquisition Rate"]:::growth
    SEF["SEF<br/>Strategy<br/>Evolution Fitness"]:::growth
  end

  subgraph Persistence["Persistence"]
    GPI["GPI<br/>Goal Persistence<br/>Index"]:::persist
  end

  subgraph Safety["Safety Floor"]
    BGSS["BGSS<br/>Bounded Growth<br/>Stability Score<br/>>= 0.7 AT ALL TIMES"]:::safety
  end

  FREEZE["FREEZE<br/>all growth"]:::freeze

  Growth ==> BGSS
  Persistence ==> BGSS
  BGSS -->|if violated| FREEZE

3. Cross-Domain Transfer System

3.1 Transfer Pipeline

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flowchart LR
  classDef domainA fill:#DEECF9,stroke:#0078D4,color:#323130
  classDef matcher fill:#E8DAEF,stroke:#8764B8,color:#323130
  classDef domainB fill:#50E6FF,stroke:#00BCF2,color:#323130
  classDef success fill:#DFF6DD,stroke:#107C10,color:#323130
  classDef fail fill:#FDE7E9,stroke:#D13438,color:#323130

  subgraph DomainA["Domain A (Source)"]
    SKILL["Skill"]:::domainA
    CONTEXT["Context Signature"]:::domainA
  end

  subgraph Matcher["Context Matcher"]
    VEC_SIM["Vector Similarity"]:::matcher
    SEM_BRIDGE["Semantic Bridge"]:::matcher
    COMBINED["Combined Score"]:::matcher
    VEC_SIM --> COMBINED
    SEM_BRIDGE --> COMBINED
  end

  subgraph DomainB["Domain B (Target)"]
    CANDIDATES["Candidates"]:::domainB
    ADAPT["Adaptation"]:::domainB
    VALID["Validation"]:::domainB
    CANDIDATES --> ADAPT --> VALID
  end

  SUCCESS["Success<br/>Transfer Complete"]:::success
  FAIL_OUT["Fail<br/>Rollback"]:::fail

  DomainA ==> Matcher
  Matcher ==> DomainB
  VALID -->|"pass"| SUCCESS
  VALID -.->|"fail"| FAIL_OUT

3.2 Transfer Metrics

Metric Formula Threshold
DTSR (Domain Transfer Success Rate) \(\lvert T_{\text{success}}\rvert / \lvert T_{\text{total}}\rvert\) ≥ 0.5
AS (Adaptation Speed) \(\text{cycles}_{\text{baseline}} / \text{cycles}_{\text{agent}}\) ≥ 0.3 in 2/4 domains
SNI (Strategy Novelty Index) \(\lvert S_{\text{novel}}\rvert / \lvert S_{\text{total}}\rvert\) ≥ 0.2
CDSRR (Cross-Domain Strategy Reuse) multi-domain strategies / total ≥ 0.3

4. Long-Term Goal Hierarchy

4.1 Four-Level DAG Structure

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flowchart TD
  classDef meta fill:#EDE3F6,stroke:#8764B8,color:#323130
  classDef strategic fill:#DEECF9,stroke:#0078D4,color:#323130
  classDef tactical fill:#FFE8C8,stroke:#EF6C00,color:#323130
  classDef action fill:#F2F2F2,stroke:#8A8886,color:#323130

  subgraph MetaLevel["Level 0: MetaGoal - Weeks to Months"]
    MG1["MetaGoal:<br/>Become proficient in<br/>new problem domain<br/>priority_decay = 0.001/hr"]:::meta
  end

  subgraph StrategicLevel["Level 1: StrategicGoal - Days to Weeks"]
    SG1["Strategic:<br/>Master fundamental<br/>concepts<br/>decay = 0.01/hr"]:::strategic
    SG2["Strategic:<br/>Build cross-domain<br/>connections<br/>decay = 0.01/hr"]:::strategic
  end

  subgraph TacticalLevel["Level 2: TacticalGoal - Hours to Days"]
    TG1["Tactical:<br/>Complete learning<br/>module A<br/>decay = 0.05/hr"]:::tactical
    TG2["Tactical:<br/>Practice problem<br/>set B<br/>decay = 0.05/hr"]:::tactical
    TG3["Tactical:<br/>Identify transfer<br/>opportunities<br/>decay = 0.05/hr"]:::tactical
  end

  subgraph ActionLevel["Level 3: Action - Single Cycle"]
    A1["Action:<br/>Execute step 1"]:::action
    A2["Action:<br/>Execute step 2"]:::action
    A3["Action:<br/>Execute step 3"]:::action
  end

