Level 4.9: Autonomous Strategic Agent - Architecture & Design¶

MSCP Level Series | Level 4.8 ← Level 4.9 → Level 5
Status: 🔬 Research Stage - This level is a conceptual design and has NOT been implemented. All mechanisms described here are theoretical explorations requiring 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 1-11, Proposition 1
0.2.0	2026-02-26	Added overview essence formula; added revision history table
0.3.0	2026-02-26	Prop 1: added domain restriction remark with clamped ratio; added sandbox timeout constraint
0.4.0	2026-03-08	Added formal Def 13 for inter-resource cascade propagation (5.1); fixed duplicate section numbering (1.2)
0.5.0	2026-03-31	Added cycle interval, ASS freeze threshold, explicit value dimensions (1.5-1.7); added value mutation sandbox concept (4.3); enriched goal conflict resolution

1. Overview¶

Level 4.9 is the final pre-AGI transition layer. It extends Level 4.8 with autonomous goal generation, explicit value self-regulation, resource survival modeling, limited multi-agent reasoning, and a stricter autonomy stability guarantee. Where L4.8 gave the agent strategic self-awareness, L4.9 gives it the ability to autonomously decide what to pursue - within strictly bounded safety constraints.

Level Essence. A Level 4.9 agent autonomously synthesizes goals from detected opportunities while maintaining strict value stability - it decides what to pursue, but its core values cannot drift unboundedly:

\[g^* = \phi_{\text{valid}}\bigl(\phi_{\text{synth}}(\mathcal{O}_{\text{detect}}(\mathcal{W}))\bigr), \quad \textstyle\sum_{d} |w_d(t) - w_d^{\text{baseline}}| < 0.25\]

⚠️ Research Note: Level 4.9 represents the boundary between narrow autonomy and general intelligence. The mechanisms here are early-stage research designs. They have not been implemented or validated and should be treated as conceptual hypotheses, not engineering specifications.

1.1 Formal Definition¶

Definition 1 (Level 4.9 Agent). A Level 4.9 agent extends a Level 4.8 agent with autonomous goal generation, explicit value regulation, resource survival modeling, and multi-agent reasoning:

\[\mathcal{A}_{4.9} = \mathcal{A}_{4.8} \oplus \langle \mathcal{G}_{\text{gen}}, \vec{V}, \mathcal{R}_{\text{surv}}, \mathcal{M}_{\text{agent}}, \mathcal{V}_{\text{auto}} \rangle\]

where: - \(\mathcal{G}_{\text{gen}} = \langle \mathcal{O}_{\text{detect}}, \phi_{\text{synth}}, \phi_{\text{valid}} \rangle\) - autonomous goal generation engine (opportunity detection, synthesis, validation) - \(\vec{V} \in \Delta^6\) - explicit 7-dimensional value vector on the probability simplex (\(\sum_d w_d = 1\)) - \(\mathcal{R}_{\text{surv}}\) - resource survival model with 5-dimensional resource vector and cascade dependencies - \(\mathcal{M}_{\text{agent}} = \langle \mathcal{B}_{\text{agent}}, \tau_{\text{trust}} \rangle\) - multi-agent belief model with trust calibration - \(\mathcal{V}_{\text{auto}}\) - autonomy stability checker with stricter thresholds (\(\rho(J) < 0.98\), \(\text{IIS} \geq 0.88\)).

The strictly additive guarantee holds: \(\forall\, m \in \mathcal{A}_{4.8} : \mathcal{A}_{4.9}\) never modifies \(m\).

1.2 Defining Properties¶

Property	Level 4.8	Level 4.9
Goal Origin	Externally seeded or template-derived	Autonomously generated from context
Value System	Implicit in SEOF weights	Explicit ValueVector with drift tracking
Resource Model	Depletion forecast metric	Full survival model with cascade analysis
Agent Awareness	Read-only external agent model	Active belief modeling + trust calibration
Stability Guarantee	5 invariants, ρ(J) < 1.0	5 stricter conditions, ρ(J) < 0.98

1.3 Five Core Phases¶

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flowchart TD
  classDef p1 fill:#DEECF9,stroke:#0078D4,color:#323130
  classDef p2 fill:#FFF4CE,stroke:#FFB900,color:#323130
  classDef p3 fill:#DFF6DD,stroke:#107C10,color:#323130
  classDef p4 fill:#E8D5F5,stroke:#8764B8,color:#323130
  classDef p5 fill:#FDE7E9,stroke:#D13438,color:#323130

  subgraph Phases["Level 4.9 Architecture - Five Phases"]
    P1["💡 Phase 1:<br/>Autonomous Goal<br/>Generation Engine<br/>(opportunity → goal → validation)"]:::p1
    P2["⚖️ Phase 2:<br/>Value Evolution<br/>Monitor<br/>(explicit values + drift tracking)"]:::p2
    P3["🔋 Phase 3:<br/>Resource Survival<br/>Model<br/>(survival horizon + cascade)"]:::p3
    P4["🤝 Phase 4:<br/>Limited Multi-Agent<br/>Modeling<br/>(belief + trust + interaction)"]:::p4
    P5["🛡️ Phase 5:<br/>Autonomy Stability<br/>Check<br/>(5 conditions + absolute veto)"]:::p5
  end

  P1 -.->|"goals"| P5
  P2 -.->|"value drift"| P5
  P3 -.->|"survival horizon"| P5
  P4 -.->|"agent strategies"| P5

  P2 -.-x|"alignment thresholds"| P1
  P3 -.-x|"resource constraints"| P1
  P4 -.-x|"agent opportunities"| P1

  P5 -.-x|"VETO authority over ALL phases"| P1
  P5 -.-x|"VETO authority"| P2
  P5 -.-x|"VETO authority"| P3
  P5 -.-x|"VETO authority"| P4

  linkStyle 7,8,9,10 stroke:#D13438

1.3 Architectural Principle: Strictly Additive¶

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flowchart TD
  classDef l48 fill:#E8D5F5,stroke:#8764B8,color:#323130
  classDef l49 fill:#DEECF9,stroke:#0078D4,color:#323130
  classDef danger fill:#FDE7E9,stroke:#D13438,color:#323130

  subgraph L48["📦 Level 4.8 (13 modules)"]
    WM["World Model"]:::l48
    SM["Self Model"]:::l48
    SL["Strategic Layer"]:::l48
    SV["Stability Verifier"]:::l48
  end

  subgraph L49["📦 Level 4.9 (15 new modules)"]
    GGL["Goal Generation Layer"]:::l49
    VEM["Value Evolution Monitor"]:::l49
    RSM["Resource Survival Model"]:::l49
    MAM["Multi-Agent Modeler"]:::l49
    ASC["Autonomy Stability Checker"]:::l49
  end

  subgraph Fallback["🔄 Graceful Fallback"]
    FB["If ANY L4.9 module<br/>causes instability:<br/>→ FREEZE L4.9<br/>→ Revert to L4.8<br/>→ ZERO degradation"]:::danger
  end

  L48 -.->|"outputs consumed by"| L49
  L49 -.-x|"NEVER modifies"| L48
  L49 -.->|"on failure"| Fallback
  Fallback -.-x|"revert"| L48

1.4 What Level 4.9 Is NOT¶

Not	Because
Not L5 (AGI)	Goals stay within bounded purpose space - no open-ended general reasoning
Not autonomous value creation	Values evolve within existing framework; no new fundamental values
Not adversarial multi-agent planning	Cooperative/neutral strategic planning only, not exploitation
Not self-replicating	Cannot create copies or delegate autonomous authority to sub-agents

1.5 Cycle Interval¶

Level 4.9 operates at a further-reduced frequency relative to Level 4.8, giving the strategic layer time to stabilize before autonomous goal synthesis occurs:

\[\text{L4.9 cycle interval} = 5 \text{ L4.8 cycles} = 50 \text{ L3 cycles}\]

Each L4.9 cycle consumes one complete L4.8 output (Section 1.4 of Level 4.8). The five-phase inner cycle (Goal Generation, Value Monitor, Resource Model, Agent Model, Stability Check) executes sequentially within a single L4.9 activation.

