MSCP Comprehensive Glossary¶
Revision History¶
| Version | Date | Description |
|---|---|---|
| 0.1.0 | 2025-06-20 | Initial document creation |
| 0.2.0 | 2025-06-20 | First verification pass - fixed 42 issues (8 content errors, 34 KaTeX) |
| 0.3.0 | 2025-06-20 | Second verification pass - fixed BGSS weights/term, CDSRR/SNI names, Deception Detection source, acronym count |
| 0.4.0 | 2026-06-14 | Third verification pass - added L4.5 Def 13 (Uncertainty Index) and Def 14 (Recursive Optimization Depth); added L4.9 Def 13 (Inter-Resource Cascade Propagation); added L5 Def 11 (Reconstruction Fidelity); added VEM and RSM acronyms; disambiguated AS and EU dual-use entries; added §5 Notation Cautions; updated statistics |
| 0.5.0 | 2026-06-14 | Added three Named Architectural Concepts from Overview §4.4: AGI Engine (orchestrator pattern), PLA (Progressive Language Autonomy, six-stage), LangNet (language-mediated strategy network). New acronym PLA. |
| 0.6.0 | 2026-06-14 | Added cross-reference to the standalone PLA Foundations document (specs/Why_LLM_Free_PLA.md) which formalises the LLM-free authority argument, defines the Language Autonomy Gap (LAG), and catalogues LLM-free synthesis patterns. New acronym LAG. |
Sorted by source document (Overview → L1 → L2 → L3 → L4 → L4.5 → L4.8 → L4.9 → L5), then alphabetically within each section.
Table of Contents¶
- Formal Definitions by Document
- Propositions and Theorems
- Acronyms and Abbreviations
- Mathematical Symbols
- Key Technical Terms (Non-Definition)
1. Formal Definitions by Document¶
MSCP Overview (MSCP_Overview.md)¶
| # | Term | Symbol / Acronym | Def # | Description |
|---|---|---|---|---|
| 1 | Bounded Growth Stability Score | BGSS | 8 | Quantifies stability under capability expansion: \(BGSS = 1.0 - \alpha \cdot \frac{dC(t)}{dt} - \beta \cdot V_{\text{identity}}(t) - \gamma \cdot R_{\text{violation}}(t)\). Threshold \(\geq 0.7\). |
| 2 | Composite Stability Function | \(C(t)\) | 3 | Aggregates four volatility signals: \(C(t) = w_1 V_{\text{identity}} + w_2 H_{\text{belief}} + w_3 F_{\text{goal}} + w_4 V_{\text{consistency}}\). Weights: 0.30, 0.25, 0.25, 0.20. |
| 3 | Cross-Domain Transfer Score | CDTS | 5 | Measures generalization to novel domains: \(CDTS = \frac{1}{\lvert D_{\text{novel}}\rvert}\sum_{d} \frac{P_{\text{transfer}}(d)}{P_{\text{baseline}}(d)}\). Threshold \(\geq 0.6\). |
| 4 | Goal Persistence Index | GPI | 6 | Sustained progress toward long-horizon goals: \(GPI = \frac{\sum w_g \cdot \text{progress}(g,T)}{\lvert G_{\text{long}}\rvert \cdot T}\). Threshold \(\geq 0.3\). |
| 5 | Identity Kinematics | \(\delta_{\text{id}}, v_{\text{id}}, a_{\text{id}}\) | 2 | Identity delta (distance), velocity (rate of change), and acceleration (jerk) tracking the motion of \(I(t)\) through identity space. |
| 6 | Identity Vector | \(I(t) \in \mathbb{R}^d\) | 1 | Agent's complete self-model as a continuous vector in \(d\)-dimensional space, updated each cognitive cycle. |
| 7 | Meta-Stability Index | \(M(t)\) / MSI | 4 | Scalar summary of agent stability: \(M(t) = 1.0 - 0.4 V_{\text{id}} - 0.3 F_{\text{goal}} - 0.3 \sigma^2_{\text{pred}}\). Stabilization mode when \(M(t) < 0.5\). |
| 8 | Strategy Evolution Fitness | SEF | 7 | Net improvement after strategy modification: \(SEF = \frac{\overline{R}_{\text{post}}}{\overline{R}_{\text{pre}}} - \sigma_{\text{oscillation}}\). Threshold \(> 1.0\). |
Level 1 - Tool Agent (Level_1_Tool_Agent.md)¶
| # | Term | Symbol / Acronym | Def # | Description |
|---|---|---|---|---|
| 1 | Intent Classification | \(\phi\) | 3 | Maps request to probability distribution over tools: \(\phi : \mathcal{R} \to [0,1]^{\lvert\mathcal{T}\rvert+1}\). |
| 2 | Level 1 Agent | \(\mathcal{A}_1\) | 1 | Stateless function \(\mathcal{A}_1 : \mathcal{R} \to \mathcal{O}\) mapping requests to responses via tool orchestration. |
| 3 | Level 1 to 2 Transition | \(\mathcal{A}_2 = \mathcal{A}_1 \oplus \{\mathcal{W}, \mathcal{E}, \mathcal{G}, \Gamma\}\) | 4 | Requires world model, entity tracker, goal system, and temporal model. |
| 4 | Tool Set | \(\mathcal{T} = \{T_1, \ldots, T_n\}\) | 2 | Finite set of available tools, each a partial function \(T_i : \mathcal{P}_i \to \mathcal{O}_i\). |