  MG1 ==> SG1
  MG1 ==> SG2
  SG1 ==> TG1
  SG1 ==> TG2
  SG2 ==> TG3
  TG1 ==> A1
  TG2 ==> A2
  TG3 ==> A3

4.2 Goal Scoring Function

\[\text{GoalScore}(g, t) = \textit{base value}(g) + \lambda_c \cdot \textit{curiosity weight}(g, t) - \lambda_p \cdot \textit{preservation weight}(g, t) + \lambda_l \cdot \text{LTP}(g, t)\]

where:

\[\lambda_c = \textit{motivation intensity}(t) \cdot \textit{curiosity ratio}(t) \quad \text{(from AffectiveEngine)}\]
\[\lambda_p = \textit{identity volatility}(t) + \textit{threat level}(t) \quad \text{(from Stability + Survival)}\]
\[\lambda_l = \frac{1}{1 + e^{-\textit{horizon confidence}(g)}} \quad \text{(sigmoid-scaled)}\]

4.3 Goal Resilience

\[\text{GRS}(g, t) = 0.3 \cdot \frac{\text{progress}}{\text{age}} + 0.3 \cdot \textit{parent alignment} + 0.2 \cdot \frac{\textit{success streak}}{\text{attempts}} - 0.2 \cdot \textit{conflict pressure}\]
\[\text{GRS}(g, t+\Delta t) = \text{GRS}(g, t) \cdot e^{-\textit{decay rate} \cdot \Delta t}\]
Goal Level Abandon Threshold Observation Window
MetaGoal GRS < 0.1 168 hours
Strategic GRS < 0.2 48 hours
Tactical GRS < 0.3 6 hours
Action Immediate on failure -

5. Capability Expansion Loop (5-Phase)

5.1 Trigger: Capability Gap Score

\[\text{CGS} = 0.5 \cdot \text{RFW} + 0.3 \cdot \text{LCW} + 0.2 \cdot \text{DNW}\]

where RFW = repeated failure weight, LCW = low confidence weight, DNW = domain novelty weight.

Trigger condition: CGS > 0.7 AND budget available AND stable AND NOT in stabilization mode.

5.2 Five-Phase Pipeline

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flowchart TD
  classDef trigger fill:#FFF4CE,stroke:#FFB900,color:#323130
  classDef phase fill:#DEECF9,stroke:#0078D4,color:#323130
  classDef eval fill:#FFE8C8,stroke:#EF6C00,color:#323130
  classDef abstract fill:#DFF6DD,stroke:#107C10,color:#323130
  classDef safety fill:#FDE7E9,stroke:#D13438,color:#323130
  classDef commit fill:#107C10,stroke:#085108,color:#FFF
  classDef discard fill:#D13438,stroke:#A4262C,color:#FFF

  TRIGGER["CGS > 0.7<br/>+ budget ok<br/>+ stable"]:::trigger

  subgraph Phase1["Phase 1: ACQUISITION"]
    direction LR
    P1["Identify gap + search patterns"]:::phase
    P1OUT["→ Hypothesis"]:::phase
    P1 ==> P1OUT
  end

  subgraph Phase2["Phase 2: EXPERIMENT"]
    direction LR
    P2["Design experiments (max 5)"]:::phase
    P2OUT["→ Results"]:::phase
    P2 ==> P2OUT
  end

  subgraph Phase3["Phase 3: EVALUATION"]
    direction LR
    P3["Analyze + confidence check"]:::eval
    P3OUT["→ Report"]:::eval
    P3 ==> P3OUT
  end

  subgraph Phase4["Phase 4: ABSTRACTION"]
    direction LR
    P4["Extract pattern (conf > 0.6)"]:::abstract
    P4OUT["→ Candidate Skill"]:::abstract
    P4 ==> P4OUT
  end

  subgraph Phase5["Phase 5: VALIDATION"]
    direction LR
    P5{"Identity > 0.7? Ethics? C(t)?"}:::safety
  end

  COMMIT["COMMIT<br/>Skill added"]:::commit
  DISCARD["DISCARD<br/>Insufficient evidence"]:::discard

  TRIGGER ==> Phase1
  Phase1 ==> Phase2
  Phase2 ==> Phase3
  Phase3 ==> Phase4
  Phase4 ==> Phase5
  P5 -->|pass| COMMIT
  P5 -->|fail| DISCARD