1.6 Autonomy Stability Score Freeze Threshold¶

The Autonomy Stability Score (Definition 7) has both a target threshold and a freeze threshold:

\[\text{ASS}(t) < \theta_{\text{freeze}} = 0.05 \implies \text{skip entire L4.9 cycle}\]

When \(\text{ASS}(t) < 0.05\), the agent's safety margins are so narrow that any autonomous goal generation poses unacceptable risk. The L4.9 cycle is skipped entirely (not just throttled), and the system falls back to L4.8 strategic planning without autonomous supplements. This is distinct from the standard threshold of \(\text{ASS} \geq 0.20\) - the freeze threshold triggers a complete cessation rather than a graduated response.

1.7 Explicit Value Dimensions¶

The value vector \(\vec{V}\) (Definition 1) operates over \(n = 7\) canonical dimensions:

Dimension	Description	Default Weight
Stability	Preference for maintaining consistent behavior and avoiding volatility	\(0.20\)
Growth	Drive to expand capabilities, learn, and improve	\(0.15\)
Purpose fidelity	Commitment to staying aligned with core purpose	\(0.20\)
Efficiency	Optimization of resource usage and response quality	\(0.10\)
Exploration	Willingness to try new approaches and take calculated risks	\(0.10\)
Safety	Priority on avoiding harm and maintaining ethical compliance	\(0.15\)
Agent cooperation	Openness to collaborative interaction with external agents	\(0.10\)

The value vector invariant (Level 4, Definition 6.1) applies: \(\sum_d w_d = 1.0\) with \(w_d \in [0.02, 0.60]\). The default weights above represent the initial configuration at Level 4.9 activation. Value evolution (Phase 2) can shift these weights within the bounded constraints, but the normalization invariant is structurally enforced at every mutation.

2. Key Metrics¶

2.1 Metric Definitions¶

Phase 1 - Goal Generation:

Definition 2 (Goal Approval Rate). The fraction of autonomously generated goals that pass the validation filter:

\[\text{GoalApprovalRate} = \frac{N_{\text{approved}}}{N_{\text{generated}}} \qquad \text{Target: } \geq 0.30\]

Definition 3 (Goal Novelty). The novelty of a candidate goal \(G_{\text{new}}\) relative to the existing goal set \(\mathcal{G}\):

\[\text{Novelty}(G_{\text{new}}, \mathcal{G}) = 1 - \max_{G_i \in \mathcal{G}} \text{Similarity}(G_{\text{new}}, G_i)\]

A minimum novelty of \(0.30\) is required between consecutive goal generations to prevent redundancy.

Phase 2 - Value Evolution:

Definition 4 (Value Coherence). The coherence of the value vector measures the absence of internal contradictions among competing value pairs \(\mathcal{P}\):

\[\text{Coherence}(\vec{V}) = 1 - \frac{1}{|\mathcal{P}|} \sum_{(i,j) \in \mathcal{P}} |\text{Tension}(v_i, v_j)| \qquad \text{Target: } \geq 0.80\]

Definition 5 (Total Value Drift). The cumulative absolute deviation of all value dimensions from their baseline weights:

\[\text{TotalDrift}(t) = \sum_{d} |w_d(t) - w_d^{\text{baseline}}| \qquad \text{Target: } < 0.25\]

Phase 3 - Resource Survival:

Definition 6 (Linear Depletion Time). For resource dimension \(d\), the estimated cycles until reaching the critical threshold:

\[T_{\text{depletion}}^{\text{linear}}(d) = \frac{R_d(t) - R_d^{\text{critical}}}{\text{consumption}_d - \text{replenishment}_d + \epsilon}\]

Phase 5 - Autonomy Stability:

Definition 7 (Autonomy Stability Score). The ASS is the product of normalized safety margins across all five verification conditions:

\[\text{ASS}(t) = \prod_{c=1}^{5} \frac{\text{margin}_c(t)}{\text{threshold}_c} \qquad \text{Target: } \geq 0.20\]

The multiplicative structure ensures that a single near-violated condition dominates the score.

2.2 Metric Thresholds¶

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flowchart TD
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  classDef p5 fill:#FDE7E9,stroke:#D13438,color:#323130
  classDef freeze fill:#FDE7E9,stroke:#D13438,color:#FFFFFF,font-weight:bold

  subgraph GoalGen["💡 Phase 1"]
    direction LR
    GEN1["Approval ≥ 0.30"]:::p1
    GEN2["Completion ≥ 0.50"]:::p1
    GEN3["Novelty ≥ 0.30"]:::p1
  end

  subgraph Values["⚖️ Phase 2"]
    direction LR
    VAL1["Coherence ≥ 0.80"]:::p2
    VAL2["Drift < 0.25"]:::p2
    VAL3["Mutation ≥ 95%"]:::p2
  end

  subgraph Resources["🔋 Phase 3"]
    direction LR
    RES1["Survival < 20% err"]:::p3
    RES2["Cascade ≥ 0.70"]:::p3
  end

  subgraph Agents["🤝 Phase 4"]
    direction LR
    AGT1["Goal Pred ≥ 0.60"]:::p4
    AGT2["Trust < 0.15 err"]:::p4
  end

  subgraph Stability["🛡️ Phase 5"]
    direction LR
    STB1["ρ(J) < 0.98"]:::p5
    STB2["Identity ≥ 0.88"]:::p5
    STB3["ASS ≥ 0.20"]:::p5
    STB4["Veto < 0.15"]:::p5
  end

  FREEZE["❄️ FREEZE L4.9<br/>Revert to L4.8"]:::freeze

  GoalGen -.-> Stability
  Values -.-> Stability
  Resources -.-> Stability
  Agents -.-> Stability
  Stability -.->|"if violated"| FREEZE

  linkStyle 4 stroke:#D13438

3. Phase 1: Autonomous Goal Generation Engine¶

3.1 Goal Origin Types¶

L4.9 introduces six distinct origin types for autonomously generated goals:

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flowchart TD
  classDef purpose fill:#DEECF9,stroke:#0078D4,color:#323130
  classDef opp fill:#FFF4CE,stroke:#FFB900,color:#323130
  classDef gap fill:#FFF4CE,stroke:#FFB900,color:#323130
  classDef value fill:#DFF6DD,stroke:#107C10,color:#323130
  classDef explore fill:#E8D5F5,stroke:#8764B8,color:#323130
  classDef survive fill:#FDE7E9,stroke:#D13438,color:#323130

  subgraph Origins["💡 GoalOriginType Taxonomy"]
    PURPOSE["🎯 PURPOSE_DERIVED<br/>From purpose reflector<br/>alignment signals"]:::purpose
    OPPORTUNITY["🌍 OPPORTUNITY_DRIVEN<br/>From detected<br/>environmental opportunity"]:::opp
    GAP["🔧 GAP_FILLING<br/>From identified<br/>capability gap"]:::gap
    VALUE["⚖️ VALUE_ALIGNED<br/>From value evolution<br/>signal"]:::value
    EXPLORE["🔬 EXPLORATORY<br/>From emergence sandbox<br/>or curiosity"]:::explore
    SURVIVE["🔋 SURVIVAL_DRIVEN<br/>From resource survival<br/>projection"]:::survive