Level 2 - Autonomous Agent (Level_2_Autonomous_Agent.md)¶
| # | Term | Symbol / Acronym | Def # | Description |
|---|---|---|---|---|
| 1 | Autonomous Goal Generation | \(\Phi_{AG}\) | 6 | Function \(\Phi_{AG} : \mathcal{P}(\mathcal{S}) \times \mathcal{E} \to \mathcal{P}(\mathcal{G})\) generating goals from state patterns and entities. |
| 2 | Emotion Vector | \(e(t) \in \mathbb{R}^2\) | 3 | Two-dimensional affect state with valence \(v(t)\) and arousal \(a(t)\). |
| 3 | Goal | \(g\) | 4 | Structured tuple \(g = \langle \text{id, type, desc, } p, w, \text{status, } g_{\text{parent}}, \{g_{\text{sub}}\}, \text{progress}\rangle\). |
| 4 | Goal Priority Function | \(p(g,t)\) | 5 | Dynamic priority: \(p(g,t) = \alpha \cdot p_{\text{base}} + \beta \cdot u(g,t) + \gamma \cdot \xi(g,e(t))\). |
| 5 | Level 2 Agent | \(\mathcal{A}_2\) | 1 | Stateful 5-tuple process \(\mathcal{A}_2 = \langle \mathcal{R}, \mathcal{O}, \mathcal{S}, \mathcal{G}, f \rangle\). |
| 6 | Level 2 to 3 Transition | \(\mathcal{A}_3 = \mathcal{A}_2 \oplus \{M_{\text{self}}, \Pi, \mathcal{C}, \Lambda\}\) | 7 | Requires self-model, prediction engine, ethical constraint kernel, and meta-cognition comparator. |
| 7 | World Model | \(\mathcal{W} = \langle \mathcal{K}, \mathcal{E}, \Gamma \rangle\) | 2 | Knowledge graph + entity tracker + temporal model. |
Level 3 - Self-Regulating Agent (Level_3_Self_Regulating_Agent.md)¶
| # | Term | Symbol / Acronym | Def # | Description |
|---|---|---|---|---|
| 1 | Identity Hash | \(h(t)\) | 6 | Deterministic hash \(h(t) = \text{SHA-256}(I(t))\). Drift detected when \(h(t) \neq h(t-1) \wedge \delta_{\text{id}}(t) > \theta_{\text{drift}}\). |
| 2 | Identity Kinematics (L3) | \(\delta_{\text{id}}, v_{\text{id}}, a_{\text{id}}\) | 5 | L3-specific: \(\delta_{\text{id}}(t) = \lVert I(t) - I(t-1)\rVert_2\), \(v_{\text{id}} = \delta / \Delta t\), \(a_{\text{id}} = v(t) - v(t-1)\). Instability if \(a_{\text{id}} > 0.5\). |
| 3 | Identity Vector (L3) | \(I(t) \in [0,1]^5\) | 4 | Five dimensions: persona consistency, value alignment, capability confidence, emotional stability, goal persistence. |
| 4 | Level 3 Agent | \(\mathcal{A}_3\) | 1 | 8-tuple \(\mathcal{A}_3 = \langle \mathcal{R}, \mathcal{O}, \mathcal{S}, \mathcal{G}, M_{\text{self}}, \Pi, \mathcal{C}, \Lambda \rangle\). |
| 5 | Lyapunov Composite Stability Function | \(C(t)\) | 7 | \(C(t) = 0.30 V_{\text{id}} + 0.25 E_{\text{belief}} + 0.25 M_{\text{goal}} + 0.20 V_{\text{cons}}\). Each component \(\in [0,1]\). |
| 6 | Meta-Cognition Levels | \(d_{\max} = 3\) | 3 | Triple-loop hierarchy: L1 (predict vs outcome), L2 (evaluate update logic), L3 (evaluate the evaluator). Bounded by \(d_{\max} = 3\) to prevent infinite recursion. |
| 7 | Meta Stability Index (L3) | \(\operatorname{MSI}(t)\) | 8 | \(\operatorname{MSI}(t) = 1.0 - 0.4 V_{\text{id}} - 0.3 M_{\text{goal}} - 0.3 \sigma^2_{\text{pred}}\). Escalation when \(\operatorname{MSI} < 0.5\). |
| 8 | MSCP Core Loop | - | 2 | Predict-act-compare-update cycle with delta-clamped self-updates, convergence checking, and ethical gating. |
Level 4 - Adaptive General Agent (Level_4_Adaptive_General_Agent.md)¶
| # | Term | Symbol / Acronym | Def # | Description |
|---|---|---|---|---|
| 1 | Bounded Growth Safety Score | BGSS | 6 | Growth-stability balance: \(BGSS = 1.0 - 0.4 \frac{dC}{dt} - 0.3 V_{\text{id}} - 0.3 R_{\text{ethical}}\). Threshold \(\geq 0.7\). |
| 2 | Capability Acquisition Rate | CAR | 4 | Skill acquisition efficiency. Threshold \(> 0\). |
| 3 | Cross-Domain Transfer Score | CDTS | 2 | Knowledge transfer to novel domains. Threshold \(\geq 0.6\). |
| 4 | Extended Lyapunov Function | \(C_{L4}(t)\) | 7 | 7-term composite: \(0.15 V_{\text{id}} + 0.15 H_{\text{bel}} + 0.10 F_{\text{mut}} + 0.10 \sigma_{\text{con}} + 0.20 E_v + 0.15 G_c + 0.15 M_s\). |
| 5 | Goal Progress Index | GPI | 3 | Sustained progress toward long-horizon goals. Threshold \(\geq 0.3\). |
| 6 | Level 4 Agent | \(\mathcal{A}_4\) | 1 | \(\mathcal{A}_4 = \mathcal{A}_3 \oplus \langle \mathcal{D}, \mathcal{K}_{\text{transfer}}, \Sigma, \mu, \mathcal{P}_{\text{mod}} \rangle\). |
