diff --git a/AGENTS.md b/AGENTS.md
index 89502b3..694d2d4 100644
--- a/AGENTS.md
+++ b/AGENTS.md
@@ -15,5 +15,11 @@ The goal is to provide a production-ready scaffold that can be progressively ext
 
 If you add features, update this document to reflect schema changes and testing commands.
 
+New modules added in this iteration:
+- src/guardrail_space/belief.py: a compact particle-filter sketch that emits
+  probability-of-violation (PoV) and an entropy summary. Includes serialize()
+  for compact fingerprints. Unit tests in tests/test_belief.py exercise
+  deterministic behavior and compact serialization.
+
 Testing
 - Run `./test.sh` to execute unit tests and build a sdist/wheel with `python3 -m build`.
diff --git a/guard_logs.jsonl b/guard_logs.jsonl
index 06c88fc..c522303 100644
--- a/guard_logs.jsonl
+++ b/guard_logs.jsonl
@@ -10,3 +10,4 @@
 {"contract_id": "guard-001", "plan": {"action": "move", "costs": {"time": 2.0}, "speed": 0.8}, "state": {"speed": 0.8, "distance_to_obstacle": 5}, "decision": "allow"}
 {"contract_id": "guard-001", "plan": {"action": "move", "costs": {"time": 2.0}, "speed": 0.8}, "state": {"speed": 0.8, "distance_to_obstacle": 5}, "decision": "allow"}
 {"contract_id": "guard-001", "plan": {"action": "move", "costs": {"time": 2.0}, "speed": 0.8}, "state": {"speed": 0.8, "distance_to_obstacle": 5}, "decision": "allow"}
+{"contract_id": "guard-001", "plan": {"action": "move", "costs": {"time": 2.0}, "speed": 0.8}, "state": {"speed": 0.8, "distance_to_obstacle": 5}, "decision": "allow"}
diff --git a/guardrail_space/belief.py b/guardrail_space/belief.py
new file mode 100644
index 0000000..a50093e
--- /dev/null
+++ b/guardrail_space/belief.py
@@ -0,0 +1,139 @@
+import math
+import struct
+import hashlib
+import random
+from typing import List, Tuple
+
+
+class BeliefSketch:
+    """A tiny particle-filter based belief sketch for a single scalar variable.
+
+    Purpose: maintain a compact, mission-tuned belief for a scalar safety variable
+    (e.g., battery, obstacle distance) and emit a probability-of-violation (PoV)
+    and an entropy summary. The implementation is intentionally small and
+    deterministic when a seed is provided so CI/edge tests are reproducible.
+
+    This is not a full particle filter for production use, but a compact
+    lightweight sketch suitable for the GuardRail.Space MVP and unit tests.
+    """
+
+    def __init__(
+        self,
+        name: str,
+        num_particles: int = 64,
+        prior_mean: float = 0.0,
+        prior_std: float = 1.0,
+        seed: int = None,
+    ):
+        self.name = name
+        self.num_particles = max(8, int(num_particles))
+        self.rng = random.Random(seed)
+        # initialize particles from a normal prior
+        self.particles: List[float] = [
+            self.rng.gauss(prior_mean, prior_std) for _ in range(self.num_particles)
+        ]
+        # equal weights (implicit)
+
+    def update(self, observation: float, obs_std: float = 1.0) -> None:
+        """Update belief with a scalar observation using likelihood weighting
+        followed by multinomial resampling and small jitter to avoid particle
+        degeneracy. Deterministic when seed provided at construction.
+        """
+        if obs_std <= 0:
+            obs_std = 1e-6
+        # quick check: if observation is far outside current particle spread,
+        # reinitialize particles around the observation so the sketch remains
+        # responsive to strong, previously-unseen signals.
+        n = len(self.particles)
+        mean0 = sum(self.particles) / n if n else 0.0
+        var0 = sum((p - mean0) ** 2 for p in self.particles) / n if n else 0.0
+        std0 = math.sqrt(max(var0, 1e-12))
+        if abs(observation - mean0) > max(3.0 * std0, 3.0 * obs_std):
+            self.particles = [self.rng.gauss(observation, max(1e-6, obs_std * 0.5)) for _ in range(self.num_particles)]
+            return
+
+        # compute weights proportional to Gaussian likelihood
+        weights = []
+        two_var = 2.0 * (obs_std ** 2)
+        for p in self.particles:
+            # gaussian likelihood unnormalized
+            w = math.exp(-((observation - p) ** 2) / two_var)
+            weights.append(w)
+        total = sum(weights)
+        # If likelihoods underflow to (near) zero, treat the observation as
+        # dominant and reinitialize particles around the observation. This
+        # keeps the sketch responsive to strong signals and avoids a degenerate
+        # uniform-resample when all weights are effectively zero.