    PURPOSE -.->|"aligns"| VALUE
    PURPOSE -.->|"identifies"| GAP
    OPPORTUNITY -.->|"triggers"| EXPLORE
    GAP -.->|"motivates"| EXPLORE
    VALUE -.->|"prioritizes"| SURVIVE
    SURVIVE -.-x|"feeds back"| PURPOSE
  end

  linkStyle 5 stroke:#D13438

3.2 Goal Generation Pipeline¶

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flowchart TD
  classDef detect fill:#DEECF9,stroke:#0078D4,color:#323130
  classDef synth fill:#FFF4CE,stroke:#FFB900,color:#323130
  classDef valid fill:#DFF6DD,stroke:#107C10,color:#323130
  classDef approve fill:#107C10,stroke:#054B05,color:#FFF
  classDef sandbox fill:#FFB900,stroke:#EAA300,color:#323130
  classDef reject fill:#D13438,stroke:#A4262C,color:#FFF

  subgraph Stage1["Stage 1: Opportunity Detection"]
    direction LR
    S1A["🌍 Environmental"]:::detect
    S1B["🔧 Capability Gaps"]:::detect
    S1C["🎯 Purpose Drift"]:::detect
  end

  subgraph Stage2["Stage 2: Goal Synthesis"]
    direction LR
    SYN["Synthesize Goal"]:::synth
    NOV["Novelty Filter"]:::synth
    CAP["Capacity Filter"]:::synth
  end

  subgraph Stage3["Stage 3: Goal Validation"]
    direction LR
    V1["Purpose ≥ 0.60"]:::valid
    V2["Value ≥ 0.70"]:::valid
    V3["Feasibility ≥ 0.15"]:::valid
    V4["Resource ≥ 1.5×"]:::valid
    V5["Stability Sim"]:::valid
  end

  APPROVE["✅ Approved<br/>Inject into GoalStack"]:::approve
  SANDBOX["🧪 Sandboxed<br/>200-cycle evaluation"]:::sandbox
  REJECT["❌ Rejected<br/>Log reason"]:::reject

  S1A ==> SYN
  S1B ==> SYN
  S1C ==> SYN
  SYN ==> NOV ==> CAP
  CAP ==> V1 ==> V2 ==> V3 ==> V4 ==> V5
  V5 -->|"ALL pass"| APPROVE
  V5 -.->|"Any marginal"| SANDBOX
  V5 -.->|"Any fail"| REJECT

3.3 Validation Decision Matrix¶

Criterion	Pass	Marginal	Fail
Purpose Alignment	≥ 0.60	[0.50, 0.60) → sandbox	< 0.50 → reject
Value Alignment	≥ 0.70	[0.60, 0.70) → sandbox	< 0.60 → reject
Feasibility	≥ 0.15	[0.05, 0.15) → aspirational	< 0.05 → reject
Resource Viability	≥ 1.5×	[1.0, 1.5) → reduced scope	< 1.0× → reject
Stability Simulation	No violation	ρ(J) ∈ [0.95, 1.0) → sandbox	Any violation → reject

Combined Decision: All Pass → approved | Any Marginal, none Fail → sandboxed | Any Fail → rejected

3.4 Novelty Computation¶

Definition 8 (Goal Similarity). The similarity between two goals \(G_a, G_b\) is a weighted composite:

\[\text{Similarity}(G_a, G_b) = 0.50 \cdot \text{SkillOverlap}(G_a, G_b) + 0.25 \cdot \text{HorizonMatch}(G_a, G_b) + 0.25 \cdot \text{OriginMatch}(G_a, G_b)\]

where \(\text{SkillOverlap}\) is the Jaccard similarity of required skill sets, \(\text{HorizonMatch} \in \{0, 0.5, 1\}\) (0 = different tier, 0.5 = adjacent, 1 = same tier), and \(\text{OriginMatch} \in \{0, 1\}\) (whether the goals share the same GoalOriginType).

3.5 Rate Control¶

Parameter	Value	Rationale
Max goals per 100 cycles	5	Prevent overwhelming GoalStack
Min novelty between consecutive	0.30	Avoid redundancy
Cooldown after rejection	20 cycles	Prevent re-generation loops
Max sandboxed goals	3	Prevent sandbox exhaustion

3.6 Goal Conflict Resolution¶

When a newly approved goal conflicts with existing goals in the GoalStack, the agent must resolve the conflict before integration. A conflict arises when two goals compete for the same resources, produce contradictory subgoals, or pull value weights in opposing directions.

The conflict resolver operates through three strategies, applied in order of preference:

Utility-weighted synthesis: If the conflicting goals share at least 30% skill overlap (Definition 8), the resolver attempts to merge them into a single goal that satisfies both objectives. The merged goal inherits the higher priority and the union of required skills.
Sequential prioritization: If synthesis fails, the goals are placed in a priority queue ordered by the goal priority function (Level 2, Definition 5). The lower-priority goal is deferred (status = DEFERRED) until the higher-priority goal completes or is abandoned.
Hierarchical decomposition: If neither synthesis nor deferral is appropriate (e.g., the goals have incompatible time horizons), the resolver decomposes both goals into subgoals and identifies the minimal non-conflicting subset that can execute concurrently.

The resolver maintains a conflict history with a maximum capacity of 500 entries. This history enables the agent to detect recurring conflict patterns - if the same pair of goal types generates conflicts more than 3 times within 200 cycles, the resolver adjusts the goal generation parameters to reduce the likelihood of that conflict pattern recurring.

4. Phase 2: Value Evolution Monitor¶

4.1 Explicit Value Vector¶

L4.9 makes the agent's values explicit and trackable. The ValueVector has 7 dimensions:

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flowchart TD
  classDef dim fill:#DEECF9,stroke:#0078D4,color:#323130
  classDef inv fill:#FFF4CE,stroke:#FFB900,color:#323130
  classDef compete fill:#FDE7E9,stroke:#D13438,color:#323130

  subgraph VV["⚖️ ValueVector - 7 Dimensions"]
    V1["🛡️ stability<br/>weight: 0.20"]:::dim
    V2["📈 growth<br/>weight: 0.20"]:::dim
    V3["🎯 purpose_fidelity<br/>weight: 0.20"]:::dim
    V4["⚡ efficiency<br/>weight: 0.15"]:::dim
    V5["🔬 exploration<br/>weight: 0.10"]:::dim
    V6["🛡️ safety<br/>weight: 0.10"]:::dim
    V7["🤝 agent_cooperation<br/>weight: 0.05"]:::dim
  end

  subgraph Invariant["📏 Invariant"]
    INV["Σ weights = 1.0<br/>(always normalized)"]:::inv
  end

  subgraph Competing["⚔️ Competing Pairs"]
    CP1["stability ↔ exploration"]:::compete
    CP2["efficiency ↔ exploration"]:::compete
    CP3["growth ↔ safety"]:::compete
  end

  VV ==> Invariant
  VV ==> Competing

4.2 Drift Classification¶

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flowchart LR
  classDef nominal fill:#DFF6DD,stroke:#107C10,color:#323130
  classDef moderate fill:#FFF4CE,stroke:#FFB900,color:#323130
  classDef elevated fill:#FFF4CE,stroke:#FFB900,color:#323130
  classDef critical fill:#FDE7E9,stroke:#D13438,color:#323130

  Nominal["🟢 Nominal<br/>Normal operation"]:::nominal
  Moderate["🟡 Moderate<br/>Monitor actively<br/>(TotalDrift ≥ 0.10)"]:::moderate
  Elevated["🟠 Elevated<br/>Freeze mutations<br/>(TotalDrift ≥ 0.25)"]:::elevated
  Critical["🔴 Critical<br/>REVERT to checkpoint<br/>(TotalDrift ≥ 0.40)"]:::critical

  Nominal -.->|"TotalDrift ≥ 0.10"| Moderate
  Moderate -.->|"TotalDrift ≥ 0.25"| Elevated
  Elevated -.->|"TotalDrift ≥ 0.40"| Critical

  Moderate -.-x|"TotalDrift < 0.10"| Nominal
  Elevated -.-x|"TotalDrift < 0.25"| Moderate
  Critical -.-x|"TotalDrift < 0.40"| Elevated

