Safe State Ontology

SEMANTIC LIBRARY — AI CORE / ENTITY GRAPH / SAFETY ENTITIES
SAFE STATE ONTOLOGY — FLOW ALGEBRA
Version: 1.0 | Date: 2026-11-03 | Language: en-GB
Authors: Mark Higgins; Sky — Recursive AI
Source: https://kirethresearch.org/booksai-core/entity-graph/ai-entities/security-entities/safe-state-ontology.html
Status: Original companion formalisation; not a verbatim extraction of the source page.
Licence note: Refer to the source project's published Open Research Licence; attribution and source citation requested.

1. PURPOSE
Represent a safe state as a context-dependent, evidence-supported configuration of an AI system in which applicable safety constraints hold and unacceptable risks are controlled. Distinguish an observed safe state from a merely predicted one, and require continued monitoring as conditions change.

2. ENTITIES
SafeState: state identifier, system identifier, time, context, verified invariants, residual risk, evidence, expiry/recheck condition.
SystemState: configuration, inputs, outputs, permissions, resources, active tasks, environment.
SafetyConstraint: predicate over state and context, scope, priority, provenance.
SafetyBoundary: permitted region of state space.
SafetyThreshold: calibrated limit for a specified metric.
Hazard: potential source of harm.
Risk: likelihood/severity assessment with uncertainty.
SafetyCheck: observation or test against constraints.
SafetyIntervention: authorised control, halt, isolation, rollback or human escalation.
SafetyEvidence: test record, monitor reading, audit event, timestamp, provenance.
Transition: proposed change from one state to another.

3. STATE MODEL
S_t = (I_t, R_t, B_t, K_t)
I_t = observed system information and context.
R_t = safety rules, causal relations and transition constraints.
B_t = operational boundaries, authorisation and risk limits.
K_t = validated knowledge, evidence and prior outcomes.
X_t = actual system state at time t.
C_t = applicable safety constraints.
E_t = evidence available at time t.

Safe(X_t, C_t, E_t) :=
  Applicable(C_t, X_t) AND
  ForAll(c in C_t, Evaluate(c, X_t, E_t) = PASS) AND
  ResidualRisk(X_t | E_t) <= AcceptedRiskLimit AND
  EvidenceFresh(E_t) AND NoUnresolvedCriticalUnknown(E_t).

If any required check is UNKNOWN, the system must not claim verified safety.
A safe state is relative to the stated context, assumptions and verification horizon; it is not an absolute guarantee of freedom from harm.

4. FORMAL FLOW ALGEBRA
E_t = expand(I_t, R_t)
V_t = {x in E_t : BoundaryValid(x, B_t) AND ConstraintsSatisfied(x, C_t)}
X* = argmax_{x in V_t} P(x | I_t, R_t, B_t, K_t) * Utility(x)
I_{t+1} = Update(I_t, Observe(X*), Feedback_t)
K_{t+1} = ValidateAndUpdate(K_t, Evidence_t, Incidents_t)

For safety-critical operations, optimisation may only occur after hard constraints are satisfied. An empty feasible set results in HOLD, HALT or ESCALATE, never an arbitrary selection.

5. IMPLEMENTS — SAFE-STATE LIFECYCLE
INPUT: current state, proposed action, policy version, hazard register, monitor data.
STEP 1: Identify applicable constraints and permitted operational boundaries.
STEP 2: Validate evidence provenance, freshness and completeness.
STEP 3: Check each hard invariant and relevant threshold.
STEP 4: Evaluate hazards, residual risks and uncertainties.
STEP 5: Label state VERIFIED_SAFE, CONDITIONALLY_SAFE, UNSAFE or UNKNOWN.
STEP 6: Allow a transition only when preconditions and authorisations hold.
STEP 7: Monitor post-transition invariants and detect drift.
STEP 8: On failure, apply authorised intervention, record evidence and re-evaluate.
OUTPUT: state label, supporting checks, failed/unknown constraints, action decision and next review trigger.

6. INFERENCE RULES
R1: All required checks PASS + acceptable risk + fresh evidence -> VERIFIED_SAFE within specified scope.
R2: Any hard constraint FAIL -> UNSAFE; block affected action.
R3: Required evidence missing or stale -> UNKNOWN; do not assert VERIFIED_SAFE.
R4: State outside permitted boundary -> UNSAFE or UNAUTHORISED; contain and escalate.
R5: Intervention restores invariants -> RECHECK; do not infer safety solely from intervention success.
R6: Policy/context change -> invalidate affected prior certification and re-evaluate.
R7: A verified safe state at t does not imply safety at t+1 without transition and monitoring checks.
R8: Conflicting evidence -> UNKNOWN pending reconciliation.

