feat(rules): add ongoing spell damage

Acid Arrow (SRD spells/acid-arrow.md) deals 2d4 acid, then 2d4 again at the start of each of the target's turns for 1 round + 1 per three caster levels (max 6). DamageEffect gains a RecurringDamageSpec (JSON 'recurring'); a landed hit attaches a RecurringDamage source to CombatantState.recurring_damage, ticked in _turn_gate (after bleed), reduced by energy resistance/immunity but never DR (spell damage), cleared at expiry, and exposed in the observation snapshot. Extracted _resolve_one_projectile to keep _apply_damage_effect under the complexity ceiling. Updated acid_arrow.json, added tests/test_recurring_damage.py, and the README.

Ultraworked with [Sisyphus](https://github.com/code-yeongyu/oh-my-openagent)

Co-authored-by: Sisyphus <clio-agent@sisyphuslabs.ai>

README.md

@@ -961,6 +961,22 @@ Règles modélisées :
   Missile (auto-touché, pas d'attaque) et Scorching Ray sont ainsi SRD-conformes
   sur le nombre de projectiles ; la fiche dorée du liche (niveau d'incanteur 11)
   tire désormais ses cinq missiles.
+- Dégâts récurrents de sort (S2c) : un `DamageEffect` peut déclarer
+  `"recurring": {"formula": "2d4", "types": ["acid"], "base_rounds": 1,
+  "per_levels": 3, "max": 6}` — le nombre de rounds de récurrence vaut
+  `base_rounds + niveau // per_levels`, plafonné à `max` (SRD Acid Arrow :
+  « For every three caster levels you possess, the acid [...] lasts for another
+  round [...] dealing another 2d4 points of damage in each round » → 1 round au
+  niveau 1, 2 au niveau 3, 6 au niveau 18+). À l'attaque initiale réussie, une
+  source de dégâts récurrents (`RecurringDamage` sur le `CombatantState`, liste
+  `recurring_damage`) est posée sur la cible vivante ; au **début du tour** de
+  la cible (dans `_turn_gate`, après le tick de saignement), chaque source
+  jetle ses dés, est **réduite par la résistance/immunité énergétique** (acide)
+  mais **jamais par la RD** (c'est un dégât de sort), inflige ce dégât, puis
+  perd un round ; arrivée à 0 round elle est retirée. L'observation expose
+  chaque source sous `recurring_damage` (`{formula, types, rounds_left}`).
+  Simplification documentée : la neutralisation d'acide (immersion/eau) n'est
+  pas modélisée — le dégât court jusqu'à l'expiration de sa durée.
 - Résistance aux sorts (SR) et résistances/immunités énergétiques : un combattant
   avec `spell_resistance > 0` oppose sa SR à chaque sort qui le cible — jet
   `d20 + niveau du jeteur` contre la SR ; si le total est inférieur, le sort est
@@ -1340,7 +1356,10 @@ Règles modélisées :
     son tour), running (bool — course en cours jusqu'au prochain tour du
     combattant : il perd son bonus de Dextérité à la CA), bleed_damage (int —
     dégâts de saignement subis au début du tour du combattant, 0 = ne saigne
-    pas ; V5b ; `bleeding`/`confused` sont visibles via `conditions`).
+    pas ; V5b ; `bleeding`/`confused` sont visibles via `conditions`),
+    recurring_damage (S2c — liste des sources de dégâts récurrents de sort
+    actives, chacune `{formula, types, rounds_left}` ; tick au début du tour,
+    réduit par résistance énergétique, jamais par la RD).
   - Par paire combattant actif × cible : target_index, distance_ft, weapon_for,
     range_penalty, can_charge, can_step5_to_attack, has_line_of_effect,
     flanking, movement_cost_ft, target_threatens_me, enemies_threatening_me,
@@ -1415,13 +1434,6 @@ plutôt que bricolées) :
 Limites de sorts (conformance D6-D9, documentées plutôt que bricolées — le
 moteur n'a pas encore de sauvegarde partielle) :
 