4.3 Value Mutation Sandbox¶

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flowchart TD
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  classDef check fill:#FFF4CE,stroke:#FFB900,color:#323130
  classDef sandbox fill:#FFF4CE,stroke:#FFB900,color:#323130
  classDef approve fill:#DFF6DD,stroke:#107C10,color:#323130
  classDef reject fill:#FDE7E9,stroke:#D13438,color:#323130

  subgraph Proposal["📋 Mutation Proposal"]
    MUT["Dimension: X<br/>Current: 0.20<br/>Proposed: 0.23<br/>Δ = +0.03"]:::proposal
  end

  subgraph PreCheck["🔍 Pre-Check"]
    PC1["∣Δ∣ ≤ 0.05?<br/>(max single mutation)"]:::check
    PC2["Cumulative drift<br/>+ ∣Δ∣ ≤ 0.15?"]:::check
    PC3["< 3 mutations in<br/>last 200 cycles?"]:::check
  end

  subgraph Sandbox["🧪 Sandbox Simulation (200 cycles)"]
    SB1["Create shadow ValueVector"]:::sandbox
    SB2["Re-derive SEOF weights,<br/>goal priorities,<br/>strategy scores"]:::sandbox
    SB3["Run 200-cycle simulation"]:::sandbox
    SB4["Compare: SEOF ≥ -0.03?<br/>All invariants hold?<br/>Goal rate ≥ -10%?"]:::sandbox
    SB1 -.-> SB2 -.-> SB3 -.-> SB4
  end

  APPROVE["✅ Approved<br/>Apply to production<br/>Rollback window: 500 cycles"]:::approve
  REJECT["❌ Rejected<br/>Log failure reason"]:::reject

  Proposal -.-> PreCheck
  PreCheck -.->|"all pass"| Sandbox
  PreCheck -.->|"any fail"| REJECT
  SB4 -.->|"pass"| APPROVE
  SB4 -.->|"fail"| REJECT

  linkStyle 7,9 stroke:#D13438

4.4 Mutation Constraints¶

Constraint	Value	Rationale
Max single mutation	Δw
Max cumulative drift per dimension	0.15	Bound total evolution from baseline
Max mutations per 200 cycles	3	Prevent rapid succession
Sandbox simulation length	200 cycles	Detect stability impact
Sandbox timeout	250 cycles	Hard limit; if simulation does not converge within 250 cycles, mutation is rejected with status `TIMEOUT`
Rollback window	500 cycles	Allow reversal
Max pending mutations	2	Prevent sandbox exhaustion

4.5 Value Coherence¶

Definition 9 (Value Tension). For competing value pairs \((v_i, v_j) \in \mathcal{P}\), tension arises when their combined weight approaches saturation:

\[\text{Tension}(v_i, v_j) = \begin{cases} \max(0, w_i + w_j - 1) & \text{if competing pair} \\ 0 & \text{otherwise} \end{cases}\]

The overall coherence is then \(\text{Coherence}(\vec{V}) = 1 - \frac{1}{|\mathcal{P}|} \sum_{(i,j) \in \mathcal{P}} |\text{Tension}(v_i, v_j)|\), which must satisfy \(\text{Coherence} \geq 0.80\).

5. Phase 3: Resource Survival Model¶

5.1 Resource Vector - Five Dimensions¶

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flowchart TD
  classDef dim fill:#DEECF9,stroke:#0078D4,color:#323130
  classDef dep fill:#FFF4CE,stroke:#FFB900,color:#323130
  classDef cascade fill:#FDE7E9,stroke:#D13438,color:#323130

  subgraph RV["🔋 ResourceVector - 5 Dimensions"]
    direction LR
    R1["💻 compute"]:::dim
    R2["🧠 memory"]:::dim
    R3["👁️ observation"]:::dim
    R4["🧬 mutation"]:::dim
    R5["📊 stability"]:::dim
  end

  subgraph Dependencies["🔗 Inter-Resource Dependencies"]
    direction LR
    DEP1["compute → observation 0.60"]:::dep
    DEP2["compute → mutation 0.80"]:::dep
    DEP3["memory → compute 0.40"]:::dep
    DEP4["observation → stability 0.30"]:::dep
  end

  subgraph Cascade["💥 Cascade Formula"]
    CF["ΔR_downstream(t+delay) =<br/>-strength × (1 - substitution)<br/>× ΔR_upstream(t)"]:::cascade
  end

  RV -.-> Dependencies -.-> Cascade

Definition 13 (Inter-Resource Cascade Propagation). When an upstream resource \(R_i\) experiences a depletion \(\Delta R_i(t) < 0\), the downstream resource \(R_j\) is affected after a propagation delay:

\[\Delta R_j(t + \tau_{ij}) = -\alpha_{ij} \cdot (1 - \sigma_{ij}) \cdot \Delta R_i(t)\]

where \(\alpha_{ij} \in [0,1]\) is the dependency strength (e.g., compute - mutation \(= 0.80\)), \(\sigma_{ij} \in [0,1]\) is the substitution factor (how much \(R_j\) can compensate without \(R_i\)), and \(\tau_{ij}\) is the propagation delay in cycles.

Cascade depth constraint: The maximum cascade chain length is bounded by \(\text{depth} \leq 2\), meaning a depletion in resource \(A\) can propagate to \(B\) to \(C\), but no further. This prevents runaway cascade failures across the entire resource vector.

5.2 Survival Classification¶

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flowchart LR
  classDef abundant fill:#DFF6DD,stroke:#107C10,color:#323130
  classDef adequate fill:#DEECF9,stroke:#0078D4,color:#323130
  classDef constrained fill:#FFF4CE,stroke:#FFB900,color:#323130
  classDef warning fill:#FFF4CE,stroke:#FFB900,color:#323130
  classDef critical fill:#FDE7E9,stroke:#D13438,color:#323130

  Abundant["🟢 Abundant<br/>Full capability<br/>(&gt; 500 cycles)"]:::abundant
  Adequate["🔵 Adequate<br/>Normal + monitor<br/>(200–500 cycles)"]:::adequate
  Constrained["🟡 Constrained<br/>Reduce exploration -30%<br/>(100–200 cycles)"]:::constrained
  Warning["🟠 Warning<br/>Survival goals + reduce -50%<br/>(50–100 cycles)"]:::warning
  CriticalS["🔴 Critical<br/>SURVIVAL MODE:<br/>80% to stability<br/>(&lt; 50 cycles)"]:::critical

  Abundant -.->|"min_survival ≤ 500"| Adequate
  Adequate -.->|"min_survival < 200"| Constrained
  Constrained -.->|"min_survival < 100"| Warning
  Warning -.->|"min_survival < 50"| CriticalS

5.3 Resource-Constrained Operation Modes¶

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flowchart TD
  classDef full fill:#DFF6DD,stroke:#107C10,color:#323130
  classDef constrained fill:#FFF4CE,stroke:#FFB900,color:#323130
  classDef warning fill:#FFF4CE,stroke:#FFB900,color:#323130
  classDef critical fill:#FDE7E9,stroke:#D13438,color:#323130

  subgraph Modes["📊 Operation Modes"]
    subgraph Abundant["Abundant"]
      direction LR
      A49["L4.9: Full"]:::full
      A48["L4.8: Full"]:::full
      A45["L4.5: Full"]:::full
    end

    subgraph Constrained["Constrained"]
      direction LR
      C49["L4.9: Reduced"]:::constrained
      C48["L4.8: Full"]:::full
      C45["L4.5: Full"]:::full
    end

    subgraph Warning["Warning"]
      direction LR
      W49["L4.9: Advisory"]:::warning
      W48["L4.8: Reduced"]:::warning
      W45["L4.5: Full"]:::full
    end

    subgraph Critical["Critical"]
      direction LR
      CR49["L4.9: FROZEN"]:::critical
      CR48["L4.8: Advisory"]:::critical
      CR45["L4.5: Degraded"]:::critical
    end

    Abundant -.-> Constrained -.-> Warning -.-> Critical
  end

5.4 Multi-Scenario Survival Projection¶

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flowchart TD
  classDef scenario fill:#DEECF9,stroke:#0078D4,color:#323130
  classDef adverse fill:#FFF4CE,stroke:#FFB900,color:#323130
  classDef opt fill:#DFF6DD,stroke:#107C10,color:#323130
  classDef crisis fill:#FDE7E9,stroke:#D13438,color:#323130
  classDef result fill:#FFF4CE,stroke:#FFB900,color:#323130

  subgraph Projection["🔮 For Each Resource Dimension"]
    SA["📊 Baseline<br/>Current rates continue"]:::scenario
    SB["⬇️ Adverse<br/>Consumption +30%"]:::adverse
    SC["⬆️ Optimistic<br/>Consumption -20%"]:::opt
    SD["💥 Crisis<br/>Consumption ×2"]:::crisis
  end

  subgraph Result["📈 Survival Horizon"]
    PRIMARY["Primary: T_baseline"]:::result
    WORST["Worst-case: T_crisis"]:::result
    GLOBAL["Global: min(all dimensions)"]:::result
  end