+        if total <= 1e-12:
+            self.particles = [self.rng.gauss(observation, max(1e-6, obs_std * 0.5)) for _ in range(self.num_particles)]
+            return
+        probs = [w / total for w in weights]
+
+        # multinomial resampling
+        cumulative = []
+        c = 0.0
+        for p in probs:
+            c += p
+            cumulative.append(c)
+
+        new_particles = []
+        for _ in range(self.num_particles):
+            u = self.rng.random()
+            # find first cumulative >= u
+            for idx, c in enumerate(cumulative):
+                if u <= c:
+                    new_particles.append(self.particles[idx])
+                    break
+            else:
+                new_particles.append(self.particles[-1])
+
+        # jitter with small gaussian noise proportional to obs_std
+        jitter_scale = max(1e-3, obs_std * 0.01)
+        self.particles = [p + self.rng.gauss(0.0, jitter_scale) for p in new_particles]
+
+    def pov(self, threshold: float, operator: str = ">") -> float:
+        """Return probability-of-violation (PoV) that the scalar meets the
+        violation predicate defined by (operator, threshold). Supported
+        operators: '>' (default), '<', '>=', '<='.
+        """
+        if operator == ">":
+            count = sum(1 for p in self.particles if p > threshold)
+        elif operator == "<":
+            count = sum(1 for p in self.particles if p < threshold)
+        elif operator == ">=":
+            count = sum(1 for p in self.particles if p >= threshold)
+        elif operator == "<=":
+            count = sum(1 for p in self.particles if p <= threshold)
+        else:
+            raise ValueError(f"unsupported operator: {operator}")
+        return float(count) / float(len(self.particles))
+
+    def entropy(self) -> float:
+        """Return a simple continuous-entropy proxy (Gaussian entropy using
+        empirical variance). This is cheap and stable for small sketches.
+        """
+        n = len(self.particles)
+        if n == 0:
+            return 0.0
+        mean = sum(self.particles) / n
+        var = sum((p - mean) ** 2 for p in self.particles) / n
+        var = max(var, 1e-12)
+        # differential entropy of Gaussian: 0.5*ln(2*pi*e*var)
+        return 0.5 * math.log(2 * math.pi * math.e * var)
+
+    def summarize(self, threshold: float, operator: str = ">") -> dict:
+        """Return a compact summary dictionary with PoV and entropy.
+        """
+        return {"name": self.name, "pov": self.pov(threshold, operator), "entropy": self.entropy()}
+
+    def serialize(self) -> bytes:
+        """Produce a tiny deterministic byte fingerprint of the sketch. Format:
+        8 bytes mean (double) + 8 bytes variance (double) + 8 bytes crc64-like
+        truncated using sha256. This keeps the sketch small (<64 bytes).
+        """
+        n = len(self.particles)
+        mean = sum(self.particles) / n if n else 0.0
+        var = sum((p - mean) ** 2 for p in self.particles) / n if n else 0.0
+        packed = struct.pack("!dd", mean, var)
+        digest = hashlib.sha256(packed).digest()[:16]
+        return packed + digest
diff --git a/src/guardrail_space/belief.py b/src/guardrail_space/belief.py
new file mode 100644
index 0000000..a50093e
--- /dev/null
+++ b/src/guardrail_space/belief.py
@@ -0,0 +1,139 @@
+import math
+import struct
+import hashlib
+import random
+from typing import List, Tuple
+
+
+class BeliefSketch:
+    """A tiny particle-filter based belief sketch for a single scalar variable.
+
+    Purpose: maintain a compact, mission-tuned belief for a scalar safety variable
+    (e.g., battery, obstacle distance) and emit a probability-of-violation (PoV)
+    and an entropy summary. The implementation is intentionally small and
+    deterministic when a seed is provided so CI/edge tests are reproducible.
+
+    This is not a full particle filter for production use, but a compact
+    lightweight sketch suitable for the GuardRail.Space MVP and unit tests.