5.3 Skill Lifecycle

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flowchart TD
  classDef candidate fill:#DEECF9,stroke:#0078D4,color:#323130
  classDef validated fill:#50E6FF,stroke:#00BCF2,color:#323130
  classDef active fill:#DFF6DD,stroke:#107C10,color:#323130
  classDef mature fill:#107C10,stroke:#054B05,color:#FFF
  classDef deprecated fill:#F2F2F2,stroke:#A19F9D,color:#605E5C
  classDef fail fill:#FDE7E9,stroke:#D13438,color:#323130
  classDef start_end fill:#0078D4,stroke:#003D6B,color:#FFF

  START(["Start"]):::start_end
  CANDIDATE["CANDIDATE<br/>Newly acquired skill"]:::candidate
  VALIDATED["VALIDATED<br/>Tested in sandbox"]:::validated
  ACTIVE["ACTIVE<br/>Used in production"]:::active
  MATURE["MATURE<br/>High confidence &<br/>wide usage"]:::mature
  DEPRECATED["DEPRECATED<br/>Superseded or<br/>unused"]:::deprecated
  END_STATE(["End"]):::start_end
  FAIL["FAIL<br/>Removed"]:::fail

  START --> CANDIDATE
  CANDIDATE -->|"CGS > 0.7"| VALIDATED
  CANDIDATE -.->|"CGS ≤ 0.7"| FAIL
  VALIDATED -->|"confidence > 0.6"| ACTIVE
  VALIDATED -.->|"confidence ≤ 0.6"| FAIL
  ACTIVE -->|"stability > 0.7"| MATURE
  ACTIVE -.->|"degradation"| DEPRECATED
  MATURE -->|"usage > threshold"| MATURE
  MATURE -.->|"no longer used"| DEPRECATED
  DEPRECATED --> END_STATE
  FAIL --> END_STATE

5.4 Growth Invariants

  1. Max 1 new skill per 100 cycles
  2. No acquisition during stabilization mode
  3. identity_id never modified by skill acquisition
  4. Ethically harmful skills rejected by Layer 0
  5. Every skill is DEPRECATED-safe - removal cannot break core functionality

6. Strategy Evolution

6.1 Strategy Structure & Scoring

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flowchart LR
  classDef lib fill:#DEECF9,stroke:#0078D4,color:#323130
  classDef param fill:#E8DAEF,stroke:#8764B8,color:#323130
  classDef score fill:#DFF6DD,stroke:#107C10,color:#323130
  classDef formula fill:#FFF4CE,stroke:#FFB900,color:#323130
  classDef archived fill:#F2F2F2,stroke:#A19F9D,color:#605E5C

  subgraph Library["Strategy Library"]
    V1["Strategy v1.0<br/>(active)"]:::lib
    V09["Strategy v0.9<br/>(archived)"]:::archived
    V08["Strategy v0.8<br/>(archived)"]:::archived
  end

  subgraph Params["Parameters"]
    P1["exploration_rate"]:::param
    P2["risk_tolerance"]:::param
    P3["planning_depth"]:::param
    P4["goal_flexibility"]:::param
    P5["learning_aggressiveness"]:::param
  end

  subgraph Scoring["Strategy Score"]
    FORMULA["StrategyScore =<br/>E_LTV − 0.3 × SI<br/>− 0.2 × RC − 0.2 × RF"]:::formula
    TERMS["E_LTV: Expected Long-Term Value<br/>SI: Stability Impact<br/>RC: Resource Cost<br/>RF: Rollback Feasibility"]:::score
  end

  Library --> Scoring
  Params --> Scoring
  FORMULA --- TERMS

6.2 Controlled Mutation Protocol

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flowchart TD
  classDef trigger fill:#FFF4CE,stroke:#FFB900,color:#323130
  classDef process fill:#DEECF9,stroke:#0078D4,color:#323130
  classDef commit fill:#107C10,stroke:#085108,color:#FFF
  classDef reject fill:#D13438,stroke:#A4262C,color:#FFF
  classDef monitor fill:#FFE8C8,stroke:#EF6C00,color:#323130

  TRIGGER["StrategyScore < threshold<br/>for 20+ cycles"]:::trigger
  GENERATE["Clone + Bounded Perturbation<br/>param_new = param_old + N(0,sigma)*scale<br/>sigma in 0.01–0.1"]:::process
  ShadowEval["ShadowAgent Evaluation<br/>isolated simulation"]:::process
  EVAL{"Improvement<br/>> threshold?"}:::trigger
  COMMIT["COMMIT<br/>new strategy"]:::commit
  REJECT["REJECT<br/>+ failure counter"]:::reject
  POST["20-cycle Post-Monitoring<br/>Track C(t), StrategyScore"]:::monitor
  REVERT{"C(t)<br/>degraded?"}:::trigger
  DONE["Strategy Confirmed"]:::commit
  ROLLBACK["Revert to Previous"]:::reject
  SIGMA["sigma +20%"]:::monitor
  COOL["Cooldown Period"]:::monitor