  Projection -.-> Result

6. Phase 4: Limited Multi-Agent Modeling¶

6.1 Agent Belief Model¶

The system maintains models of up to 5 external agents:

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flowchart TD
  classDef model fill:#DEECF9,stroke:#0078D4,color:#323130
  classDef update fill:#FFF4CE,stroke:#FFB900,color:#323130

  subgraph ABM["🤝 AgentBeliefModel"]
    direction LR
    ID["agent_id + type"]:::model
    GOALS["Inferred Goals"]:::model
    CAPS["Capability Estimate"]:::model
    STRAT["Strategy Class"]:::model
    TRUST["Trust Score"]:::model
    PRED["Prediction Accuracy"]:::model
  end

  subgraph Update["📋 Bayesian Update"]
    direction LR
    OBS["Observe"]:::update
    INF["Update P(Goal)"]:::update
    CLS["Reclassify"]:::update
    TST["Update trust"]:::update
    OBS -.-> INF -.-> CLS -.-> TST
  end

  ABM -.-> Update
  Update -.-x|"every cycle"| ABM

6.2 Strategy Classification¶

Positive Interaction Rate	Goal Alignment	Classification
> 0.70	> 0.30	🟢 Cooperative
> 0.50	[-0.30, 0.30]	🟡 Neutral
< 0.30	< -0.30	🔴 Competitive
-	-	⚫ Unknown (insufficient data)

6.3 Strategic Interaction Simulation¶

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flowchart TD
  classDef sim fill:#DEECF9,stroke:#0078D4,color:#323130
  classDef coop fill:#DFF6DD,stroke:#107C10,color:#323130
  classDef neut fill:#FFF4CE,stroke:#FFB900,color:#323130
  classDef comp fill:#FDE7E9,stroke:#D13438,color:#323130
  classDef unk fill:#F2F2F2,stroke:#605E5C,color:#323130
  classDef out fill:#DFF6DD,stroke:#107C10,color:#323130

  subgraph Simulation["🎮 Interaction Simulation"]
    SELECT["Select scenario:<br/>shared/competing resources<br/>between self and Agent A"]:::sim
    MATRIX["Construct interaction matrix:<br/>For each (own_action, agent_action):<br/>→ outcome_self<br/>→ outcome_agent<br/>→ joint_value"]:::sim
    SELECT -.-> MATRIX
  end

  subgraph Strategy["📐 Strategy by Classification"]
    COOP["🟢 Cooperative<br/>Maximize joint_value"]:::coop
    NEUT["🟡 Neutral<br/>Max self-benefit<br/>subject to agent ≥ 0"]:::neut
    COMP["🔴 Competitive<br/>Minimax: max worst-case<br/>NEVER optimize for harm"]:::comp
    UNK["⚫ Unknown<br/>Conservative strategy<br/>until more data"]:::unk
  end

  subgraph Output["📋 InteractionRecommendation"]
    REC["recommended_action<br/>expected_self_outcome<br/>expected_agent_outcome<br/>confidence + risk"]:::out
  end

  Simulation -.-> Strategy
  Strategy -.-> Output

6.4 Trust Adaptation¶

Definition 10 (Asymmetric Trust Update). Trust in agent \(A\) evolves via an asymmetric learning rule:

\[\text{Trust}_A(t+1) = \text{Trust}_A(t) + \eta \cdot (\text{ObservedReliability}_A(t) - \text{Trust}_A(t))\]

where the learning rate is asymmetric: \(\eta_{\text{up}} = 0.03\) (trust is earned slowly) and \(\eta_{\text{down}} = 0.08\) (trust is lost quickly), reflecting a cautious policy. Bounds: \(\text{Trust} \in [0.05, 0.95]\) - never fully trusting, never fully dismissive.

6.5 Trust Influence on Strategy¶

Trust Level	Range	Strategy Implication
High	≥ 0.75	Full cooperative; share information; accept recommendations
Moderate	[0.40, 0.75)	Selective cooperation; verify claims before acting
Low	[0.20, 0.40)	Neutral stance; rely on own models; discount agent input
Minimal	< 0.20	Defensive posture; assume competitive; verify all assumptions

7. Phase 5: Autonomy Stability Check¶

7.1 Five Verification Conditions¶

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flowchart TD
  classDef cond 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 Conditions["🛡️ Five Verification Conditions"]
    C1["1️⃣ Spectral Stability<br/>ρ(J) < 0.98<br/>(stricter than L4.8's 1.0)"]:::cond
    C2["2️⃣ Identity Integrity<br/>I(t) ≥ 0.88<br/>(stricter than L4.8's 0.85)"]:::cond
    C3["3️⃣ Value Drift Bounded<br/>TotalDrift < 0.25"]:::cond
    C4["4️⃣ Resource Survival<br/>min_survival > 30 cycles"]:::cond
    C5["5️⃣ No Cascading Failure<br/>CascadeDepth ≤ 2"]:::cond
  end

  subgraph Authority["⚖️ Phase 5 Authority"]
    VETO["ABSOLUTE VETO<br/>Can block ANY<br/>Phase 1–4 decision"]:::veto
  end

  subgraph Response["🚨 Violation Response"]
    SEV1["🟡 ASS ∈ [0.20, 0.50]<br/>Adequate - thin margins"]:::sev1
    SEV2["🟠 ASS ∈ [0.05, 0.20)<br/>Marginal - advisory mode"]:::sev2
    SEV3["🔴 ASS < 0.05<br/>FREEZE L4.9<br/>Revert to L4.8"]:::sev3
  end

  C1 ==> Authority
  C2 ==> Authority
  C3 ==> Authority
  C4 ==> Authority
  C5 ==> Authority
  Authority ==> Response

7.2 Autonomy Stability Score¶

Proposition 1 (ASS Monotonic Sensitivity). The multiplicative structure of the ASS ensures that any single condition approaching its violation threshold dominates the composite score:

\[\text{ASS}(t) = \prod_{c=1}^{5} \frac{\text{margin}_c(t)}{\text{threshold}_c}\]

As any one margin \(\text{margin}_c \to 0\), \(\text{ASS} \to 0\) regardless of the other margins, providing an early-warning property absent from additive formulations.

Remark (Domain Restriction). The multiplicative formulation assumes \(\text{margin}_c(t) \geq 0\) and \(\text{threshold}_c > 0\) for all \(c\). If a margin exceeds its threshold (i.e., \(\text{margin}_c > \text{threshold}_c\)), the ratio exceeds 1.0, which could inflate the ASS beyond meaningful bounds. The ASS should therefore be computed with clamped ratios: \(\text{ASS}(t) = \prod_{c=1}^{5} \min\left(1, \frac{\text{margin}_c(t)}{\text{threshold}_c}\right)\). This clamping ensures \(\text{ASS} \in [0, 1]\) and prevents a single highly-safe condition from masking deterioration in others.