+    """
+
+    def __init__(
+        self,
+        name: str,
+        num_particles: int = 64,
+        prior_mean: float = 0.0,
+        prior_std: float = 1.0,
+        seed: int = None,
+    ):
+        self.name = name
+        self.num_particles = max(8, int(num_particles))
+        self.rng = random.Random(seed)
+        # initialize particles from a normal prior
+        self.particles: List[float] = [
+            self.rng.gauss(prior_mean, prior_std) for _ in range(self.num_particles)
+        ]
+        # equal weights (implicit)
+
+    def update(self, observation: float, obs_std: float = 1.0) -> None:
+        """Update belief with a scalar observation using likelihood weighting
+        followed by multinomial resampling and small jitter to avoid particle
+        degeneracy. Deterministic when seed provided at construction.
+        """
+        if obs_std <= 0:
+            obs_std = 1e-6
+        # quick check: if observation is far outside current particle spread,
+        # reinitialize particles around the observation so the sketch remains
+        # responsive to strong, previously-unseen signals.
+        n = len(self.particles)
+        mean0 = sum(self.particles) / n if n else 0.0
+        var0 = sum((p - mean0) ** 2 for p in self.particles) / n if n else 0.0
+        std0 = math.sqrt(max(var0, 1e-12))
+        if abs(observation - mean0) > max(3.0 * std0, 3.0 * obs_std):
+            self.particles = [self.rng.gauss(observation, max(1e-6, obs_std * 0.5)) for _ in range(self.num_particles)]
+            return
+
+        # compute weights proportional to Gaussian likelihood
+        weights = []
+        two_var = 2.0 * (obs_std ** 2)
+        for p in self.particles:
+            # gaussian likelihood unnormalized
+            w = math.exp(-((observation - p) ** 2) / two_var)
+            weights.append(w)
+        total = sum(weights)
+        # If likelihoods underflow to (near) zero, treat the observation as
+        # dominant and reinitialize particles around the observation. This
+        # keeps the sketch responsive to strong signals and avoids a degenerate
+        # uniform-resample when all weights are effectively zero.
+        if total <= 1e-12:
+            self.particles = [self.rng.gauss(observation, max(1e-6, obs_std * 0.5)) for _ in range(self.num_particles)]
+            return
+        probs = [w / total for w in weights]
+
+        # multinomial resampling
+        cumulative = []
+        c = 0.0
+        for p in probs:
+            c += p
+            cumulative.append(c)
+
+        new_particles = []
+        for _ in range(self.num_particles):
+            u = self.rng.random()
+            # find first cumulative >= u
+            for idx, c in enumerate(cumulative):
+                if u <= c:
+                    new_particles.append(self.particles[idx])
+                    break
+            else:
+                new_particles.append(self.particles[-1])
+
+        # jitter with small gaussian noise proportional to obs_std
+        jitter_scale = max(1e-3, obs_std * 0.01)
+        self.particles = [p + self.rng.gauss(0.0, jitter_scale) for p in new_particles]
+
+    def pov(self, threshold: float, operator: str = ">") -> float:
+        """Return probability-of-violation (PoV) that the scalar meets the
+        violation predicate defined by (operator, threshold). Supported
+        operators: '>' (default), '<', '>=', '<='.
+        """
+        if operator == ">":
+            count = sum(1 for p in self.particles if p > threshold)
+        elif operator == "<":
+            count = sum(1 for p in self.particles if p < threshold)
+        elif operator == ">=":
+            count = sum(1 for p in self.particles if p >= threshold)
+        elif operator == "<=":
+            count = sum(1 for p in self.particles if p <= threshold)
+        else:
+            raise ValueError(f"unsupported operator: {operator}")
+        return float(count) / float(len(self.particles))
+
+    def entropy(self) -> float:
+        """Return a simple continuous-entropy proxy (Gaussian entropy using
+        empirical variance). This is cheap and stable for small sketches.
+        """
+        n = len(self.particles)
+        if n == 0:
+            return 0.0
+        mean = sum(self.particles) / n
+        var = sum((p - mean) ** 2 for p in self.particles) / n
+        var = max(var, 1e-12)
+        # differential entropy of Gaussian: 0.5*ln(2*pi*e*var)
+        return 0.5 * math.log(2 * math.pi * math.e * var)
+
+    def summarize(self, threshold: float, operator: str = ">") -> dict:
+        """Return a compact summary dictionary with PoV and entropy.
+        """
+        return {"name": self.name, "pov": self.pov(threshold, operator), "entropy": self.entropy()}
+
+    def serialize(self) -> bytes:
+        """Produce a tiny deterministic byte fingerprint of the sketch. Format:
+        8 bytes mean (double) + 8 bytes variance (double) + 8 bytes crc64-like
+        truncated using sha256. This keeps the sketch small (<64 bytes).