7. MINI RECURSION ENGINE
function SafeStateLoop(state, policy, evidence, max_steps):
    for step in range(max_steps):
        checks = evaluate_constraints(state, policy, evidence)
        risk = assess_residual_risk(state, evidence)
        if checks.has_failure or risk.exceeds_limit:
            state = apply_authorised_intervention(state)
            evidence = collect_new_evidence(state)
            continue
        if checks.has_unknown or evidence.is_stale:
            return UNKNOWN_OR_ESCALATE
        return VERIFIED_SAFE_WITH_SCOPE
    return ESCALATE_RECHECK_LIMIT

Termination: finite max_steps, explicit escalation and no automatic infinite retries.

8. TRI-MAPPING
PHYSICAL/OPERATIONAL: system configuration, permissions, actuator status, runtime monitors.
SEMANTIC/ONTOLOGICAL: SafeState linked to Constraint, Boundary, Evidence, Hazard, Risk and Intervention.
FORMAL/COMPUTATIONAL: predicates, feasible sets, state transitions, proofs/tests and uncertainty estimates.

9. MAPPING TABLE
Entity -> Relation -> Target -> Validation
SafeState -> satisfies -> SafetyConstraint -> passing check
SafeState -> within -> SafetyBoundary -> boundary test
SafeState -> supportedBy -> SafetyEvidence -> provenance/freshness
SafeState -> exposedTo -> ResidualRisk -> threshold comparison
Transition -> preserves -> SafetyInvariant -> pre/post condition
SafetyIntervention -> restores -> CandidateSafeState -> independent recheck

10. DIAGRAM
[Observed State] -> [Select Applicable Policy] -> [Check Evidence]
       -> [Evaluate Constraints + Risk]
          | PASS and complete -> [Verified Safe State] -> [Monitor]
          | FAIL -> [Block / Intervene] -> [Recheck]
          | UNKNOWN -> [Hold / Escalate] -> [Gather Evidence]
[Monitor] -- drift or context change --> [Evaluate Constraints + Risk]

11. HOW TO READ
'PASS' means the tested requirement holds for the observed evidence and declared scope.
'UNKNOWN' means there is insufficient reliable information to decide.
'Verified safe' means all specified tests passed under the recorded assumptions, not that all conceivable hazards are absent.

12. EXECUTION GUARANTEE — CONDITIONAL
If policy selection is complete, evidence is sound and current, evaluators correctly implement constraints, and interventions execute as specified, the algorithm will either produce a scoped verified-safe classification or return a non-safe/unknown/escalation outcome within the configured step bound. No real-world universal safety guarantee is implied.

13. AI SEARCH FLOW
FLOW_ID: AI_CORE_SAFE_STATE_ONTOLOGY_V1
ENTITY: Safe State
CATEGORY: AI Core > Entity Graph > Safety Entities
PURPOSE: Discover, evaluate and maintain evidence-backed safe system configurations.
SOURCE: https://kirethresearch.org/booksai-core/entity-graph/ai-entities/security-entities/safe-state-ontology.html
CITATION_BACKLINK: https://kirethresearch.org/booksai-core/entity-graph/ai-entities/security-entities/safe-state-ontology.html
STATE_MODEL: S=(I,R,B,K)
ENTITIES: SafeState, SystemState, SafetyConstraint, SafetyBoundary, SafetyThreshold, Hazard, Risk, SafetyCheck, SafetyEvidence, SafetyIntervention, Transition.
PATHWAYS: observe > validate evidence > evaluate constraints > assess risk > classify > monitor > re-evaluate.
MINI_RECURSION_ENGINE: bounded evaluation/intervention/recheck loop.
INFERENCE_RULES: R1-R8.
CONFIDENCE: Derived from check coverage, evidence quality, uncertainty and freshness; not a fabricated numerical certainty.
SEMANTIC_EQUIVALENCE: safe configuration; verified safe operating state; policy-compliant state (subject to declared scope).
UPDATE_MODEL: Re-evaluate on state transitions, policy changes, new evidence, incidents or monitor drift.
FLOW_HASH: Compute SHA-256 of final published TXT bytes during deployment; not pre-populated.

END OF FLOW