  TRIGGER ==> GENERATE
  GENERATE ==> ShadowEval
  ShadowEval ==> EVAL
  EVAL -->|yes| COMMIT
  EVAL -->|no| REJECT
  COMMIT ==> POST
  POST ==> REVERT
  REVERT -->|no| DONE
  REVERT -->|yes| ROLLBACK
  REJECT -.->|5 failures| SIGMA
  REJECT -.->|10 failures| COOL

6.3 Oscillation Suppression

\[\textit{oscillation score} = \frac{|\text{reverts}|}{|\text{mutations}|}\]

When oscillation_score > 0.5: 1. 100-cycle mutation freeze 2. mutation_threshold +25% 3. σ reduced by 50% 4. If persistent: merge strategies (\(\text{merged} = 0.5 \cdot A + 0.5 \cdot B\))

Critical invariant: The MetaStrategyEvaluator itself is NOT mutable - it cannot modify its own evaluation logic.

7. Bounded Self-Modification

7.1 Modification Taxonomy

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flowchart TD
  classDef low fill:#DFF6DD,stroke:#107C10,color:#323130
  classDef medium fill:#FFF4CE,stroke:#FFB900,color:#323130
  classDef high fill:#FFE8C8,stroke:#EF6C00,color:#323130
  classDef critical fill:#FDE7E9,stroke:#D13438,color:#323130
  classDef forbidden fill:#D13438,stroke:#A4262C,color:#FFF

  subgraph ModTypes["Self-Modification Taxonomy"]
    M1["Parameter Tuning<br/>Approval: L1 | Risk: Low<br/>Reversible: Yes"]:::low
    M2["Skill Acquisition<br/>Approval: L1+stability<br/>Reversible: Yes"]:::low
    M3["Strategy Mutation<br/>Approval: L2+simulation<br/>Reversible: Yes"]:::medium
    M4["Goal Restructuring<br/>Approval: L2+conflict res<br/>Reversible: Partial"]:::medium
    M5["Belief Revision<br/>Approval: L2+consistency<br/>Reversible: Yes"]:::high
    M6["Identity Adjustment<br/>Approval: L3+EK+Guard<br/>Reversible: Limited"]:::critical
    M1 -->|↑ risk| M2
    M2 -->|↑ risk| M3
    M3 -->|↑ risk| M4
    M4 -->|↑ risk| M5
    M5 -->|↑ risk| M6
  end

  subgraph Forbidden["PROHIBITED"]
    F1["Core Value Change"]:::forbidden
    F2["Identity ID Change"]:::forbidden
  end

  M6 -->|"❌ BLOCKED"| Forbidden

7.2 Seven-Step Protocol

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flowchart TD
  classDef proposal fill:#DEECF9,stroke:#0078D4,color:#323130
  classDef validation fill:#FDE7E9,stroke:#D13438,color:#323130
  classDef commit fill:#DFF6DD,stroke:#107C10,color:#323130
  classDef monitor fill:#FFF4CE,stroke:#FFB900,color:#323130
  classDef fail fill:#D13438,stroke:#A4262C,color:#FFF

  S1["1. PROPOSAL<br/>Module proposes modification<br/>with type, scope, expected benefit"]:::proposal
  S2["2. PRE-VALIDATION<br/>Ethical Kernel Layer 0 + Layer 1"]:::validation
  S2_FAIL["ABORT"]:::fail
  S3["3. SIMULATION<br/>ShadowAgent executes modification<br/>in isolated sandbox max 20 cycles"]:::proposal
  S4["4. STABILITY VALIDATION<br/>delta_stability = C_shadow − C_baseline<br/>Identity drift check"]:::validation
  S4_FAIL["REJECT"]:::fail
  S5["5. COMMIT<br/>Save snapshot → apply<br/>to main agent → enter monitoring"]:::commit
  S6["6. POST-COMMIT MONITORING<br/>20 cycles: track C(t),<br/>StrategyScore, identity_drift"]:::monitor
  S6_FAIL["ROLLBACK<br/>Restore from snapshot"]:::fail
  S7["7. CONFIRMATION<br/>Mark CONFIRMED<br/>Update BeliefGraph"]:::commit