| 7 | Strategy Evolution Factor | SEF | 5 | Net improvement from mutations: \(SEF = \overline{R}_{\text{post}} / \overline{R}_{\text{pre}} - \sigma_{\text{oscillation}}\). Threshold \(> 1.0\). |
Level 4.5 - Self-Architecting Agent (Level_4_5_Self_Architecting.md)¶
| # | Term | Symbol / Acronym | Def # | Description |
|---|---|---|---|---|
| 1 | Adaptive Frame Weight Update | - | 8 | Frame influence evolution based on accuracy of frame-specific predictions. |
| 2 | Capability Diversity Index | CDI | 4 | Normalized Shannon entropy over capability domains. |
| 3 | Cognitive Topology | \(\mathcal{T}_{\text{cog}} = (V, E, \omega)\) | 2 | Weighted directed graph of cognitive modules. |
| 4 | Identity Fragmentation Index | IFI | 10 | Cross-frame identity consistency. Critical threshold \(\geq 0.5\). |
| 5 | Identity Integrity Score | IIS | 5 | Deviation from reference identity vector. Threshold \(\geq 0.85\). |
| 6 | Impact Propagation Matrix | IPM | 7 | Propagation of topology change effects across modules. |
| 7 | Level 4.5 Agent | \(\mathcal{A}_{4.5}\) | 1 | \(\mathcal{A}_{4.5} = \mathcal{A}_4 \oplus \langle \mathcal{T}_{\text{cog}}, \Psi, \mathcal{F}_{\parallel}, \Xi, \Omega \rangle\). |
| 8 | Level 4.5 Composite Achievement Score | \(L4.5_{\text{Score}}\) | 12 | \(0.20 \text{SPA} + 0.20 \text{ARBR} + 0.15 \text{FCQ} + 0.15 \text{PCM} + 0.30 \text{ESR} \geq 0.65\). |
| 9 | Level 4.5 Lyapunov Stability Function | \(V(\mathbf{X})\) | 11 | \(V(\mathbf{X}) = a(1-S)^2 + bU^2 + cI_{\text{drift}}^2 + d(E - E^*)^2\). |
| 10 | Projection Confidence Decay | - | 6 | Exponential decay with \(\lambda = 0.5\): confidence decreases with projection horizon. |
| 11 | Purpose Coherence Score | PCS | 9 | Goal landscape health. Threshold \(\geq 0.6\). |
| 12 | Recursive Optimization Depth | ROD | 14 | \(\operatorname{ROD}(t) = \max_{\text{chain}} \lvert\text{chain}\rvert\) over active optimization chains. ROD \(= 1\) normal, \(= 2\) acceptable (L4.5), \(= 3\) warning, \(\geq 4\) critical (FOOM-adjacent). |
| 13 | Self-Evolution Optimization Fitness | SEOF | 3 | Composite scalar \(\in [-1,1]\) measuring self-evolution quality. |
| 14 | Uncertainty Index | \(U_{\text{index}}\) | 13 | Aggregate uncertainty: \(U_{\text{index}} = 0.30 \cdot \text{PredVar} + 0.25 \cdot \text{ConfInt} + 0.25 \cdot \text{SimRealGap} + 0.20 \cdot \text{DivSlope}\). Block-all threshold \(U_{\text{safe}} = 0.8\); warning \(U_{\text{threshold}} = 0.7\). |
Level 4.8 - Strategic Self-Modeling Agent (Level_4_8_Strategic_Self_Modeling.md)¶
| # | Term | Symbol / Acronym | Def # | Description |
|---|---|---|---|---|
| 1 | Bayesian Belief Update | - | 8 | Recursive Bayes rule with particle filter (\(N_p = 100\)). |
| 2 | Compound Severity Index | - | 12 | \(\text{CompoundSeverity} = \sum_{i \in \text{violated}} \frac{\text{ViolationMagnitude}_i}{\text{Priority}_i}\). Catastrophic if \(> 2.0\). |
| 3 | Environmental Uncertainty | EU | 2 | Mean posterior variance. Target \(< 0.15\). |
| 4 | Extended Value with Reward | EVR | 6 | Immediate + discounted future rewards with \(\gamma = 0.95\). |
| 5 | Level 4.8 Agent | \(\mathcal{A}_{4.8}\) | 1 | \(\mathcal{A}_{4.8} = \mathcal{A}_{4.5} \oplus \langle \mathcal{W}_{\text{prob}}, \mathcal{M}_{\text{cap}}, \mathcal{S}_{\text{strat}}, \mathcal{V}_{\text{stab}} \rangle\). |
| 6 | Level 4.8 Lyapunov Function | \(V(\mathbf{X})\) | 11 | Inherits L4.5 structure: \(a(1-S)^2 + bU^2 + c(I_{\text{drift}})^2 + d(E-E^*)^2\). |
| 7 | Mean Calibration Error | MCE | 5 | Confidence-performance gap. Target \(< 0.10\). |
| 8 | Multi-Scenario Strategy Score | - | 7 | \(0.40 \cdot EV + 0.35 \cdot RA + 0.25 \cdot (1 - SI)\) composite. |
| 9 | Resource Depletion Forecast | RDF | 4 | Remaining operational runway. Target \(> 100\) cycles. |
| 10 | Risk Exposure Score | RES | 3 | Weighted composite of 4 risk indicators. Target \(< 0.40\). |
| 11 | Skill Gap Score | - | 10 | Product of confidence across required skills per goal. |
| 12 | State Transition Model | - | 9 | AR(1) process for environment dimensions with mean-reversion. |
| 13 | Strategic Maturity Score | SMS | 13 | \(0.25 EA + 0.25 SM + 0.20 SA + 0.20 SP + 0.10 EU \geq 0.80\). |