-- **Acid Arrow — sans dégâts continus** (SRD spells/acid-arrow.md : portée
-  **longue** — corrigée, conformance D7 — et « For every three caster levels
-  you possess, the acid, unless neutralized, lasts for another round [...],
-  dealing another 2d4 points of damage in each round ») : le moteur n'a pas de
-  subsystem de dégâts continus par sort (ni neutralisation d'acide) ; seuls les
-  2d4 de dégâts initiaux sont modélisés, les rounds de dégâts persistants sont
-  hors périmètre.
 - **Fear — sauvegarde totale** (SRD spells/fear.md : « each
   living creature in the area [...] becomes panicked unless it succeeds on a
   Will save [...]. If the Will save succeeds, the creature is shaken for 1

data/spells/acid_arrow.json

@@ -12,8 +12,15 @@
       "type": "damage",
       "formula": "2d4",
       "types": ["acid"],
-      "half_on_save": false
+      "half_on_save": false,
+      "recurring": {
+        "formula": "2d4",
+        "types": ["acid"],
+        "base_rounds": 1,
+        "per_levels": 3,
+        "max": 6
+      }
     }
   ],
-  "description": "SRD spells/acid-arrow.md: ranged touch attack dealing 2d4 acid damage, plus another 2d4 per round for 1 extra round per three caster levels (max 6 additional rounds). The engine has no damage-over-time subsystem, so only the initial 2d4 is modeled - the ongoing acid is documented as a limitation. No save."
+  "description": "SRD spells/acid-arrow.md: ranged touch attack dealing 2d4 acid damage, plus another 2d4 acid damage at the start of each of the target's turns for 1 round + 1 round per three caster levels (maximum 6 additional rounds). Recurring damage is reduced by energy resistance/immunity, not by DR. No save."
 }

src/pf1e_simulator/combat.py

@@ -123,7 +123,7 @@ from typing import TYPE_CHECKING, Literal
 
 from pf1e_simulator.areas import cone_cells, line_cells
 from pf1e_simulator.conditions import CONDITIONS_BY_NAME, Condition
-from pf1e_simulator.dice import dice_to_str
+from pf1e_simulator.dice import DiceExpr, dice_to_str
 from pf1e_simulator.effects import ActiveBuff, ActiveCondition, StatModifier, resolve_modifiers
 from pf1e_simulator.loaders.combatant import CombatantLoadError, load_combatant
 from pf1e_simulator.models import PREDEFINED_SKILLS
@@ -134,6 +134,7 @@ from pf1e_simulator.spells import (
     ConditionEffect,
     DamageEffect,
     HealEffect,
+    RecurringDamageSpec,
     SaveType,
     SpellEffect,
     SummonEffect,
@@ -560,6 +561,23 @@ def _is_pc_combatant(combatant: Combatant) -> bool:
     return combatant.source.startswith(_PC_SOURCE_PREFIX)
 
 
+@dataclass(frozen=True)
+class RecurringDamage:
+    """One active damage-over-time source on a combatant (S2c, Acid Arrow).
+
+    - ``formula``: dice rolled each recurring round (2d4)
+    - ``types``: energy types, reduced by resistance/immunity (never DR)
+    - ``rounds_left``: rounds this source still deals damage (decremented and
+      removed at the start of the owner's turn once it ticks)
+    - ``source``: human-readable origin for the transcript
+    """
+
+    formula: DiceExpr
+    types: frozenset[str]
+    rounds_left: int
+    source: str
+
+
 @dataclass
 class CombatantState:
     """Mutable runtime state of one combatant on the grid."""
@@ -633,6 +651,11 @@ class CombatantState:
     # Bleeding (V5b, not in the frozen data model): damage taken at the start
     # of each turn; any effect that restores hit points clears it.
     bleed_damage: int = 0
+    # PF1e recurring spell damage (S2c, not in the frozen data model): each
+    # entry is one damage-over-time source (Acid Arrow's lingering acid) that
+    # deals its dice at the start of this combatant's turn for `rounds_left`
+    # rounds, reduced by energy resistance/immunity (never DR).
+    recurring_damage: list[RecurringDamage] = field(default_factory=list)
 