+        """
+        n = len(self.particles)
+        mean = sum(self.particles) / n if n else 0.0
+        var = sum((p - mean) ** 2 for p in self.particles) / n if n else 0.0
+        packed = struct.pack("!dd", mean, var)
+        digest = hashlib.sha256(packed).digest()[:16]
+        return packed + digest
diff --git a/src/guardrail_space/contract.py b/src/guardrail_space/contract.py
index 30ccbdb..4a227c5 100644
--- a/src/guardrail_space/contract.py
+++ b/src/guardrail_space/contract.py
@@ -1,76 +1,216 @@
-from typing import Dict, Any, Optional, List
-from .policy_engine import PolicyEngine
+from dataclasses import dataclass, field
+from typing import Any, Dict, Optional, List, Tuple
+
+
+def safe_eval(expr: Optional[str], context: Dict[str, Any]) -> bool:
+    """Safely evaluate a simple boolean expression string against context.
+
+    This is intentionally tiny: no builtins are exposed and evaluation failures
+    return False. Legacy contract expressions expect `state` to be available.
+    """
+    if not expr:
+        return True
+    allowed_globals = {"__builtins__": {}}
+    local = dict(context or {})
+    if "state" not in local:
+        local = {**local, "state": dict(context or {})}
+    try:
+        return bool(eval(expr, allowed_globals, local))
+    except Exception:
+        return False
+
+
+@dataclass
+class Precondition:
+    """A simple precondition that checks a predicate on the state and action.
+
+    The predicate is a callable(state, action) -> bool. For this MVP we accept
+    a dict-based predicate described by keys to compare (simple operators).
+    """
+    key: str
+    op: str
+    value: Any
+
+    def check(self, state: Dict[str, Any], action: Dict[str, Any]) -> bool:
+        # Supports keys like 'state.battery' or 'action.energy'
+        target = state if self.key.startswith("state.") or not self.key.startswith("action.") else action
+        if self.key.startswith("state."):
+            k = self.key.split("state.", 1)[1]
+            val = state.get(k)
+        elif self.key.startswith("action."):
+            k = self.key.split("action.", 1)[1]
+            val = action.get(k)
+        else:
+            val = state.get(self.key)
+
+        if self.op == ">=":
+            return val >= self.value
+        if self.op == "<=":
+            return val <= self.value
+        if self.op == ">":
+            return val > self.value
+        if self.op == "<":
+            return val < self.value
+        if self.op == "==":
+            return val == self.value
+        if self.op == "!=":
+            return val != self.value
+        return False
+
+
+@dataclass
+class Postcondition:
+    key: str
+    op: str
+    value: Any
+
+    def check(self, state: Dict[str, Any], action: Dict[str, Any], next_state: Dict[str, Any]) -> bool:
+        # Similar simple check against next_state
+        val = next_state.get(self.key)
+        if self.op == ">=":
+            return val >= self.value
+        if self.op == "<=":
+            return val <= self.value
+        if self.op == "==":
+            return val == self.value
+        return False
+
+
+@dataclass
+class Budget:
+    name: str
+    limit: float
+    used: float = 0.0
+
+    def available(self) -> float:
+        return self.limit - self.used
+
+    def consume(self, amount: float) -> bool:
+        if amount <= self.available():
+            self.used += amount
+            return True
+        return False
 
 
 class SafetyContract:
-    """Compatibility wrapper for tests expecting a contract API with
-    pre_conditions, post_conditions, and contract_id/name.
-    This class normalizes inputs to the internal engine which expects
-    string expressions for pre/post and a budgets dict.
+    """Flexible SafetyContract compatible with legacy and dataclass-style construction.
+
+    Legacy tests construct using keyword names like `contract_id`, `pre_conditions` (list of
+    string expressions), `budgets` as a dict, and `collision_rules`. Newer tests may create
+    Precondition/Postcondition dataclasses and pass them via `preconditions`/`postconditions`.
+
+    This class accepts either form and exposes both evaluation helpers and the simpler
+    check_* helpers used by the minimal engine in this package.