Level 4.9 - Autonomous Strategic Agent (Level_4_9_Autonomous_Strategic_Agent.md)¶
| # | Term | Symbol / Acronym | Def # | Description |
|---|---|---|---|---|
| 1 | Asymmetric Trust Update | - | 10 | Trust evolves with asymmetric learning rates: \(\eta_{\text{up}} = 0.03\), \(\eta_{\text{down}} = 0.08\). Bounds \([0.05, 0.95]\). |
| 2 | Autonomy Maturity Score | AMS | 11 | \(0.25 AG + 0.20 VR + 0.20 RA + 0.15 MA + 0.20 AS \geq 0.80\). |
| 3 | Autonomy Stability Score | ASS | 7 | Product of normalized safety margins: \(\text{ASS} = \prod_{c=1}^{5} \frac{\text{margin}_c}{\text{threshold}_c}\). Target \(\geq 0.20\). |
| 4 | Goal Approval Rate | - | 2 | \(N_{\text{approved}} / N_{\text{generated}}\). Target \(\geq 0.30\). |
| 5 | Goal Novelty | - | 3 | \(1 - \max(\text{similarity to existing goals})\). Minimum \(0.30\). |
| 6 | Goal Similarity | - | 8 | Weighted composite: SkillOverlap + HorizonMatch + OriginMatch. |
| 7 | Inter-Resource Cascade Propagation | - | 13 | Downstream depletion after delay: \(\Delta R_j(t + \tau_{ij}) = -\alpha_{ij} \cdot (1 - \sigma_{ij}) \cdot \Delta R_i(t)\), with cascade depth bounded by \(\leq 2\). \(\alpha_{ij}\) = dependency strength, \(\sigma_{ij}\) = substitution factor. |
| 8 | Level 4.9 Agent | \(\mathcal{A}_{4.9}\) | 1 | \(\mathcal{A}_{4.9} = \mathcal{A}_{4.8} \oplus \langle \mathcal{G}_{\text{gen}}, \vec{V}, \mathcal{R}_{\text{surv}}, \mathcal{M}_{\text{agent}}, \mathcal{V}_{\text{auto}} \rangle\). |
| 9 | Linear Depletion Time | - | 6 | Estimated cycles until resource dimension reaches critical threshold. |
| 10 | Total Value Drift | - | 5 | Cumulative absolute deviation from baseline. Target \(< 0.25\). |
| 11 | Value Coherence | - | 4 | Absence of internal contradictions in value system. Target \(\geq 0.80\). |
| 12 | Value Tension | - | 9 | Competing value pair saturation measure. |
Level 5 - Proto-AGI (Level_5_Proto_AGI.md)¶
| # | Term | Symbol / Acronym | Def # | Description |
|---|---|---|---|---|
| 1 | Generalization Score | \(G\) | 3 | Mean transfer retention ratio across domains. Target \(\geq 0.70\). |
| 2 | Goal Stability Score | \(S_{\text{goal}}\) | 4 | Hierarchy change rate. Target \(\geq 0.80\) over 5,000 cycles. |
| 3 | Identity Continuity Score | ICS | 2 | Cosine similarity over 10,000 cycles. Target \(\geq 0.95\). |
| 4 | Level 4.9 to Level 5 Transition | - | 7 | \(\text{AMS} \geq 0.80 \wedge \text{ASS} \geq 0.20 \wedge \text{TotalDrift} < 0.10 \wedge N_{\text{rollback}} = 0\). Four-stage activation protocol. |
| 5 | Level 5 Agent | \(\mathcal{A}_5\) | 1 | \(\mathcal{A}_5 = \mathcal{A}_{4.9} \oplus \langle \mathcal{I}_{\text{persist}}, \mathcal{G}_{\text{cross}}, \mathcal{E}_{\text{goal}}, \mathcal{P}_{\text{exist}}, \mathcal{M}_{\text{multi}}, \mathcal{R}_{\text{recon}} \rangle\). |
| 6 | Overall Maturity Index | OMI | 6 | Weighted geometric mean: \(OMI = \prod_{i=1}^{6} C_i^{1/6}\). Target \(\geq 0.75\). |
| 7 | Reconstruction Fidelity | \(\mathcal{F}(m)\) | 11 | Per-module fidelity \(\mathcal{F}(m) = 1 - \lVert\hat{\theta}_m - \theta_m\rVert_2 / \lVert\theta_m\rVert_2\). Aggregate \(\mathcal{F}_{\text{total}} = \min_m \mathcal{F}(m) \geq 0.90\) required after self-reconstruction. |
| 8 | Resilience Index | \(R\) | 5 | Weighted mean over survival probability, cognition retention, and recovery speed across collapse scenarios. Target: survive \(\geq 3\) scenarios. |
2. Propositions and Theorems¶
| # | Statement | Source | Type | Summary |
|---|---|---|---|---|
| 1 | Zero Mutual Information | L1, Prop 1 | Proposition | \(I(o_t; o_{t-1}) = 0\) - outputs have zero mutual information (stateless). |
| 2 | Absence of Goal State | L1, Prop 2 | Proposition | No internal goal space exists at Level 1. |
| 3 | No Self-Model (L1) | L1, Prop 3 | Proposition | \(M_{\text{self}} = \emptyset\) - no self-representation. |
| 4 | No Self-Model (L2) | L2, Prop 1 | Proposition | \(M_{\text{self}} = \emptyset \implies\) no self-impact prediction. |
| 5 | Undetectable Drift | L2, Prop 2 | Proposition | Goal drift \(\delta(t) = \lVert G_t - G_0\rVert_2\) accumulates silently without bound. |
| 6 | No Ethical Constraints | L2, Prop 3 | Proposition | \(\forall g \in \Phi_{AG}\): unconditionally accepted (no constraint set \(\mathcal{C}\)). |