     def usable_attacks(self) -> list[AttackSpec]:
         return [
@@ -1303,6 +1326,14 @@ class CombatEngine:
             "aid_ac_bonus": state.aid_ac_bonus,
             "running": state.running,
             "bleed_damage": state.bleed_damage,
+            "recurring_damage": [
+                {
+                    "formula": dice_to_str(entry.formula),
+                    "types": tuple(sorted(entry.types)),
+                    "rounds_left": entry.rounds_left,
+                }
+                for entry in state.recurring_damage
+            ],
             "aoo_remaining": max(
                 0,
                 self._aoo_allowance(state) - self._aoo_used.get(state.combatant.id, 0),
@@ -1796,15 +1827,17 @@ class CombatEngine:
             state.bleed_damage = 0
 
     def _turn_gate(self, state: CombatantState) -> bool | None:
-        """Start-of-turn effects: bleed tick, confused d% roll, cant_act flag.
+        """Start-of-turn effects: bleed tick, recurring spell damage, confused
+        d% roll, cant_act flag.
 
         Returns None when the turn proceeds to the policy; otherwise the turn
         is forfeited and the value is the battle-over flag.
         """
         self._apply_bleed_damage(state)
+        self._apply_recurring_damage(state)
         if not state.active:
-            # Bleeding knocked the combatant out (dying or dead); the winner
-            # check covers the death case.
+            # Bleeding / acid knocked the combatant out (dying or dead); the
+            # winner check covers the death case.
             return self._winner_side() is not None
         confused_over = self._apply_confusion(state)
         if confused_over is not None:
@@ -1825,6 +1858,34 @@ class CombatEngine:
             f"bleed {state.bleed_damage} (hp {old_hp}->{state.hp})"
         )
 
+    def _apply_recurring_damage(self, state: CombatantState) -> None:
+        """PF1e recurring spell damage (S2c, Acid Arrow): at the start of the
+        owner's turn each active source rolls its dice, is reduced by energy
+        resistance/immunity (never DR — it is spell damage), deals that damage,
+        then loses one round; sources that reach 0 rounds are cleared."""
+        if not state.recurring_damage:
+            return
+        remaining: list[RecurringDamage] = []
+        for entry in state.recurring_damage:
+            raw = entry.formula.roll(self._rng)
+            dmg = self._apply_energy_resistance(raw, entry.types, state)
+            old_hp = state.hp
+            state.hp -= dmg
+            self._log(
+                f"round {self._current_round} {state.combatant.id}: "
+                f"{entry.source} {dmg} (hp {old_hp}->{state.hp})"
+            )
+            if entry.rounds_left > 1:
+                remaining.append(
+                    RecurringDamage(
+                        formula=entry.formula,
+                        types=entry.types,
+                        rounds_left=entry.rounds_left - 1,
+                        source=entry.source,
+                    )
+                )
+        state.recurring_damage[:] = remaining
+
     def _apply_confusion(self, state: CombatantState) -> bool | None:
         """PF1e confused: roll d% at the start of the turn to act randomly (CRB).
 