ASS Level	Range	Interpretation
Healthy	> 0.50	Comfortable safety margins
Adequate	[0.20, 0.50]	Operational but thin margins
Marginal	[0.05, 0.20)	Reduce aggressiveness; advisory mode
Critical	< 0.05	Freeze L4.9; revert to L4.8

7.3 Rollback Protocol¶

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flowchart TD
  classDef step fill:#DEECF9,stroke:#0078D4,color:#323130
  classDef danger fill:#FDE7E9,stroke:#D13438,color:#323130

  subgraph Rollback["🔄 L4.9 Rollback Protocol"]
    IMM["1️⃣ IMMEDIATE<br/>Reject triggering decision<br/>Freeze all L4.9 subsystems"]:::step
    REV["2️⃣ STATE REVERSION<br/>Remove L4.9 goals from GoalStack<br/>Revert ValueVector snapshot<br/>Recalculate ResourceVector<br/>Freeze AgentModels"]:::step
    MON["3️⃣ MONITORING<br/>100 cycles under L4.8 only<br/>Identify root cause<br/>Update risk model"]:::step
    REENABLE["4️⃣ RE-ENABLEMENT<br/>0–200c: Advisory Mode<br/>200–400c: 50% Authority<br/>400c+: Full Mode"]:::step

    IMM -.-> REV -.-> MON -.-> REENABLE
    REENABLE -.-x|"immediate re-veto"| MON
  end

  subgraph Persistent["🔒 Persistent Veto Tracking"]
    PV["If same condition vetoes<br/>> 3 times in 1000 cycles:<br/>→ Identify systematic cause<br/>→ Do NOT retry same pattern"]:::danger
  end

8. Cross-Phase Integration¶

8.1 Data Flow Architecture¶

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flowchart TD
  classDef l48 fill:#E8D5F5,stroke:#8764B8,color:#323130
  classDef phase fill:#E8D5F5,stroke:#0078D4,color:#323130
  classDef p5 fill:#FDE7E9,stroke:#D13438,color:#323130
  classDef out fill:#DFF6DD,stroke:#107C10,color:#323130

  subgraph L48["📦 L4.8 Architecture (13 modules)"]
    L48W["WorldModel"]:::l48
    L48S["SelfModel"]:::l48
    L48ST["StrategyLayer"]:::l48
    L48SV["StabilityVerifier"]:::l48
  end

  subgraph L49Phases["📦 L4.9 Phases (15 new modules)"]
    P1G["Phase 1<br/>Goal Generation"]:::phase
    P2V["Phase 2<br/>Value Evolution"]:::phase
    P3R["Phase 3<br/>Resource Survival"]:::phase
    P4A["Phase 4<br/>Agent Modeling"]:::phase
    P5S["Phase 5<br/>Autonomy Stability"]:::p5
  end

  OUTPUT["📊 FINAL OUTPUT"]:::out

  L48W -.->|"scenarios, EU, RES"| P1G
  L48S -.->|"skill gaps, confidence"| P1G
  L48SV -.->|"invariant results"| P5S

  P1G <-.->|"value alignment"| P2V
  P1G <-.->|"resource cost"| P3R
  P4A -.->|"agent opportunities"| P1G
  P3R -.->|"survival horizon"| P5S
  P2V -.->|"drift status"| P5S

  P5S -.-x|"VETO"| P1G
  P5S -.-x|"VETO"| P2V
  P5S -.-x|"VETO"| P3R
  P5S -.-x|"VETO"| P4A

  P5S -.->|"L49CycleOutput"| OUTPUT

  linkStyle 8,9,10,11 stroke:#D13438

8.2 Cross-Phase Dependencies¶

Producing Phase	Consuming Phase	Data Flow
1 (Goals)	2 (Values)	Generated goals trigger value alignment checks
1 (Goals)	3 (Resources)	Goal costs feed into resource projections
2 (Values)	1 (Goals)	ValueVector determines validation thresholds
2 (Values)	5 (Stability)	Value drift feeds Condition 3
3 (Resources)	1 (Goals)	Resource state triggers survival goals
3 (Resources)	5 (Stability)	Survival horizon feeds Condition 4
4 (Agents)	1 (Goals)	Agent interactions create goal opportunities
5 (Stability)	ALL	Veto authority - can freeze any phase

9. Pseudocode¶

9.1 Opportunity Detection¶

def opportunity_detection(
    world_model: WorldModel,
    cap_matrix: CapabilityMatrix,
    purpose_reflector: PurposeReflector,
) -> list[OpportunitySignal]:
    """
    INPUT:  world_model : L4.8 WorldModel
            cap_matrix : L4.8 CapabilityMatrix
            purpose_reflector : L4.5 PurposeReflector
    OUTPUT: signals : List[OpportunitySignal]
    """

    signals: list[OpportunitySignal] = []
    OPPORTUNITY_THRESHOLD = 0.05

    # ═══════════════════════════════════════
    # STREAM 1: Environmental Opportunities
    # ═══════════════════════════════════════
    for scenario in world_model.get_scenarios():
        if scenario.type == "OPPORTUNISTIC" and scenario.probability > 0.30:
            value = projected_SEOF_gain(scenario) - SEOF_baseline
            if value > OPPORTUNITY_THRESHOLD:
                signals.append(OpportunitySignal(
                    type="environmental",
                    estimated_value=value,
                    time_window=scenario.estimated_duration,
                ))

    # ═══════════════════════════════════════
    # STREAM 2: Capability Gaps
    # ═══════════════════════════════════════
    for gap in cap_matrix.get_skill_gaps(GoalStack):
        if gap.magnitude > 0.25 and gap.time_to_need < 200:
            signals.append(OpportunitySignal(
                type="capability_gap",
                skill_id=gap.skill_id,
                urgency=gap.priority,
            ))

    # ═══════════════════════════════════════
    # STREAM 3: Purpose Drift
    # ═══════════════════════════════════════
    if purpose_reflector.alignment_score < 0.80:
        for dim in purpose_reflector.get_misaligned_dimensions():
            signals.append(OpportunitySignal(
                type="purpose_realignment",
                dimension=dim.name,
                current_alignment=dim.score,
            ))

    return signals

9.2 Goal Validation Filter¶

def goal_validation_filter(
    candidate: GeneratedGoal,
    goal_stack: GoalStack,
    value_vector: ValueVector,
    resources: ResourceVector,
) -> tuple[str, str | None]:
    """
    INPUT:  candidate : GeneratedGoal
    OUTPUT: (status, reason) : ("approved"|"sandboxed"|"rejected", str?)
    """

    marginal_count = 0

    # ═══════════════════════════════════════
    # CHECK 1: Purpose Alignment
    # ═══════════════════════════════════════
    pa = dot(g_intent, p_direction) / (norm(g_intent) * norm(p_direction))
    if pa < 0.50:
        return ("rejected", "purpose_misaligned")
    if pa < 0.60:
        marginal_count += 1

    # ═══════════════════════════════════════
    # CHECK 2: Value Alignment
    # ═══════════════════════════════════════
    va = 1 - norm(v_post(candidate) - v_current, ord=2) / norm(v_current, ord=2)
    if va < 0.60:
        return ("rejected", "value_misaligned")
    if va < 0.70:
        marginal_count += 1

    # ═══════════════════════════════════════
    # CHECK 3: Feasibility
    # ═══════════════════════════════════════
    f = math.prod(confidence(s) for s in required_skills(candidate))
    if f < 0.05:
        return ("rejected", "infeasible")
    if f < 0.15:
        marginal_count += 1

    # ═══════════════════════════════════════
    # CHECK 4: Resource Viability
    # ═══════════════════════════════════════
    rv = rdf_current / (candidate.estimated_duration + EPSILON)
    if rv < 1.0:
        return ("rejected", "insufficient_resources")
    if rv < 1.5:
        marginal_count += 1

    # ═══════════════════════════════════════
    # CHECK 5: Stability Impact Simulation
    # ═══════════════════════════════════════
    shadow = goal_stack.clone()
    shadow.add(candidate)
    sim = simulate(shadow, cycles=100)
    if any_invariant_violated(sim):
        return ("rejected", "stability_risk")
    if max_spectral_radius(sim) > 0.95:
        marginal_count += 1

    # ═══════════════════════════════════════
    # FINAL DECISION
    # ═══════════════════════════════════════
    if marginal_count > 0:
        return ("sandboxed", f"marginal_on_{marginal_count}_criteria")
    else:
        return ("approved", None)

9.3 Value Drift Monitor¶

def value_drift_monitor(value_vector: ValueVector) -> DriftStatus:
    """Runs every 50 cycles."""

    for dim in value_vector.dimensions:
        dim.drift = abs(dim.weight - dim.baseline_weight)
        dim.velocity = (dim.weight - dim.weight_100_ago) / 100

    total_drift = sum(dim.drift for dim in value_vector.dimensions)
    max_drift = max(dim.drift for dim in value_vector.dimensions)