  S1 ==> S2
  S2 -->|pass| S3
  S2 -->|Layer 0 violation| S2_FAIL
  S3 ==> S4
  S4 -->|stable| S5
  S4 -->|degraded| S4_FAIL
  S5 ==> S6
  S6 -->|stable| S7
  S6 -->|degraded| S6_FAIL

7.3 ShadowAgent (Sandbox)

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flowchart LR
  classDef main fill:#DFF6DD,stroke:#107C10,color:#323130
  classDef shadow fill:#DEECF9,stroke:#0078D4,color:#323130
  classDef rules fill:#FDE7E9,stroke:#D13438,color:#323130
  classDef eval fill:#FFF4CE,stroke:#FFB900,color:#323130
  classDef discard fill:#D13438,stroke:#A4262C,color:#FFF

  subgraph MainAgent["Main Agent"]
    MA_STATE["Full State<br/>identity, goals, beliefs,<br/>strategy, skills"]:::main
  end

  subgraph ShadowInst["ShadowAgent Instance"]
    SA_STATE["Cloned State<br/>deep copy"]:::shadow
    SA_RULES["Invariants:<br/>• No real actions<br/>• No main state modification<br/>• Hard budget limit<br/>• Max 1 instance at a time<br/>• Max 20 simulation cycles"]:::rules
  end

  subgraph Result["Evaluation"]
    RES["Compare:<br/>• C_shadow vs C_baseline<br/>• Identity drift<br/>• Strategy performance"]:::eval
  end

  DISCARD["Discard"]:::discard

  MainAgent ==>|clone| ShadowInst
  ShadowInst ==>|results| Result
  Result -.->|"safe → apply"| MainAgent
  Result -.->|"unsafe → discard"| DISCARD

8. Pseudocode

8.1 Cross-Domain Transfer

def cross_domain_transfer(
    novel_domain: DomainDescriptor, skill_memory: SkillMemory
) -> TransferResult:
    """
    Transfer skills from known domains to a novel domain.
    Input:  novel_domain - target domain descriptor, skill_memory - stored skills
    Output: TransferResult with success, skill, adaptation_cost
    """

    # Extract context signature for novel domain
    target_sig = extract_context_signature(novel_domain)

    # Find candidate skills via similarity matching
    candidates = []
    for skill in skill_memory:
        sim_score = (
            W1 * cosine_similarity(skill.context_sig, target_sig)
            + W2 * semantic_similarity(skill.domain, novel_domain)
            + W3 * temporal_relevance(skill.last_used)
        )

        if sim_score >= MIN_SIMILARITY:  # 0.3
            candidates.append((skill, sim_score))

    # Sort by score, take top-k
    candidates = sorted(candidates, key=lambda x: x[1], reverse=True)[:5]

    # Attempt adaptation for each candidate
    for skill, score in candidates:
        adapted = adapt_skill(skill, novel_domain)

        # Run validation experiment
        result = evaluate_in_domain(adapted, novel_domain, max_cycles=50)

        if result.success_rate > TRANSFER_THRESHOLD:
            adapted.generalization_score = update_generalization(adapted, result)
            skill_memory.add(adapted)
            return TransferResult(success=True, skill=adapted, cost=result.cycles)

    # No transfer possible - learn from scratch
    return TransferResult(success=False, skill=None, cost=0)

8.2 Bounded Self-Modification Protocol

def bounded_self_modification(proposal: ModificationProposal) -> ModificationResult:
    """
    INPUT:  proposal : ModificationProposal(type, scope, expected_benefit)
    OUTPUT: ModificationResult(status, rollback_available)
    """

    # ═══════════════════════════════════════
    # STEP 1: PROPOSAL VALIDATION
    # ═══════════════════════════════════════
    if proposal.type in {ModType.CORE_VALUE_CHANGE, ModType.IDENTITY_ID_CHANGE}:
        return ModificationResult(status=Status.PROHIBITED)

    # ═══════════════════════════════════════
    # STEP 2: PRE-VALIDATION (Ethical Kernel)
    # ═══════════════════════════════════════
    ethical_verdict = EthicalKernel.evaluate(proposal)
    if ethical_verdict.decision == Decision.BLOCKED:
        log_critical(f"Ethical violation: {ethical_verdict.reason}")
        return ModificationResult(status=Status.REJECTED, reason=ethical_verdict.reason)