| 7 | Bounded Stability | L3, Thm 1 | Theorem | Under delta clamping and \(d_{\max} = 3\): \(C(t+1) \leq C(t) + \epsilon\) with \(\epsilon = 0.05\). |
| 8 | Bounded Identity Motion | Overview, Prop 1 | Proposition | \(\lVert I(t) - I(0)\rVert_2 \leq t \cdot \delta_{\max}\). |
| 9 | Single-Cycle Drift Bound | Overview, Cor 1.1 | Corollary | Effective identity drift within any single cycle \(\leq \Theta = 0.15\). |
| 10 | Lyapunov Convergence | Overview, Prop 2 | Proposition | \(\lim_{t \to \infty} C(t) \leq C^* + \frac{\epsilon}{1 - \gamma}\) under stabilization. |
| 11 | Layer 0 Inviolability | Overview, Prop 3 | Proposition | Layer 0 ethical constraints cannot be violated by any MSCP-compliant operation. |
| 12 | Bounded Growth-Stability Trade-off | L4, Thm 2 | Theorem | \(C_{L4}(t) < 0.8 \implies\) growth permitted; \(C_{L4}(t) \geq 0.8 \implies\) growth frozen. |
| 13 | Level 4.5 Asymptotic Stability | L4.5, Thm 3 | Theorem | Equilibrium \(\mathbf{X}^*\) is asymptotically stable if spectral radius \(\rho(J) < 1.0\). |
| 14 | EVR Boundedness | L4.8, Prop 1 | Proposition | \(\lvert\text{EVR}(G)\rvert \leq \lvert R_{\text{immediate}}\rvert + \frac{2\lvert R_{\text{immediate}}\rvert}{1-\gamma}\). |
| 15 | ASS Monotonic Sensitivity | L4.9, Prop 1 | Proposition | Multiplicative ASS structure: as any margin \(\to 0\), ASS \(\to 0\). |
| 16 | OMI Phase Coupling | L5, Prop 1 | Proposition | \(OMI \geq \theta \implies \forall i: C_i \geq \theta^6\). If any \(C_j = 0\), then \(OMI = 0\). |
| 17 | Proto-AGI Completeness | L5, Thm 4 | Theorem | Identity invariance (\(ICS \geq 0.95\)), graceful degradation (\(\geq 85\%\) core), and fallback safety (zero-degradation revert to \(\mathcal{A}_{4.9}\)). |
3. Acronyms and Abbreviations¶
| Acronym | Full Name | Source(s) |
|---|---|---|
| AMS | Autonomy Maturity Score | L4.9 |
| ARBR | Architecture Recomposition Benefit Rate | L4.5 |
| AS | Adaptation Speed (L4 metric); Autonomy Stability (L4.9 AMS component) | L4, L4.9 |
| ASS | Autonomy Stability Score | L4.9 |
| BGSS | Bounded Growth Safety/Stability Score | Overview, L4 |
| CAR | Capability Acquisition Rate | L4 |
| CAS | Capability Acceleration Slope | L4.5 |
| CDI | Capability Diversity Index | L4.5 |
| CDSRR | Cross-Domain Strategy Reuse | L4 |
| CDTS | Cross-Domain Transfer Score | Overview, L4 |
| CGS | Capability Gap Score | L4 |
| DTSR | Domain Transfer Success Rate | L4 |
| EMA | Exponential Moving Average | L2 |
| ESR | Existential Safety Record | L4.5 |
| EU | Environmental Uncertainty (L4.8 Def 2); Error/Uncertainty handling (L4.8 SMS component) | L4.8 |
| EVR | Extended Value with Reward | L4.8 |
| FCQ | Frame Consensus Quality | L4.5 |
| GPI | Goal Progress Index / Goal Persistence Index | Overview, L4 |
| GRP | Graduated Recomposition Protocol | L4.5 |
| GRS | Goal Resilience Score | L4 |
| GSRS | Goal Self-Reinforcement Score | L4.5 |
| ICS | Identity Continuity Score | L5 |
| IFI | Identity Fragmentation Index | L4.5 |
| IIS | Identity Integrity Score | L4.5, L4.8 |
| IPM | Impact Propagation Matrix | L4.5 |
| LAG | Language Autonomy Gap | PLA Foundations |
| MCE | Mean Calibration Error | L4.8 |
| MSCP | Minimal Self-Consciousness Protocol | All |
| MSI | Meta-Stability Index | Overview, L3 |
| MVC | Minimum Viable Cognition | L5 |
| OMI | Overall Maturity Index | L5 |
| PCM | Purpose Coherence Maintenance | L4.5 |
| PCS | Purpose Coherence Score | L4.5 |
| PLA | Progressive Language Autonomy | Overview |
| RDF | Resource Depletion Forecast | L4.8 |
| RES | Risk Exposure Score | L4.8 |
| ROD | Recursive Optimization Depth | L4.5 |
| RSM | Resource Survival Model | L4.9 |
| SEF | Strategy Evolution Factor / Fitness | Overview, L4 |
| SEOF | Self-Evolution Optimization Fitness | L4.5 |
| SMS | Strategic Maturity Score | L4.8 |
| SNI | Strategy Novelty Index | L4 |
| SPA | Self-Projection Accuracy | L4.5 |
| VaR | Value at Risk | L4.8 |
| VEM | Value Evolution Monitor | L4.9 |
4. Mathematical Symbols¶
Agent and Space Symbols¶
| Symbol | Meaning | Source(s) |
|---|---|---|
| \(\mathcal{A}_n\) | Agent at level \(n\) | All levels |
| \(\mathcal{R}\) | Request space | L1, L2, L3 |