@@ -5804,6 +5865,7 @@ class CombatEngine:
                 effect, target, caster_live, target_live,
                 saved=saved, empower=empower, maximize=maximize, caster=caster,
                 crit=crit, ranged_touch=ranged_touch, attack_penalty=attack_penalty,
+                spell_name=spell_name,
             )
         if isinstance(effect, ConditionEffect):
             return self._apply_condition_effect(effect, target, saved=saved, spell_name=spell_name)
@@ -5825,6 +5887,7 @@ class CombatEngine:
         crit: bool = False,
         ranged_touch: bool = False,
         attack_penalty: int = 0,
+        spell_name: str = "",
     ) -> str:
         # PF1e (CRB, Magic — Caster Level): per-level spell damage is resolved
         # against the caster's level at cast time; the scaled formula then
@@ -5842,34 +5905,13 @@ class CombatEngine:
         )
         total = 0
         for _ in range(count):
-            proj_crit = crit
-            if ranged_touch:
-                # Each ray rolls its own ranged touch attack (cover,
-                # concealment and critical threat included).
-                hit, proj_crit = self._spell_ranged_touch_attack_hits(
-                    caster, target,
-                    attack_penalty=attack_penalty, deals_damage=True,
-                )
-                if not hit:
-                    continue
-            raw = formula.roll(self._rng)
-            if maximize:
-                raw = formula.max_value()
-            if proj_crit:
-                # PF1e (CRB "Range — Touch"): a touch/ranged-touch spell that
-                # deals damage threatens on a natural 20 and deals double
-                # damage on a successful critical hit.
-                raw *= 2
-            if saved and effect.half_on_save:
-                dmg = max(0, raw // 2)
-            elif saved and effect.save_negates:
-                dmg = 0
-            else:
-                dmg = raw
-            if empower:
-                dmg = int(dmg * 1.5)
-            dmg = self._apply_energy_resistance(dmg, frozenset(effect.types), target)
-            target.hp -= dmg
+            dmg = self._resolve_one_projectile(
+                effect, formula, target, caster,
+                saved=saved, empower=empower, maximize=maximize,
+                crit=crit, ranged_touch=ranged_touch, attack_penalty=attack_penalty,
+            )
+            if dmg is None:
+                continue  # this ray missed — no damage, no stat/reaction
             caster_live.damage_dealt += dmg
             target_live.damage_taken += dmg
             self._check_reactions(
@@ -5882,8 +5924,83 @@ class CombatEngine:
             # are lost (the engine's existing multi-attack convention).
             if not target.active:
                 break
+        # PF1e recurring damage (S2c, Acid Arrow): a landed hit leaves acid
+        # that keeps burning for rounds_for(caster_level) rounds. Only attached
+        # while the target is still standing (a dead target has no turns).
+        if effect.recurring is not None and target.active:
+            self._attach_recurring_damage(effect.recurring, target, caster, spell_name)
         return f"{total} damage"
 
+    def _resolve_one_projectile(
+        self,
+        effect: DamageEffect,
+        formula: DiceExpr,
+        target: CombatantState,
+        caster: CombatantState,
+        *,
+        saved: bool,
+        empower: bool,
+        maximize: bool,
+        crit: bool,
+        ranged_touch: bool,
+        attack_penalty: int,
+    ) -> int | None:
+        """Resolve one projectile's hit + damage; None when the ray misses.
+
+        Rolls the projectile's own ranged touch attack (when the spell is a
+        ray), then its own damage dice through maximize / crit / save /
+        empower / energy resistance, and applies the damage to the target.
+        """
+        proj_crit = crit
+        if ranged_touch:
+            # Each ray rolls its own ranged touch attack (cover, concealment
+            # and critical threat included).
+            hit, proj_crit = self._spell_ranged_touch_attack_hits(
+                caster, target,
+                attack_penalty=attack_penalty, deals_damage=True,
+            )
+            if not hit:
+                return None
+        raw = formula.roll(self._rng)
+        if maximize:
+            raw = formula.max_value()
+        if proj_crit:
+            # PF1e (CRB "Range — Touch"): a touch/ranged-touch spell that
+            # deals damage threatens on a natural 20 and deals double
+            # damage on a successful critical hit.
+            raw *= 2
+        if saved and effect.half_on_save:
+            dmg = max(0, raw // 2)
+        elif saved and effect.save_negates:
+            dmg = 0
+        else:
+            dmg = raw
+        if empower:
+            dmg = int(dmg * 1.5)
+        dmg = self._apply_energy_resistance(dmg, frozenset(effect.types), target)
+        target.hp -= dmg
+        return dmg
+
+    def _attach_recurring_damage(
+        self,
+        spec: RecurringDamageSpec,
+        target: CombatantState,
+        caster: CombatantState,
+        spell_name: str,
+    ) -> None:
+        """Add a recurring-damage source to a target that just took the hit."""
+        rounds = spec.rounds_for(caster.combatant.level)
+        if rounds <= 0:
+            return
+        target.recurring_damage.append(
+            RecurringDamage(
+                formula=spec.formula,
+                types=frozenset(spec.types),
+                rounds_left=rounds,
+                source=f"acid: {spell_name}",
+            )
+        )
+
     def _apply_condition_effect(
         self,
         effect: ConditionEffect,