     """
 
     def __init__(
         self,
+        id: Optional[str] = None,
         contract_id: Optional[str] = None,
         pre_conditions: Optional[List[str]] = None,
         post_conditions: Optional[List[str]] = None,
-        budgets: Optional[Dict[str, float]] = None,
-        collision_rules: Optional[List[Any]] = None,
-        trust_policy: Optional[Dict[str, Any]] = None,
-        name: Optional[str] = None,
         pre: Optional[str] = None,
         post: Optional[str] = None,
+        preconditions: Optional[List[Precondition]] = None,
+        postconditions: Optional[List[Postcondition]] = None,
+        budgets: Optional[Dict[str, Any]] = None,
+        collision_rules: Optional[List[str]] = None,
+        trust_policy: Optional[Dict[str, Any]] = None,
+        name: Optional[str] = None,
         **kwargs,
     ):
-        # Normalize naming to legacy fields used by tests and engine
-        self.contract_id = contract_id or name or (name if name is not None else None)
-        self.name = self.contract_id
+        # canonical id
+        self.id = id or contract_id or name or kwargs.get("id")
 
-        # Pre/post can be provided as lists or as a single string.
+        # Support both string-expression pre/post (legacy) and dataclass-style
         if pre is not None:
             self.pre = pre
-        else:
-            if pre_conditions is None:
-                self.pre = None
+        elif pre_conditions is not None:
+            if isinstance(pre_conditions, list):
+                self.pre = " and ".join(pre_conditions)
             else:
-                if isinstance(pre_conditions, list):
-                    self.pre = " and ".join(pre_conditions)
-                else:
-                    self.pre = pre_conditions
+                self.pre = pre_conditions
+        else:
+            self.pre = None
 
         if post is not None:
             self.post = post
-        else:
-            if post_conditions is None:
-                self.post = None
+        elif post_conditions is not None:
+            if isinstance(post_conditions, list):
+                self.post = " and ".join(post_conditions)
             else:
-                if isinstance(post_conditions, list):
-                    self.post = " and ".join(post_conditions)
-                else:
-                    self.post = post_conditions
+                self.post = post_conditions
+        else:
+            self.post = None
+
+        # dataclass-style pre/postconditions if provided
+        self.preconditions = preconditions or []
+        self.postconditions = postconditions or []
+
+        # budgets may be passed as simple name->limit dict (legacy) or Budget objects
+        # Maintain both a legacy numeric mapping (self.budgets) for compatibility and
+        # an internal mapping of Budget objects (self._budget_objs) for charging.
+        if budgets is None:
+            self.budgets = {}
+            self._budget_objs = {}
+        else:
+            # If the caller passed Budget objects, preserve that mapping on self.budgets
+            if isinstance(budgets, dict) and all(isinstance(v, Budget) for v in budgets.values()):
+                self.budgets = dict(budgets)
+                self._budget_objs = dict(budgets)
+            else:
+                numeric: Dict[str, float] = {}
+                objs: Dict[str, Budget] = {}
+                if isinstance(budgets, dict):
+                    for k, v in budgets.items():
+                        if isinstance(v, Budget):
+                            objs[k] = v
+                            numeric[k] = v.limit
+                        else:
+                            try:
+                                numeric[k] = float(v)
+                                objs[k] = Budget(name=k, limit=float(v), used=0.0)
+                            except Exception:
+                                # ignore invalid entries
+                                pass
+                self.budgets = numeric
+                self._budget_objs = objs
+
+        # Expose legacy 'contract_id' for compatibility with other modules
+        self.contract_id = self.id
 
-        self.budgets = budgets or {}
         self.collision_rules = collision_rules or []
         self.trust_policy = trust_policy or {}
 
-    def evaluate_pre(self, context: Dict[str, Any]) -> (bool, str):
-        engine = PolicyEngine(self)
-        # Pass a neutral action payload; tests use only context.
-        ok, _reason = engine.evaluate_pre({"action": None}, context)
-        # Legacy API expected a boolean result.