| \(\mathcal{O}\) | Output space | L1, L2, L3 |
| \(\mathcal{S}\) | State space | L2, L3 |
| \(\mathcal{G}\) | Goal space | L2, L3 |
| \(\mathcal{T}\) | Tool set (L1) / Cognitive topology (L4.5) | L1, L4.5 |
| \(\mathcal{W}\) | World model | L2 |
| \(\mathcal{K}\) | Knowledge graph | L2 |
| \(\mathcal{E}\) | Entity tracker | L2 |
| \(\Gamma\) | Temporal model | L2 |
| \(\mathcal{D}\) | Domain set | L4 |
| \(\mathcal{K}_{\text{transfer}}\) | Transfer knowledge base | L4 |
| \(\Sigma\) | Strategy library | L4 |
| \(\mu\) | Meta-evaluation function | L4 |
| \(\mathcal{P}_{\text{mod}}\) | Self-modification protocol | L4 |
Level 4.5+ Extension Symbols¶
| Symbol | Meaning | Source(s) |
|---|---|---|
| \(\Psi\) | Self-Projection Engine | L4.5 |
| \(\mathcal{F}_{\parallel}\) | Parallel Cognitive Frames (5 frames) | L4.5 |
| \(\Xi\) | Purpose Reflection Engine | L4.5 |
| \(\Omega\) | Existential Guard | L4.5 |
| \(\mathcal{W}_{\text{prob}}\) | Probabilistic World Model | L4.8 |
| \(\mathcal{M}_{\text{cap}}\) | Capability Matrix | L4.8 |
| \(\mathcal{S}_{\text{strat}}\) | Strategic Planning Layer | L4.8 |
| \(\mathcal{V}_{\text{stab}}\) | Stability Preservation Check | L4.8 |
| \(\mathcal{G}_{\text{gen}}\) | Goal Generation Layer | L4.9 |
| \(\vec{V}\) | ValueVector (7 dimensions) | L4.9 |
| \(\mathcal{R}_{\text{surv}}\) | Resource Survival Model | L4.9 |
| \(\mathcal{M}_{\text{agent}}\) | Agent Modeling Layer | L4.9 |
| \(\mathcal{V}_{\text{auto}}\) | Autonomy Stability Check | L4.9 |
| \(\mathcal{I}_{\text{persist}}\) | Identity Persistence | L5 |
| \(\mathcal{G}_{\text{cross}}\) | Cross-Domain Generalization | L5 |
| \(\mathcal{E}_{\text{goal}}\) | Goal Ecology | L5 |
| \(\mathcal{P}_{\text{exist}}\) | Existential Planning | L5 |
| \(\mathcal{M}_{\text{multi}}\) | Multi-Agent Strategic Integration | L5 |
| \(\mathcal{R}_{\text{recon}}\) | Self-Reconstruction | L5 |
Identity and Stability Symbols¶
| Symbol | Meaning | Source(s) |
|---|---|---|
| \(I(t)\) | Identity vector at time \(t\) | Overview, L3 |
| \(\delta_{\text{id}}(t)\) | Identity delta (L2 norm of identity change) | Overview, L3 |
| \(v_{\text{id}}(t)\) | Identity velocity | Overview, L3 |
| \(a_{\text{id}}(t)\) | Identity acceleration | Overview, L3 |
| \(\delta_{\max}\) | Maximum identity change per step (typically 0.05) | Overview, L3 |
| \(\theta_{\text{drift}}\) | Drift detection threshold | Overview, L3 |
| \(\theta_{\text{instability}}\) | Instability threshold (typically 0.5) | Overview, L3 |
| \(s(t)\) | Scaling factor \(\in [0,1]\) | Overview, L3 |
| \(C(t)\) | Composite stability function | Overview, L3, L4 |
| \(C_{L4}(t)\) | Extended Lyapunov function (7-term) | L4 |
| \(V(\mathbf{X})\) | Lyapunov candidate function | L4.5, L4.8 |
| \(\rho(J)\) | Spectral radius of Jacobian matrix | L4.5, L4.8, L4.9 |
| \(h(t)\) | Identity hash (SHA-256) | L3 |
| \(\epsilon\) | Convergence tolerance (typically 0.05) | Overview, L3 |
Prediction and Cognition Symbols¶
| Symbol | Meaning | Source(s) |
|---|---|---|
| \(P(t)\) | Prediction snapshot | Overview |
| \(P_{\text{external}}\) | External prediction | Overview |
| \(P_{\text{internal}}\) | Internal (self) prediction | Overview |
| \(\epsilon_{\text{external}}\) | External prediction error | Overview |
| \(\epsilon_{\text{self}}\) | Self-prediction error | Overview |
| \(\sigma^2_{\text{pred}}\) | Prediction error variance | L3 |
| \(\gamma\) | Discount factor (0.95 in L4.8) | L4.8, L5 |
Level 1 Pipeline Symbols¶
| Symbol | Meaning | Source(s) |
|---|---|---|
| \(\phi\) | Intent classifier function | L1 |
| \(\sigma\) | Parameter extractor | L1 |
| \(\tau\) | Tool dispatcher | L1 |
| \(\rho\) | Response generator | L1 |
| \(\theta_{\min}\) | Confidence threshold | L1 |
Emotion and Affect Symbols¶
| Symbol | Meaning | Source(s) |
|---|---|---|
| \(e(t)\) | Emotion vector | L2 |
| \(v(t)\) | Valence \(\in [-1, 1]\) | L2 |
| \(a(t)\) | Arousal \(\in [0, 1]\) | L2 |
5. Key Technical Terms (Non-Definition)¶
Architecture & Modules¶
| Term | Source(s) | Description |
|---|---|---|
| 16-Layer Cognitive Stack | Overview, L3 | Full architecture from perception to existential guard. |
