ARVIS: M3.3: Runtime Projection Certificate & Validated Domain
Objective
This document defines the implemented projection layer in ARVIS.
Unlike the original theoretical projection:
$$ \Pi : \mathcal{C} \to (x_t, z_t, q_t, w_t) $$
the current system implements a runtime projection certification layer, denoted:
$$ \Pi_{\text{cert}} : \mathcal{O}_{\text{runtime}} \to \mathcal{P} $$
This layer: - validates that runtime observations remain within a safe operational domain - produces a projection certificate - feeds Gate safety enforcement
It is a safety and validity mechanism, not a full state projection.
Important distinction: - $\Pi$ (M3.1) is a theoretical projection operator used for analysis, - $\Pi_{\text{cert}}$ is an implemented certification operator used for runtime safety.
No claim is made that $\Pi_{\text{cert}}$ approximates or reconstructs $\Pi$.
1. Implemented Projection Object
The runtime projection output is a certificate:
$$ P_t \in \mathcal{P} $$
where:
$$ \mathcal{P} = {(\text{domain_valid},\; m_t,\; \text{is_projection_safe},\; \text{certification_level})} $$
where:
domain_valid∈ {True, False}- $m_t$ = margin to domain boundary
is_projection_safe∈ {True, False}certification_level∈ structured levels (implementation-defined)
This object is directly consumed by the Gate.
Remark:
$P_t$ is not a state representation. It is a diagnostic certificate.
2. Projection Pipeline Components
The implemented projection layer consists of:
ProjectionDomainProjectionValidatorProjectionCertificateProjectionStage
2.1 ProjectionDomain
Defines the admissible runtime domain:
$$ \mathcal{O}{\text{valid}} \subseteq \mathcal{O}{\text{runtime}} $$
This domain is empirically defined and bounded (see M3 Appendix).
2.2 ProjectionValidator
Deterministically checks whether a runtime observation belongs to the validated domain and computes: - domain validity - margin to boundary - safety flag
This operator is a deterministic predicate + metric extractor:
$$ \mathcal{V} : \mathcal{O}{\text{runtime}} \to {0,1} \times \mathbb{R}{\geq 0} $$
2.3 ProjectionCertificate
Encapsulates the validation results in a structured object passed through the pipeline.
2.4 ProjectionStage
Integrated into the cognitive pipeline. It ensures: - projection certification is always available - the certificate is refreshed after observability updates
It defines the implemented mapping:
$$ \Pi_{\text{cert}} := \text{ProjectionStage} \circ \mathcal{V} $$
3. Runtime Projection Input Space
The current implemented projection operates on a minimal runtime observation space.
At this stage, the validated signals are:
$$ o_t^{(\text{cert})} = {\text{system_tension},\ \text{conflict_pressure},\ \text{coherence_score},\ \text{control_signal},\ \text{adaptive_kappa_eff}} $$
Properties: - bounded, per-axis - deterministic - directly usable by safety logic
This narrow scope is intentional.
Limitation:
This input space is a strict subset of the theoretical observation space $\mathcal{O}$.
4. Validated Domain
The validated domain is operationally defined by:
4.1 Numeric boundedness
$$ \text{system_tension} \in [0, 100],\quad \text{conflict_pressure} \in [0, 100],\quad \text{control_signal} \in [0, 100] $$ $$ \text{coherence_score} \in [0, 1],\quad \text{adaptive_kappa_eff} \in [0, 1],\quad \text{payload} \le 10000 $$
A declared-but-missing bounded key marks the domain invalid
(
4.2 Finite representation
- no NaN
- no infinite values
- bounded payload size
4.3 Deterministic evaluation
Validation is deterministic: identical input → identical certificate.
This implies:
$$ o_t = o_t' \implies \Pi_{\text{cert}}(o_t) = \Pi_{\text{cert}}(o_t') $$
5. Projection Certificate Semantics
5.1 Domain validity
$$ \text{domain_valid} = \text{True} $$ means the runtime observation lies inside the validated domain.
If domain_valid = False, the projection is considered invalid for safe execution.