src/pf1e_simulator/spells.py

@@ -93,6 +93,29 @@ class ProjectileScaling:
         return min(self.max_projectiles, self.base + extra)
 
 
+@dataclass(frozen=True)
+class RecurringDamageSpec:
+    """Per-round recurring spell damage (PF1e Acid Arrow).
+
+    - formula: dice rolled in each recurring round (2d4)
+    - types: energy types (acid) — reduced by energy resistance/immunity,
+      never by DR (it is spell damage)
+    - base_rounds / per_levels / max_rounds: rounds of recurrence scale with
+      caster level as ``base_rounds + caster_level // per_levels`` capped at
+      ``max_rounds`` (SRD spells/acid-arrow.md: "1 round + 1 round per three
+      levels [...] to a maximum of 6 additional rounds").
+    """
+    formula: DiceExpr
+    types: tuple[str, ...]
+    base_rounds: int
+    per_levels: int
+    max_rounds: int
+
+    def rounds_for(self, caster_level: int) -> int:
+        """Recurring rounds for a caster of ``caster_level``."""
+        return min(self.max_rounds, self.base_rounds + caster_level // self.per_levels)
+
+
 @dataclass(frozen=True)
 class DamageEffect:
     formula: DiceExpr
@@ -113,6 +136,10 @@ class DamageEffect:
     # fires `count_for(caster_level)` projectiles, each rolling its own damage
     # and (for a ray) its own attack. Absent = a single projectile.
     projectiles: ProjectileScaling | None = None
+    # PF1e recurring (damage-over-time) component (Acid Arrow): after the
+    # initial hit the target takes this damage again at the start of each of
+    # its turns for `rounds_for(caster_level)` rounds. Absent = no DoT.
+    recurring: RecurringDamageSpec | None = None
 
     def effective_formula(self, caster_level: int) -> DiceExpr:
         """The damage formula resolved for a caster of ``caster_level``.
@@ -417,6 +444,30 @@ def _parse_projectiles(value: Json) -> ProjectileScaling:
     )
 