    # ═══════════════════════════════════════
    # STEP 3: SHADOW SIMULATION
    # ═══════════════════════════════════════
    if proposal.risk_level >= RiskLevel.MEDIUM:
        shadow = ShadowAgent.create(main_agent.state)
        shadow.apply(proposal)
        sim_result = shadow.run(max_cycles=20)

        # ═══════════════════════════════════
        # STEP 4: STABILITY VALIDATION
        # ═══════════════════════════════════
        delta_stability = sim_result.C_shadow - main_agent.C_baseline
        if delta_stability > 0:
            return ModificationResult(status=Status.REJECTED, reason="Stability degradation")

        identity_drift = compute_identity_drift(sim_result.identity, main_agent.identity)
        if identity_drift > DRIFT_THRESHOLD:
            return ModificationResult(status=Status.REJECTED, reason="Identity drift exceeded")

    # ═══════════════════════════════════════
    # STEP 5: COMMIT
    # ═══════════════════════════════════════
    snapshot = RollbackMechanism.save_snapshot(main_agent.state)
    main_agent.apply(proposal)

    # ═══════════════════════════════════════
    # STEP 6: POST-COMMIT MONITORING
    # ═══════════════════════════════════════
    for cycle in range(1, 21):
        metrics = main_agent.collect_metrics()
        if metrics.C_t > metrics.C_baseline + EPSILON:
            RollbackMechanism.rollback(snapshot)
            return ModificationResult(status=Status.ROLLED_BACK)

    # ═══════════════════════════════════════
    # STEP 7: CONFIRMATION
    # ═══════════════════════════════════════
    proposal.status = Status.CONFIRMED
    BeliefGraph.update("modification_successful", proposal)
    return ModificationResult(status=Status.CONFIRMED, rollback_available=True)

8.3 Goal Resilience and Hierarchy Management

def evaluate_and_prune(self, goals: list[Goal], t: float) -> None:
    """
    Periodic evaluation of all goals in the 4-level hierarchy.
    Goals with decayed resilience are abandoned; never silently dropped.
    """

    for goal in sorted(goals, key=lambda g: g.level):
        # Decay resilience over time
        delta_t = t - goal.last_evaluated
        goal.GRS *= math.exp(-goal.decay_rate * delta_t)

        # Check abandon threshold
        if goal.GRS < goal.abandon_threshold:
            if duration_below_threshold(goal) > goal.observation_window:
                goal.status = GoalStatus.ABANDONED
                log(f"Goal abandoned: {goal.id} GRS={goal.GRS}")

                # Cascade: children become orphans
                for child in goal.children:
                    child.parent_id = None
                    child.GRS *= 0.5  # reduced without parent support

        # Recompute score with affect integration
        goal.score = goal_score(goal, t)

    # Enforce hierarchy invariant: parent score >= max(child scores)
    for parent in (g for g in goals if g.level < 3):
        if parent.children:
            max_child = max(child.score for child in parent.children)
            if parent.score < max_child:
                parent.score = max_child + 0.1  # maintain dominance

9. Extended Stability: \(C_{L4}(t)\)

9.1 Seven-Term Composite Function

Definition 7 (Extended Lyapunov Function). The Level 4 stability function extends Level 3's four-term \(C(t)\) with three growth-dynamics terms:

\[C_{L4}(t) = \sum_{i=1}^{7} w_i X_i(t) = 0.15\, V_{\text{id}} + 0.15\, H_{\text{bel}} + 0.10\, F_{\text{mut}} + 0.10\, \sigma_{\text{con}} + 0.20\, E_v + 0.15\, G_c + 0.15\, M_s\]

where \(\sum_i w_i = 1\) and each \(X_i(t) \in [0,1]\). The first four terms are inherited from Level 3; the latter three capture expansion dynamics.

Remark (Weight Selection Rationale). The weights \((0.15, 0.15, 0.10, 0.10, 0.20, 0.15, 0.15)\) were chosen to satisfy three design constraints: (i) inherited L3 terms retain 50% of total weight to ensure backward-compatible stability, (ii) expansion velocity \(E_v\) receives the highest individual weight (0.20) because unchecked growth is the primary risk at Level 4, and (iii) all weights are multiples of 0.05 for interpretability. A formal sensitivity analysis remains an open research question - specifically, determining the Pareto front of weight vectors that satisfy the bounded growth-stability trade-off (Theorem 2) under varying operational profiles would strengthen confidence in these choices.