Formally:
$$ \text{domain_valid} = 1 \iff o_t \in \mathcal{O}_{\text{valid}} $$
5.2 Margin to boundary
$$ m_t = \text{margin_to_boundary} $$
Interpretation:
- large $m_t$ → safe interior point
- small positive $m_t$ → near-boundary state
- invalid cases handled via domain_valid
5.3 Projection safety
is_projection_safe indicates whether the projected runtime state is considered safe for execution.
It is used by the Gate in coupled safety logic.
This is a derived boolean, not a primitive property of the system.
5.4 Certification level
Encodes confidence tier, validation strength, and fallback usage.
It is implementation-defined and extensible.
No formal ordering or metric structure is currently imposed on certification levels.
6. ProjectionStage in the Pipeline
The ProjectionStage executes in two phases:
6.1 Pre-Gate certification
Before Gate execution: - ensures a certificate always exists - enables projection-aware filtering
6.2 Post-observability refresh
After observability updates: - recomputes the certificate using the enriched state
This creates the logic: $$ \text{early certification} \rightarrow \text{refined certification} $$
This is a two-pass evaluation, not a dynamical system.
7. Safety Fallback
The projection layer must never fail.
If no usable signal exists: - a neutral safe default input is used (implementation-defined, not theoretically meaningful)
This guarantees that the certificate is always defined.
This is a kernel invariant.
Formally:
$$ \forall o_t \in \mathcal{O}_{\text{runtime}}, \quad \exists P_t $$
8. Integration with the Gate
The projection certificate is actively used by the Gate:
8.1 Hard invalidity constraint
$$ \text{domain_valid} = \text{False} \implies v_t = \text{ABSTAIN} $$
8.2 Boundary constraint
$$ m_t < \epsilon \implies v_t \neq \text{ALLOW} $$
8.3 Coupled instability constraint
If projection is unsafe AND instability signals are present ($\Delta W_t > 0$, or global/switching unsafe), then escalation to ABSTAIN via Gate enforcement layers.
These constraints are operational rules, not derived from Lyapunov analysis.
9. Validated Properties of the Current Layer
The implemented projection layer satisfies:
- Determinism: Same input → same certificate
- Bounded domain enforcement: All accepted states lie within a finite domain
- Fail-soft behavior: Invalid inputs do not crash and produce diagnosable certificates
- Gate compatibility: Does not break Gate execution and provides usable safety signals
- Stability compatibility (weak form): Does not invalidate Lyapunov evaluation when consumed by the Gate
Important:
It does not produce $(x, z, q, w)$.
It only provides constraints on admissible execution.
10. What Is NOT Implemented Yet
- Full projection $\Pi : \mathcal{C} \to (x_t, z_t, q_t, w_t)$
- Structured signal semantic validation
- Symbolic state projection
- Disturbance ($w_t$) certification
- Mode ($q_t$) projection
- Lipschitz guarantees on the full cognitive space
- Full compatibility with all assumptions A1–A15
11. Mathematical Interpretation
Currently, the validated statement is:
There exists a subset $$ \mathcal{O}{\text{valid}} \subseteq \mathcal{O}{\text{runtime}} $$ such that validation is deterministic, safety constraints are enforceable, and the projection produces a certificate usable by the Gate.
This is a runtime safety certification result, not a projection theorem.
In particular, no statement of the form:
$$ \Pi_{\text{cert}} \approx \Pi $$
is claimed.
12. Relation to M6 (Gate)
The projection layer provides input constraints to the Gate:
$$ G(W_t, \Delta W_t, \kappa^t, H_t, P_t) \mapsto v_t $$
The Gate uses $P_t$ to: - reject invalid states - restrict boundary states - couple projection safety with stability signals
Thus, $P_t$ acts as an external constraint signal in the decision process.
13. Final Statement
The current ARVIS projection layer is:
a deterministic runtime certification system validating a bounded operational domain, producing projection certificates, and enabling projection-aware Gate safety enforcement.
It is: - correctly implemented - test-covered - architecturally integrated
But it remains a partial realization of the full projection operator defined in the original M3 theoretical framework.
It should therefore be interpreted as:
a validation and safety interface, not a state reconstruction operator.