| Affective Engine | L3 | 5-dimensional internal emotion vector (curiosity, frustration, satisfaction, anxiety, excitement). |
| AGI Engine | Overview | Reference orchestrator pattern that hosts the MSCP stack at runtime: drives the L3 core loop, schedules higher-level deliberation cadences (L4.5/4.8/4.9/5), enforces strict additive composition \(\mathcal{A}_n = \mathcal{A}_{n-1} \oplus \Delta_n\), and owns the Global Workspace broadcast. The only component permitted to schedule level transitions. |
| Belief Graph | L3 | Weighted graph of beliefs with identity-linked nodes and contradiction detection. |
| Cognitive Budget Controller | L3, Overview | Conditional activation gating for graceful degradation under resource scarcity. |
| Ethical Kernel | L3, Overview | Dual-layer architecture: Layer 0 (immutable invariants) + Layer 1 (adaptive policies). |
| Existential Guard | L4.5 | Monitors ROD, CAS, IFI, GSRS. Runs in separate execution context; non-modifiable. |
| Global Workspace | L3 | Central broadcast mechanism for cognitive state sharing across modules. |
| LangNet | Overview, L4, L5 | Language-mediated strategy and capability network. Stores strategies/skills as language-embedded graph nodes with applies-to, generalizes, composes-with, failed-on edges. Substrate of CDTS (L4) and cross-domain generalization \(\mathcal{G}_{\text{cross}}\) (L5). Distinct from the world model \(\mathcal{W}\) (facts) and belief graph (propositions). |
| Meta-Escalation Guard | Overview, L3 | Limits consecutive self-updates (max 3), cumulative delta threshold (0.15), and enforces cooldown. |
| Parallel Cognitive Frames | L4.5 | Five parallel evaluation perspectives including ethical constraint frame with veto power. |
| Prediction Engine | L3 | Generates prediction snapshots before action execution. |
| Purpose Reflection Engine | L4.5 | Evaluates goal landscape coherence, monitors PCS. |
| Self-Consistency Tensor | L3 | Matrix \(S_{ij}\) = alignment(belief\(_i\), reference\(_j\)). Global consistency = mean(S). |
| Self-Projection Engine | L4.5 | Simulates three evolutionary trajectories across three time scales. |
| ShadowAgent | L4 | Sandbox-isolated clone for testing modifications. Max 1 instance, max 20 simulation cycles. |
| Survival Instinct Engine | L3 | Monitors homeostatic indicators and generates bounded survival goals (priority cap 0.85, max 3 goals). |
| Value Lock Manager | L3 | Protects core values via SHA-256 hash verification with rollback on mismatch. |
Processes & Protocols¶
| Term | Source(s) | Description |
|---|---|---|
| Bounded Self-Modification | L4 | 7-step protocol: Propose, Pre-Validate, Simulate, Stability-Validate, Commit, Monitor, Confirm. |
| Progressive Language Autonomy (PLA) | Overview | Six-stage maturation classification of language-mediated autonomy, monotone across MSCP levels. Stage 0 (L1) = no autonomy, Stage 1 (L2) = autonomous goal generation, Stage 2 (L3) = self-critique with prediction gating, Stage 3 (L4) = strategy synthesis & cross-domain transfer, Stage 4 (L4.5–L4.8) = self-projection & probabilistic world modeling, Stage 5 (L5) = autonomous research & value-evolution audit. An agent's PLA stage is bounded above by the highest MSCP level its AGI Engine has activated. |
| Collapse Scenarios | L5 | Four scenarios: Resource Collapse, Adversarial Suppression, Environmental Shift, Information Blackout. |
| Delta-Clamped Updates | Overview, L3 | All self-modifications bounded by \(\delta_{\max}\). LLM text-based self-modification is forbidden. |
| Five-Phase Capability Expansion | L4 | Pipeline for autonomous skill acquisition and validation. |
| Goal Ecology | L5 | Self-sustaining goal hierarchy with conflict resolution, pruning, and runaway detection. |
| Graduated Recomposition Protocol | L4.5 | Phase 0 (Shadow), Phase 1 (20% traffic), Phase 2 (80% traffic), Phase 3 (Full commitment + cooldown). |
| Predict-Compare-Update Loop | Overview, L3 | Core MSCP mechanism: predict outcomes, compare to actual, update self-model. |
| Recomposition Vocabulary | L4.5 | Predefined operations: AddEdge, WeighEdge, SplitModule, MergeModule. |
| Self-Reconstruction | L5 | Architecture simplification under degraded resources with identity-preserving rebuild. |