 
+def _parse_recurring(value: Json) -> RecurringDamageSpec:
+    data = _as_dict(value)
+    formula = parse_dice(_as_str(data["formula"]))
+    base_rounds = _as_int(data.get("base_rounds", 1))
+    per_levels = _as_int(data["per_levels"])
+    max_rounds = _as_int(data["max"])
+    if base_rounds < 0:
+        msg = f"recurring base_rounds must be >= 0, got {base_rounds}"
+        raise ValueError(msg)
+    if per_levels < 1:
+        msg = f"recurring per_levels must be >= 1, got {per_levels}"
+        raise ValueError(msg)
+    if max_rounds < base_rounds:
+        msg = f"recurring max must be >= base_rounds, got {max_rounds} < {base_rounds}"
+        raise ValueError(msg)
+    return RecurringDamageSpec(
+        formula=formula,
+        types=tuple(_as_str(t) for t in _as_list(data["types"])),
+        base_rounds=base_rounds,
+        per_levels=per_levels,
+        max_rounds=max_rounds,
+    )
+
+
 def _parse_effect(data: Json) -> SpellEffect:
     effect = _as_dict(data)
     effect_type = _as_str(effect["type"])
@@ -438,6 +489,8 @@ def _parse_effect(data: Json) -> SpellEffect:
         scaling_flat = None if flat_raw is None else _parse_flat_scaling(flat_raw)
         proj_raw = effect.get("projectiles")
         projectiles = None if proj_raw is None else _parse_projectiles(proj_raw)
+        rec_raw = effect.get("recurring")
+        recurring = None if rec_raw is None else _parse_recurring(rec_raw)
         return DamageEffect(
             formula=formula,
             types=tuple(_as_str(t) for t in _as_list(effect["types"])),
@@ -446,6 +499,7 @@ def _parse_effect(data: Json) -> SpellEffect:
             scaling=scaling,
             scaling_flat=scaling_flat,
             projectiles=projectiles,
+            recurring=recurring,
         )
     if effect_type == "condition":
         return ConditionEffect(