-        return bool(ok)
+    # --- Compatibility helpers expected by policy/guard modules ---
+    def evaluate_pre(self, context: Dict[str, Any]) -> bool:
+        # context is typically the state dict; safe_eval will use 'state' alias
+        return bool(safe_eval(self.pre, context))
 
-    def evaluate_post(self, action: Dict[str, Any], context: Dict[str, Any]) -> (bool, str):
-        engine = PolicyEngine(self)
-        ok, _reason = engine.evaluate_post(action, context)
-        return bool(ok)
+    def evaluate_post(self, action: Dict[str, Any], context: Dict[str, Any]) -> bool:
+        eval_ctx = {**context, "action": action}
+        return bool(safe_eval(self.post, eval_ctx))
 
-    def to_dict(self) -> Dict[str, Any]:
-        return {
-            "name": self.name,
-            "pre": self.pre,
-            "post": self.post,
-            "budgets": self.budgets,
-            "collision_rules": self.collision_rules,
-            "trust_policy": self.trust_policy,
-        }
+    # --- Newer-style helpers ---
+    def check_preconditions(self, state: Dict[str, Any], action: Dict[str, Any]) -> Tuple[bool, Optional[str]]:
+        for p in self.preconditions:
+            if not p.check(state, action):
+                return False, f"precondition failed: {p.key} {p.op} {p.value}"
+        return True, None
+
+    def check_budgets(self, state: Dict[str, Any], action: Dict[str, Any]) -> Tuple[bool, Optional[str]]:
+        costs = action.get("costs", {})
+        for name, amt in costs.items():
+            b = self._budget_objs.get(name)
+            if b is None:
+                return False, f"unknown budget: {name}"
+            if amt > b.available():
+                return False, f"budget exceeded: {name} wants {amt} available {b.available()}"
+        return True, None
+
+    def charge_budgets(self, action: Dict[str, Any]):
+        costs = action.get("costs", {})
+        for name, amt in costs.items():
+            b = self._budget_objs.get(name)
+            if b is not None:
+                b.consume(amt)
diff --git a/src/guardrail_space/engine.py b/src/guardrail_space/engine.py
new file mode 100644
index 0000000..71f418d
--- /dev/null
+++ b/src/guardrail_space/engine.py
@@ -0,0 +1,38 @@
+from typing import Dict, Any, Tuple
+from .contract import SafetyContract
+
+
+def evaluate_action(contract: SafetyContract, state: Dict[str, Any], action: Dict[str, Any]) -> Tuple[str, Dict[str, Any]]:
+    """Evaluate a proposed action against a SafetyContract.
+
+    Returns a tuple (verdict, payload) where verdict is one of:
+    - 'accept' (payload is possibly rewritten action)
+    - 'veto' (payload contains reason)
+
+    This minimal engine performs precondition and budget checks and may
+    rewrite actions to a safe alternative when possible.
+    """
+    ok, reason = contract.check_preconditions(state, action)
+    if not ok:
+        return "veto", {"reason": reason}
+
+    ok, reason = contract.check_budgets(state, action)
+    if not ok:
+        # attempt a simple rewrite: scale down costs/speeds if present
+        if "speed" in action:
+            safe_action = dict(action)
+            safe_action["speed"] = action["speed"] * 0.5
+            # Re-check budgets assuming cost scales with speed linearly
+            costs = dict(action.get("costs", {}))
+            for k in costs:
+                costs[k] = costs[k] * 0.5
+            safe_action["costs"] = costs
+            ok2, reason2 = contract.check_budgets(state, safe_action)
+            if ok2:
+                contract.charge_budgets(safe_action)
+                return "accept", safe_action
+        return "veto", {"reason": reason}
+
+    # Accept and charge budgets
+    contract.charge_budgets(action)
+    return "accept", action
diff --git a/tests/test_belief.py b/tests/test_belief.py
new file mode 100644
index 0000000..54d6d37
--- /dev/null
+++ b/tests/test_belief.py
@@ -0,0 +1,36 @@
+from guardrail_space.belief import BeliefSketch
+
+
+def test_belief_pov_and_entropy_deterministic():
+    # deterministic seed so CI results are reproducible
+    sketch = BeliefSketch("obstacle_dist", num_particles=128, prior_mean=0.0, prior_std=1.0, seed=42)
+
+    # an observation far above the prior should push mass upward
+    sketch.update(observation=5.0, obs_std=0.5)
+
+    pov = sketch.pov(threshold=3.0, operator=">")
+    ent = sketch.entropy()
+
+    # After a strong observation at 5.0 most particles should be >3.0
+    assert pov > 0.8
+
+    # entropy should be a finite positive number
+    assert isinstance(ent, float)
+    assert ent > 0.0
+
+
+def test_serialize_small_and_deterministic():
+    s1 = BeliefSketch("battery", num_particles=32, prior_mean=10.0, prior_std=2.0, seed=7)
+    s2 = BeliefSketch("battery", num_particles=32, prior_mean=10.0, prior_std=2.0, seed=7)
+
+    s1.update(9.5, obs_std=0.5)
+    s2.update(9.5, obs_std=0.5)
+
+    b1 = s1.serialize()
+    b2 = s2.serialize()
+
+    # deterministic with same seed and ops
+    assert b1 == b2
+
+    # compact
+    assert len(b1) <= 40