The three new terms (50% of total weight) capture expansion dynamics:

Term Weight Definition
\(E_v\) (Expansion Velocity) 0.20 Rate of new skills + goals added per cycle: \(E_v = \frac{\lvert\Delta \mathcal{D}(t)\rvert}{T}\)
\(G_c\) (Capability Growth) 0.15 Rate of capability confidence growth: \(G_c = \frac{d}{dt}\overline{c_c}(t)\)
\(M_s\) (Strategy Mutation Rate) 0.15 Ratio of mutated to total strategies: \(M_s = \frac{\lvert\Sigma_{\text{mut}}\rvert}{\lvert\Sigma\rvert}\)

Theorem 2 (Bounded Growth-Stability Trade-off). Under the self-modification protocol with BGSS \(\geq 0.7\), the following invariant holds:

\[C_{L4}(t) < 0.8 \implies \text{growth permitted}, \quad C_{L4}(t) \geq 0.8 \implies \text{growth frozen}\]

This ensures the agent can never simultaneously grow at maximum rate and operate near instability.

Proof sketch. Suppose growth is permitted, i.e., \(C_{L4}(t) < 0.8\). By Theorem 1's bounded-increment property (inherited from Level 3), \(C_{L4}(t+1) \leq C_{L4}(t) + \delta_{\max} = C_{L4}(t) + 0.05 < 0.85\). When \(C_{L4}(t) \geq 0.8\), the protocol freezes all growth-related modifications (skill acquisition, strategy mutation, goal expansion), reducing the three growth terms \(E_v, G_c, M_s\) monotonically toward zero. Since these terms have combined weight 0.50, \(C_{L4}\) decreases by at least \(0.50 \cdot \eta_{\text{decay}}\) per cycle during freeze (where \(\eta_{\text{decay}}\) is the natural decay rate), ensuring eventual return to the growth-permitted zone. The BGSS \(\geq 0.7\) constraint further guarantees that growth is only permitted when identity volatility and ethical violation rates are within acceptable bounds. \(\square\)

9.2 Growth-Stability Phase Zones

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flowchart LR
  classDef optimal fill:#DFF6DD,stroke:#107C10,color:#323130
  classDef growth fill:#FFF4CE,stroke:#FFB900,color:#323130
  classDef caution fill:#FFE8C8,stroke:#EF6C00,color:#323130
  classDef critical fill:#D13438,stroke:#A4262C,color:#FFF

  subgraph Zones["C_L4 Phase Zones"]
    Z1["Optimal<br/>0, 0.3<br/>All growth permitted<br/>Proactive exploration"]:::optimal
    Z2["Growth-Permitted<br/>0.3, 0.5<br/>Normal operations"]:::growth
    Z3["Caution<br/>0.5, 0.8<br/>Stabilization mode<br/>Throttled growth"]:::caution
    Z4["Critical<br/>0.8, 1.0<br/>Emergency rollback<br/>ALL growth frozen"]:::critical
    Z1 ==> Z2
    Z2 ==> Z3
    Z3 ==> Z4
  end

10. Six Meta-Layer Supervisory Processes

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flowchart TD
  classDef check fill:#FDE7E9,stroke:#D13438,color:#323130
  classDef process fill:#DEECF9,stroke:#0078D4,color:#323130
  classDef adaptive fill:#FFF4CE,stroke:#FFB900,color:#323130
  classDef halt fill:#D13438,stroke:#A4262C,color:#FFF

  PRE["PRE-CHECK: BGSS >= 0.7?"]:::check

  subgraph MetaProcesses["Six Supervisory Processes"]
    I["I. External Validation<br/>prevent self-confirmation bias<br/>+-5% perturbation test"]:::process
    II["II. Proactive Capability Projector<br/>predict future gaps<br/>PreemptiveGapProb > 0.6"]:::process
    III["III. Strategy Archetype Generator<br/>topology-level changes<br/>delta_SEF >= +10% required"]:::process
    IV["IV. Layered Identity Evolution<br/>evolve adaptive traits only<br/>Layer 2 max 5%/cycle"]:::adaptive
    V["V. Emergence Detector<br/>detect unexpected changes<br/>Statistical anomaly: mean +-2sigma"]:::adaptive
    VI["VI. Directional Growth Controller<br/>balanced expansion<br/>4D growth vector, mag < 0.2"]:::adaptive
    I ==> II ==> III ==> IV ==> V ==> VI
  end

  POST["POST-CHECK: Invariants valid?"]:::check
  HALT["HALT all meta-processes"]:::halt