tests/test_recurring_damage.py

@@ -0,0 +1,244 @@
+"""Ongoing (recurring) spell damage (Package S2c).
+
+PF1e (SRD spells/acid-arrow.md): "The arrow deals 2d4 points of acid damage
+[...] For every three caster levels you possess, the acid, unless neutralized,
+lasts for another round (to a maximum of 6 additional rounds at 18th level),
+dealing another 2d4 points of damage in each round."
+
+The recurring component ticks at the START of the affected creature's turn, is
+reduced by energy resistance/immunity (acid) but NOT by DR (it is spell
+damage), and is cleared when its rounds run out.
+"""
+
+from __future__ import annotations
+
+from pathlib import Path
+
+from pf1e_simulator.combat import CombatantState, CombatEngine
+from pf1e_simulator.dice import parse_dice
+from pf1e_simulator.grid import Grid
+from pf1e_simulator.map import MapSpec, TerrainType
+from pf1e_simulator.models import (
+    AbilityScores,
+    ACProfile,
+    AttackSpec,
+    Combatant,
+    DamageComponent,
+    DamageReduction,
+    Saves,
+)
+from pf1e_simulator.rng import ScriptedRng
+from pf1e_simulator.spells import DamageEffect, load_spell, load_spell_registry
+
+_SPELLS_DIR = Path(__file__).resolve().parent.parent / "data" / "spells"
+
+
+def _caster(cid: str = "caster", *, level: int = 1) -> Combatant:
+    attack = AttackSpec(
+        id=f"{cid}-w",
+        name="dagger",
+        kind="melee",
+        attack_bonus=2,
+        damage=[DamageComponent(formula=parse_dice("1d4"), types=["piercing"])],
+    )
+    return Combatant(
+        id=cid,
+        name=cid,
+        level=level,
+        size="Medium",
+        abilities=AbilityScores(
+            str_score=10, dex_score=14, con_score=12,
+            int_score=18, wis_score=12, cha_score=10,
+        ),
+        hp_max=40,
+        ac=ACProfile(total=12, touch=12, flat_footed=10),
+        bab=2,
+        initiative_mod=2,
+        speed_land_ft=30,
+        saves=Saves(fort=3, ref=4, will=4),
+        attacks=[attack],
+        casting_ability="int",
+        spell_slots={0: 99, 1: 99, 2: 99, 3: 99, 4: 99, 5: 99, 6: 99},
+    )
+
+
+def _victim(
+    cid: str = "victim",
+    *,
+    hp_max: int = 200,
+    resistances: dict[str, int] | None = None,
+    dr: DamageReduction | None = None,
+) -> Combatant:
+    return Combatant(
+        id=cid,
+        name=cid,
+        level=1,
+        size="Medium",
+        abilities=AbilityScores(
+            str_score=10, dex_score=10, con_score=10,
+            int_score=10, wis_score=10, cha_score=10,
+        ),
+        hp_max=hp_max,
+        ac=ACProfile(total=10, touch=10, flat_footed=10),
+        bab=1,
+        initiative_mod=0,
+        speed_land_ft=30,
+        saves=Saves(fort=2, ref=2, will=2),
+        attacks=[],
+        resistances=resistances or {},
+        dr=dr,
+    )
+
+
+def _grid() -> Grid:
+    legend = {".": TerrainType(type="floor", move_cost=1)}
+    spec = MapSpec(name="test", terrain=tuple(["." * 12] * 12), legend=legend)
+    return Grid.from_spec(spec)
+
+
+def _engine(
+    caster: Combatant,
+    victim: Combatant,
+    queue: list[int],
+) -> tuple[CombatEngine, CombatantState, CombatantState]:
+    c = CombatantState(combatant=caster, side="players", pos=(0, 0), hp=caster.hp_max)
+    v = CombatantState(combatant=victim, side="monsters", pos=(3, 0), hp=victim.hp_max)
+    reg = load_spell_registry(_SPELLS_DIR)
+    engine = CombatEngine(ScriptedRng(queue), _grid(), [c, v], spell_registry=reg)
+    return engine, c, v
+
+
+def _acid_rounds(level: int) -> int:
+    spell = load_spell(_SPELLS_DIR / "acid_arrow.json")
+    effect = spell.effects[0]
+    assert isinstance(effect, DamageEffect)
+    assert effect.recurring is not None
+    return effect.recurring.rounds_for(level)
+
+
+class TestAcidArrowRecurringRounds:
+    """Given: Acid Arrow's recurring scaling (1 + one round per three levels,
+    max 6)
+    When: resolved for caster levels 1 / 3 / 18
+    Then: it is 1 / 2 / 6 rounds (SRD spells/acid-arrow.md)."""
+
+    def test_one_round_at_low_level(self) -> None:
+        assert _acid_rounds(1) == 1
+
+    def test_two_rounds_at_level_3(self) -> None:
+        assert _acid_rounds(3) == 2
+
+    def test_caps_at_six(self) -> None:
+        assert _acid_rounds(18) == 6
+        assert _acid_rounds(20) == 6
+
+
+class TestAcidArrowAttachesRecurring:
+    """Given: a level-1 caster (1 recurring round) hits with Acid Arrow
+    When: the ranged touch attack lands