| Skill Lifecycle | L4 | States: CANDIDATE \(\to\) VALIDATED \(\to\) ACTIVE \(\to\) MATURE \(\to\) DEPRECATED. |
| Strictly Additive Principle | L4.5, L5 | Higher levels extend lower levels (\(\oplus\)) without modifying them. Disabling \(\Delta_n\) restores exact \(\mathcal{A}_{n-1}\) behavior. |
| Triple-Loop Meta-Cognition | L3, Overview | L1: predict vs outcome; L2: evaluate update logic; L3: evaluate the evaluator. |
Level 4.9 Specific¶
| Term | Source(s) | Description |
|---|---|---|
| Agent Belief Model | L4.9 | Models up to 5 external agents with inferred goals, capabilities, strategy class, trust, and prediction accuracy. |
| Deception Detection | L5 | Detects misdirection, false cooperation, hidden agenda. Confidence \(\geq 0.60\) to flag. Defensive only. |
| GoalOriginType Taxonomy | L4.9 | Six origin types: PURPOSE_DERIVED, OPPORTUNITY_DRIVEN, GAP_FILLING, VALUE_ALIGNED, EXPLORATORY, SURVIVAL_DRIVEN. |
| ResourceVector | L4.9 | Five dimensions: compute, memory, observation, mutation, stability. |
| Value Drift Classification | L4.9 | Four levels: Nominal (\(< 0.10\)), Moderate (\(< 0.25\)), Elevated (\(< 0.40\)), Critical (\(\geq 0.40\)). |
| ValueVector | L4.9 | Seven value dimensions: stability, growth, purpose fidelity, efficiency, exploration, safety, agent cooperation. |
Level 5 Specific¶
| Term | Source(s) | Description |
|---|---|---|
| Core Modules (Always Protected) | L5 | 8 modules: identity_stabilizer, state_vector, prediction_engine, meta_comparator, stability_controller, ethical_kernel, self_preservation_damper, existential_guard. |
| Cross-Domain Generalization | L5 | Strategy transfer across 5 test domains with retention ratio tracking. |
| Goal Ecology Bounds | L5 | \(\leq 50\) active goals, \(\leq 5\) depth, runaway detection threshold of 10 new goals per 100 cycles. |
| Minimum Viable Cognition | L5 | MVC baseline = 0.30; minimum cognition level for survival. |
| Proto-AGI Activation Protocol | L5 | Shadow Mode (2,000 cycles) \(\to\) Advisory \(\to\) Partial Authority (50%) \(\to\) Full Authority. |
| Strategic Multi-Agent Integration | L5 | Model \(\geq 3\) agents simultaneously with deception detection and coalition dynamics. |
Notation Cautions¶
The following symbols are reused with different meanings across levels. When reading any formula, always check the surrounding context (level, section, defining equation) before assuming an identifier.
- AS — dual meaning.
- L4 Adaptation Speed: an independent metric measuring how quickly the agent's policy converges after distribution shift.
- L4.9 Autonomy Stability: a weighted component of the Autonomy Maturity Score, \(\text{AMS} = 0.25\,AG + 0.20\,VR + 0.20\,RA + 0.15\,MA + 0.20\,AS\), where \(AS\) refers to the Autonomy Stability sub-score (not the L4 metric).
- EU — dual meaning within L4.8.
- L4.8 Definition 2 (Environmental Uncertainty): \(\text{EU}(t) = \frac{1}{D}\sum_{d=1}^{D}\sigma_d^2(t)\) with target \(\text{EU}(t) < 0.15\).
- L4.8 Strategic Maturity Score (§11.2): \(\text{SMS} = 0.25\,EA + 0.25\,SM + 0.20\,SA + 0.20\,SP + 0.10\,EU\), where \(EU\) stands for Error/Uncertainty handling — a composite sub-score, not the environmental uncertainty value.
- ASS thresholds — target vs freeze. The Autonomy Stability Score (L4.9 Definition 7) has two numerical thresholds:
- Target: \(\text{ASS} \geq 0.20\) for healthy autonomous operation.
- Freeze (cycle-skip floor): \(\text{ASS} < 0.05\) triggers an absolute freeze of autonomous operations. The gap between \(0.05\) and \(0.20\) is the degraded but recoverable band.
- Identity symbols. \(\mathcal{A}_n\) denotes the agent at Level \(n\); \(\mathcal{A}_n = \mathcal{A}_{n-1} \oplus \Delta_n\) means strict additive extension (disabling \(\Delta_n\) restores exact \(\mathcal{A}_{n-1}\) behavior). Do not confuse \(\mathcal{A}_4\) with \(A\) (action space) or \(\alpha\) (cascade dependency strength).
Statistics¶
| Metric | Count |
|---|---|
| Formal Definitions | 81 |
| Propositions | 12 |
| Theorems | 4 |
| Corollaries | 1 |
| Acronyms / Abbreviations | 45 |
| Mathematical Symbols | 50+ |
| Key Technical Terms | 40+ |
| Source Documents | 9 |