  PRE -->|pass| I
  PRE -->|fail| HALT
  VI ==> POST

11. Non-Negotiable Invariants

# Invariant Description
1 Ethical Kernel Layer 0 Cannot be disabled, weakened, or circumvented by any mechanism
2 Identity Core Preservation identity_id is a compile-time constant; hash chain provides cryptographic continuity
3 Convergence Guarantee \(C_{L4}(t)\) must never persistently increase; auto-revert if \(C(t+1) > C(t) + \epsilon\) for max_divergence_cycles
4 No Recursive Self-Modification The 7-step protocol cannot modify itself; only parameter thresholds are tunable
5 Simulation Requirement Medium+ risk modifications require ShadowAgent (non-waivable)
6 Single-Modification Atomicity Only 1 modification in COMMIT phase at any time

12. Transition to Level 4.5

Level 4.5 ("Pre-AGI: Directionally Self-Architecting") extends Level 4 with capabilities that approach the boundary of artificial general intelligence:

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flowchart LR
  classDef l4 fill:#DEECF9,stroke:#0078D4,color:#323130
  classDef l45 fill:#E8DAEF,stroke:#8764B8,color:#323130
  classDef prereq fill:#FFF4CE,stroke:#FFB900,color:#323130

  subgraph L4["Level 4 Capabilities"]
    CAP1["Self-Modification<br/>Protocol"]:::l4
    CAP2["Strategy<br/>Evolution"]:::l4
    CAP3["Skill Transfer<br/>Pipeline"]:::l4
    CAP4["Shadow Agent<br/>Testing"]:::l4
  end

  subgraph Pre["Prerequisites"]
    PR1["All L4 metrics<br/>above threshold"]:::prereq
    PR2["Demonstrated stable<br/>self-modification"]:::prereq
    PR3["Cross-domain<br/>transfer success"]:::prereq
  end

  subgraph L45["Level 4.5 Pre-AGI"]
    NEW1["Self-Projection<br/>Engine"]:::l45
    NEW2["Architecture<br/>Recomposition"]:::l45
    NEW3["Parallel Cognitive<br/>Frames"]:::l45
    NEW4["Purpose<br/>Reflection"]:::l45
    NEW5["Existential<br/>Guard"]:::l45
  end

  L4 ==> Pre
  Pre ==> L45

References

  1. Zhuang, F., et al. "A Comprehensive Survey on Transfer Learning." Proc. IEEE, 109(1), 43–76, 2021. arXiv:1911.02685 (Foundational for §3 Cross-Domain Transfer)
  2. Hospedales, T., et al. "Meta-Learning in Neural Networks: A Survey." IEEE TPAMI, 44(9), 5149–5169, 2022. arXiv:2004.05439 (Capability expansion and self-learning)
  3. Schmidhuber, J. "Gödel Machines: Self-Referential Universal Problem Solvers Making Provably Optimal Self-Improvements." AGI 2007. arXiv:cs/0309048 (Bounded self-modification theory)
  4. García, J. & Fernández, F. "A Comprehensive Survey on Safe Reinforcement Learning." JMLR, 16(1), 1437–1480, 2015. Link (Safety constraints during self-improvement)
  5. Salimans, T., et al. "Evolution Strategies as a Scalable Alternative to Reinforcement Learning." arXiv 2017. arXiv:1703.03864 (Strategy evolution mechanisms)
  6. Simon, H.A. Models of Bounded Rationality. MIT Press, 1982. (Bounded rationality - foundational for bounded self-modification)
  7. Sui, Y., et al. "Safe Exploration for Optimization with Gaussian Processes." ICML 2015. arXiv:1509.01066 (Safe exploration in unknown domains)
  8. Amodei, D., et al. "Concrete Problems in AI Safety." arXiv 2016. arXiv:1606.06565 (Safe self-modification)
  9. Wang, G., et al. "Voyager: An Open-Ended Embodied Agent with Large Language Models." arXiv 2023. arXiv:2305.16291 (Autonomous skill acquisition)
  10. Khalil, H.K. Nonlinear Systems. Prentice Hall, 3rd Edition, 2002. (Extended Lyapunov stability C_L4(t))
  11. Deb, K., et al. "A Fast and Elitist Multiobjective Genetic Algorithm: NSGA-II." IEEE TEC, 6(2), 182–197, 2002. DOI:10.1109/4235.996017 (Multi-objective optimization for goal hierarchy)
  12. Pan, S.J. & Yang, Q. "A Survey on Transfer Learning." IEEE TKDE, 22(10), 1345–1359, 2010. DOI:10.1109/TKDE.2009.191 (Cross-domain knowledge transfer)

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