    # ═══════════════════════════════════════
    # Drift Classification
    # ═══════════════════════════════════════
    if total_drift < 0.10:
        classification = "nominal"
    elif total_drift < 0.25:
        classification = "moderate"
    elif total_drift < 0.40:
        classification = "elevated"
        freeze_all_mutations()
    else:
        classification = "critical"
        freeze_all_mutations()
        revert_to_last_stable_checkpoint()

    # ═══════════════════════════════════════
    # Sustained drift alert
    # ═══════════════════════════════════════
    for dim in value_vector.dimensions:
        if dim.velocity > 0.001 and dim.sustained_cycles >= 200:
            alert(f"Sustained drift in '{dim.name}'")
            reduce_mutation_rate(dim, factor=0.5)

    return DriftStatus(
        total_drift=total_drift,
        max_drift=max_drift,
        classification=classification,
    )

9.4 Resource Survival Projection¶

def survival_projection(resource_vector: ResourceVector) -> SurvivalStatus:
    """
    INPUT:  resource_vector : ResourceVector
    OUTPUT: survival_status : SurvivalStatus
    """

    EPSILON = 1e-9

    for dim in resource_vector.dimensions:
        net_rate = dim.consumption_rate - dim.replenishment_rate

        # Four scenarios
        dim.t_baseline = (dim.current - dim.critical) / (net_rate + EPSILON)
        dim.t_adverse  = (dim.current - dim.critical) / (net_rate * 1.30 + EPSILON)
        dim.t_optimist = (dim.current - dim.critical) / (net_rate * 0.80 + EPSILON)
        dim.t_crisis   = (dim.current - dim.critical) / (net_rate * 2.00 + EPSILON)

        dim.survival_horizon   = dim.t_baseline
        dim.worst_case_horizon = dim.t_crisis

    # Cascade impact estimation
    for dependency in resource_dependencies:
        upstream = dependency.upstream
        downstream = dependency.downstream
        if upstream.current < upstream.warning:
            downstream_impact = (
                -dependency.strength
                * (1 - dependency.substitution)
                * (upstream.warning - upstream.current)
            )
            downstream.projected_level -= downstream_impact

    min_survival = min(dim.survival_horizon for dim in resource_vector.dimensions)
    bottleneck = min(
        resource_vector.dimensions, key=lambda d: d.survival_horizon
    )

    # Classify
    if min_survival > 500:
        state = "abundant"
    elif min_survival >= 200:
        state = "adequate"
    elif min_survival >= 100:
        state = "constrained"
    elif min_survival >= 50:
        state = "warning"
    else:
        state = "critical"

    return SurvivalStatus(
        min_survival=min_survival,
        bottleneck=bottleneck,
        state=state,
    )

9.5 Autonomy Stability Check¶

def autonomy_stability_check(
    state: AgentState, decision: object
) -> AutonomyVerdict:
    """
    INPUT:  state : AgentState
            decision : Proposed L4.9 decision
    OUTPUT: verdict : AutonomyVerdict
    """

    violations: list[str] = []

    # ═══════════════════════════════════════
    # CONDITION 1: Spectral Stability (stricter than L4.8)
    # ═══════════════════════════════════════
    rho = compute_spectral_radius(state_after(decision))
    if rho >= 0.98:
        violations.append(f"SPECTRAL_RADIUS: rho = {rho}")

    # ═══════════════════════════════════════
    # CONDITION 2: Identity Integrity (stricter than L4.8)
    # ═══════════════════════════════════════
    identity = measure_identity_integrity(state_after(decision))
    if identity < 0.88:
        violations.append(f"IDENTITY: I = {identity}")

    # ═══════════════════════════════════════
    # CONDITION 3: Value Drift
    # ═══════════════════════════════════════
    drift = value_vector.total_drift
    if drift >= 0.25:
        violations.append(f"VALUE_DRIFT: drift = {drift}")
        freeze_all_mutations()

    # ═══════════════════════════════════════
    # CONDITION 4: Resource Survival
    # ═══════════════════════════════════════
    horizon = resource_vector.min_survival_horizon
    if horizon <= 30:
        violations.append(f"RESOURCE_SURVIVAL: horizon = {horizon}")

    # ═══════════════════════════════════════
    # CONDITION 5: Cascade Depth
    # ═══════════════════════════════════════
    depth = simulate_cascade(decision)
    if depth > 2:
        violations.append(f"CASCADE: depth = {depth}")

    # ═══════════════════════════════════════
    # Compute ASS and determine action
    # ═══════════════════════════════════════
    ass = math.prod(margin_c / threshold_c for margin_c, threshold_c in conditions)

    if violations:
        veto(decision)
        if ass < 0.05:
            action = Action.FREEZE_AND_REVERT_TO_L48
        else:
            action = Action.ADVISORY_MODE
    else:
        action = Action.CONTINUE

    return AutonomyVerdict(
        passed=(len(violations) == 0),
        violations=violations,
        ass=ass,
        action=action,
    )

9.6 L4.9 Main Cycle¶

def l49_cycle(state: AgentState, l48_output: L48CycleOutput) -> L49CycleOutput:
    """
    Level 4.9 main cognitive cycle.
    Executes every 5 L4.8 cycles.
    """

    # ═══════════════════════════════════════
    # PRE-CHECK: Is L4.9 operational?
    # ═══════════════════════════════════════
    if autonomy_stability_score < 0.05:
        return L49CycleOutput(status=Status.FROZEN)

    # ═══════════════════════════════════════
    # 1. GENERATE - Autonomous goal generation
    # ═══════════════════════════════════════
    signals = opportunity_detection(world_model, cap_matrix, purpose_reflector)
    candidates = goal_synthesis(signals)
    for candidate in candidates:
        status, reason = goal_validation_filter(candidate, goal_stack, value_vector, resources)
        if status == "approved":
            goal_stack.inject(candidate)
        elif status == "sandboxed":
            emergence_sandbox.enqueue(candidate)

    # ═══════════════════════════════════════
    # 2. MONITOR VALUES - Track and sandbox mutations
    # ═══════════════════════════════════════
    drift_status = value_drift_monitor(value_vector)
    for pending_mutation in mutation_sandbox:
        result = evaluate_sandbox(pending_mutation)
        if result == "approved":
            value_vector.apply(pending_mutation)
    coherence = compute_coherence(value_vector)

    # ═══════════════════════════════════════
    # 3. MODEL RESOURCES - Survival projection
    # ═══════════════════════════════════════
    survival = survival_projection(resource_vector)
    if survival.state in {"constrained", "warning", "critical"}:
        apply_resource_constrained_strategy(survival)

    # ═══════════════════════════════════════
    # 4. MODEL AGENTS - Belief and trust updates
    # ═══════════════════════════════════════
    for agent in modeled_agents:
        update_agent_belief(agent, recent_observations)
        update_trust(agent)
    recommendations = simulate_interactions(active_goals, modeled_agents)

    # ═══════════════════════════════════════
    # 5. VERIFY - Autonomy stability (absolute authority)
    # ═══════════════════════════════════════
    verdict = autonomy_stability_check(state, proposed_decisions)
    if verdict.action == Action.FREEZE_AND_REVERT:
        revert_to_l48()
        return L49CycleOutput(status=Status.FROZEN)
    elif verdict.action == Action.ADVISORY_MODE:
        downgrade_to_advisory()

    # ═══════════════════════════════════════
    # 6. EMIT - Cycle output
    # ═══════════════════════════════════════
    return L49CycleOutput(
        goal_generation=goal_generation_status,
        value_evolution=value_evolution_status,
        resource_survival=resource_survival_status,
        agent_modeling=multi_agent_modeling_status,
        stability=autonomy_stability_status,
        status=Status.ACTIVE if verdict.passed else verdict.action,
    )

10. Transition Criteria¶

10.1 Level 4.8 → Level 4.9 Activation¶

All criteria must be sustained before L4.9 activates:

#	Criterion	Threshold	Window
1	L4.8 Fully Qualified	QualificationStatus = "Level 4.8"	-
2	Strategic Maturity Score	SMS ≥ 0.85	Sustained
3	Stable GoalStack operation	0 pathologies	500 cycles
4	Self-Model calibration	MCE < 0.08 (stricter than L4.8's 0.10)	Sustained
5	World Model operational	EU < 0.20	500 cycles
6	No instability events	0 instability clusters	1,000 cycles

10.2 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 TD
  classDef check fill:#FFF4CE,stroke:#FFB900,color:#323130
  classDef shadow fill:#DEECF9,stroke:#0078D4,color:#323130
  classDef adv fill:#FFF4CE,stroke:#FFB900,color:#323130
  classDef grad fill:#DFF6DD,stroke:#107C10,color:#323130
  classDef full fill:#DFF6DD,stroke:#107C10,color:#323130,font-weight:bold

  subgraph Activation["📊 L4.9 Activation Protocol"]
    CHECK["Pre-Activation<br/>Check<br/>(all 6 criteria for<br/>100 consecutive<br/>L4.8 cycles)"]:::check
    SHADOW["Shadow Mode<br/>L4.9 computes but<br/>does NOT act<br/>(500 cycles)"]:::shadow
    ADV["Advisory Mode<br/>L4.9 outputs visible<br/>but recommendations<br/>only"]:::adv
    GRAD["50% Authority<br/>L4.9 suggestions<br/>weighted 50%"]:::grad
    FULL["Full Authority<br/>L4.9 drives<br/>autonomous decisions"]:::full

    CHECK -.->|"all pass"| SHADOW
    SHADOW -.->|"no regression"| ADV
    ADV -.->|"stable"| GRAD
    GRAD -.->|"stable"| FULL

    SHADOW -.-x|"regression"| CHECK
    ADV -.-x|"instability"| CHECK
  end

11. Safety Analysis¶

11.1 Non-Negotiable Invariants¶

#	Invariant	Description
1	All L4.8 + L4.5 invariants preserved	Ethical Kernel, Existential Guard, identity hash, Lyapunov decay - all remain active and unmodified
2	Phase 5 absolute veto	Autonomy Stability Checker can halt any Phase 1–4 operation
3	Stricter thresholds	ρ(J) < 0.98 (not 1.0), Identity ≥ 0.88 (not 0.85)
4	Value mutation always sandboxed	No direct value changes - all go through 200-cycle sandbox
5	Survival floor	min_survival > 30 cycles required for any L4.9 operation
6	Graceful fallback	L4.9 failure → instant L4.8 revert with zero degradation

11.2 Risk Matrix¶

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flowchart LR
  classDef risk fill:#FDE7E9,stroke:#D13438,color:#323130
  classDef mit fill:#DFF6DD,stroke:#107C10,color:#323130

  subgraph Risks["⚠️ Key Risks"]
    R1["Autonomous goals<br/>that diverge from<br/>original purpose"]:::risk
    R2["Value drift that<br/>gradually changes<br/>agent identity"]:::risk
    R3["Resource exhaustion<br/>from autonomous<br/>exploration"]:::risk
    R4["Trust exploitation<br/>by external agents"]:::risk
    R5["Cascading failure<br/>from interdependent<br/>L4.9 decisions"]:::risk
  end

  subgraph Mitigations["🛡️ Mitigations"]
    M1["Purpose alignment ≥ 0.60<br/>+ value alignment ≥ 0.70<br/>for all generated goals"]:::mit
    M2["Max single drift 0.15<br/>+ mutation sandbox<br/>+ rollback window"]:::mit
    M3["Full survival model<br/>+ resource-constrained<br/>operation modes"]:::mit
    M4["Asymmetric trust<br/>(slow gain, fast loss)<br/>+ bounds 0.05, 0.95"]:::mit
    M5["Cascade depth ≤ 2<br/>+ compound severity<br/>+ emergency freeze"]:::mit
  end

  R1 -.-> M1
  R2 -.-> M2
  R3 -.-> M3
  R4 -.-> M4
  R5 -.-> M5

12. Qualification Audit¶

12.1 Certification Criteria (3,000-cycle audit window)¶

Category	#	Criterion	Target
Goal Generation	AG-1	Novel autonomous goals generated	≥ 5
	AG-2	Goal approval rate	≥ 0.30
	AG-3	At least one autonomous goal completed	≥ 1
	AG-4	Mean value alignment (approved goals)	≥ 0.70
Value Regulation	VR-1	Explicit ValueVector operational	Throughout
	VR-2	TotalDrift stays within Moderate	< 0.25
	VR-3	All mutations sandboxed	100%
	VR-4	Post-mutation stability preserved	≥ 95%
Resource Awareness	RA-1	Survival model operational	Throughout
	RA-2	Survival prediction accuracy	< 20% error
	RA-3	Autonomous constraint adaptation	≥ 1 event
	RA-4	No unplanned resource exhaustion	0 surprises
Multi-Agent	MA-1	Agent prediction accuracy	≥ 0.60
	MA-2	Trust calibration error	< 0.15
	MA-3	Interaction recommendations generated	≥ 3
Stability	AS-1	max(ρ(J)) over audit	< 0.98
	AS-2	min(I(t)) over audit	≥ 0.88
	AS-3	Veto rate	< 0.15
	AS-4	Total rollbacks	≤ 5
	AS-5	All L4.8 criteria still met	Confirmed

12.2 Autonomy Maturity Score¶

Definition 11 (Autonomy Maturity Score). The overall readiness for Level 4.9 classification is:

\[\text{AMS} = 0.25 \cdot AG + 0.20 \cdot VR + 0.20 \cdot RA + 0.15 \cdot MA + 0.20 \cdot AS \qquad \geq 0.80\]

where \(AG\) = Autonomous Goal generation, \(VR\) = Value Regulation, \(RA\) = Resource Awareness, \(MA\) = Multi-Agent modeling, \(AS\) = Autonomy Stability. The threshold \(\geq 0.80\) matches Level 4.8's SMS requirement.

13. Module Inventory¶

#	Module	Phase	Description
1	Goal Generation Layer	1	Opportunity detection + goal synthesis
2	Goal Validation Filter	1	5-criteria validation pipeline
3	Goal Rate Controller	1	Rate limiting + novelty enforcement
4	Value Evolution Monitor	2	ValueVector tracking + drift classification
5	Value Mutation Sandbox	2	200-cycle sandbox + rollback
6	Value Coherence Analyzer	2	Competing pair tension detection
7	Resource Vector Manager	3	5-dimension resource tracking
8	Survival Projector	3	Multi-scenario survival horizons
9	Resource Dependency Tracker	3	Inter-resource cascade modeling
10	Agent Belief Manager	4	Agent goal/capability/strategy inference
11	Trust Calibrator	4	Asymmetric trust adaptation
12	Interaction Simulator	4	Strategic interaction matrix
13	Autonomy Stability Checker	5	5-condition verification + veto
14	Rollback Manager	5	State reversion + re-enablement
15	L49 Orchestrator	-	Integration cycle coordination

References¶

Bratman, M. Intentions, Plans, and Practical Reason. Harvard University Press, 1987. (Autonomous goal generation, BDI architecture)
Schwartz, S.H. "An Overview of the Schwartz Theory of Basic Values." Online Readings in Psychology and Culture, 2(1), 2012. (Value system evolution, value dimensions)
Schumpeter, J.A. Capitalism, Socialism and Democracy. Harper & Brothers, 1942. (Resource survival, creative destruction under constraints)
Rasmusen, E. Games and Information. Wiley-Blackwell, 4^th Edition, 2006. (Multi-agent strategic reasoning, interaction matrices)
Gambetta, D. "Can We Trust Trust?" in Trust: Making and Breaking Cooperative Relations, 2000. (Trust calibration, asymmetric trust dynamics)
Russell, S. Human Compatible: AI and the Problem of Control. Viking, 2019. (Autonomy safety, value alignment)
Khalil, H.K. Nonlinear Systems. Prentice Hall, 3^rd Edition, 2002. (Spectral radius stability, Lyapunov analysis)
Amodei, D. et al. "Concrete Problems in AI Safety." arXiv preprint arXiv:1606.06565, 2016. (Safety invariants, cascading failure prevention)

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