+    Then: the initial 2d4 is dealt AND one recurring source is attached."""
+
+    def test_initial_hit_attaches_source(self) -> None:
+        caster = _caster(level=1)
+        victim = _victim(hp_max=200)
+        # ranged touch attack d20=15 (hits AC 10), then 2d4 initial (3+3=6)
+        engine, c, v = _engine(caster, victim, [15, 3, 3])
+        engine._cast_spell(c, v, "Acid Arrow")
+        assert v.hp == 200 - 6
+        assert len(v.recurring_damage) == 1
+        assert v.recurring_damage[0].rounds_left == 1
+
+
+class TestRecurringTicksEachRound:
+    """Given: a level-3 caster (2 recurring rounds) hits with Acid Arrow
+    When: the victim's turn starts twice
+    Then: the acid deals 2d4 on each of the two turns, then clears."""
+
+    def test_ticks_then_expires(self) -> None:
+        caster = _caster(level=3)
+        victim = _victim(hp_max=200)
+        # attack (15) + initial 2d4 (3+3) + tick1 2d4 (2+2) + tick2 2d4 (4+4)
+        engine, c, v = _engine(caster, victim, [15, 3, 3, 2, 2, 4, 4])
+        engine._cast_spell(c, v, "Acid Arrow")
+        assert v.hp == 200 - 6
+        assert len(v.recurring_damage) == 1
+        assert v.recurring_damage[0].rounds_left == 2
+        # first turn start: one tick, one round left
+        engine._apply_recurring_damage(v)
+        assert v.hp == 200 - 6 - 4
+        assert len(v.recurring_damage) == 1
+        # second turn start: final tick, then cleared
+        engine._apply_recurring_damage(v)
+        assert v.hp == 200 - 6 - 4 - 8
+        assert v.recurring_damage == []
+
+
+class TestRecurringReducedByEnergyResistance:
+    """Given: a target with acid resistance 5 is burning from Acid Arrow
+    When: the recurring acid ticks
+    Then: each tick's 2d4 is reduced by the resistance (floored at 0)."""
+
+    def test_resistance_reduces_each_tick(self) -> None:
+        caster = _caster(level=1)
+        victim = _victim(hp_max=200, resistances={"acid": 5})
+        # attack (15) + initial 2d4 (4+4=8 -> -5 = 3) + tick 2d4 (3+3=6 -> -5 = 1)
+        engine, c, v = _engine(caster, victim, [15, 4, 4, 3, 3])
+        engine._cast_spell(c, v, "Acid Arrow")
+        assert v.hp == 200 - 3  # initial reduced 8 -> 3
+        engine._apply_recurring_damage(v)
+        assert v.hp == 200 - 3 - 1  # tick reduced 6 -> 1
+
+
+class TestRecurringNotReducedByDR:
+    """Given: a target with damage reduction is burning from Acid Arrow
+    When: the recurring acid ticks
+    Then: DR does NOT reduce the spell's recurring damage (CRB: DR does not
+    negate energy damage from spells)."""
+
+    def test_dr_does_not_touch_recurring(self) -> None:
+        caster = _caster(level=1)
+        victim = _victim(hp_max=200, dr=DamageReduction(amount=10, bypass=("slashing",)))
+        # attack (15) + initial 2d4 (3+3=6) + tick 2d4 (5+5=10)
+        engine, c, v = _engine(caster, victim, [15, 3, 3, 5, 5])
+        engine._cast_spell(c, v, "Acid Arrow")
+        assert v.hp == 200 - 6
+        engine._apply_recurring_damage(v)
+        # DR 10 does not reduce the acid: full 10 dealt
+        assert v.hp == 200 - 6 - 10
+
+
+class TestRecurringImmunityZeroesTick:
+    """Given: an acid-immune target is burning from Acid Arrow
+    When: the recurring acid ticks
+    Then: immunity zeroes the tick damage."""
+
+    def test_immunity_zeroes_tick(self) -> None:
+        caster = _caster(level=1)
+        victim = _victim(hp_max=200)
+        victim = victim.model_copy(update={"immunities": ("acid",)})
+        # attack (15) + initial 2d4 (3+3, immune -> 0) + tick (4+4, immune -> 0)
+        engine, c, v = _engine(caster, victim, [15, 3, 3, 4, 4])
+        engine._cast_spell(c, v, "Acid Arrow")
+        assert v.hp == 200
+        engine._apply_recurring_damage(v)
+        assert v.hp == 200
+
+
+class TestRecurringSnapshot:
+    """Given: a target burning from Acid Arrow
+    When: the observation snapshot is built
+    Then: recurring_damage lists each active source's formula, types and
+    rounds_left."""
+
+    def test_snapshot_exposes_recurring(self) -> None:
+        caster = _caster(level=3)
+        victim = _victim(hp_max=200)
+        engine, c, v = _engine(caster, victim, [15, 3, 3])
+        engine._cast_spell(c, v, "Acid Arrow")
+        obs = engine._build_observation(v).to_dict()
+        entry = next(
+            cb for cb in obs["combatants"] if cb["id"] == "victim"
+        )
+        assert entry["recurring_damage"] == [
+            {"formula": "2d4", "types": ("acid",), "rounds_left": 2}
+        ]