diff --git a/core/CMakeLists.txt b/core/CMakeLists.txt
index a5a07cc..3c11bb9 100644
--- a/core/CMakeLists.txt
+++ b/core/CMakeLists.txt
@@ -3,13 +3,16 @@
 configure_file(src/version_config.hpp.in "${CMAKE_CURRENT_BINARY_DIR}/generated/sequa/core/version_config.hpp" @ONLY)
 
 add_library(sequa_core
-    src/version.cpp)
+    src/version.cpp
+    src/sim/simulation.cpp
+    src/sim/replay.cpp)
 add_library(sequa::core ALIAS sequa_core)
 
 target_include_directories(sequa_core
     PUBLIC
         "${CMAKE_CURRENT_SOURCE_DIR}/include"
     PRIVATE
+        "${CMAKE_CURRENT_SOURCE_DIR}/src"
         "${CMAKE_CURRENT_BINARY_DIR}/generated")
 target_compile_features(sequa_core PUBLIC cxx_std_20)
 sequa_target_defaults(sequa_core)
@@ -17,7 +20,12 @@ sequa_target_defaults(sequa_core)
 if(SEQUA_BUILD_TESTS)
     add_executable(sequa_core_tests
         tests/main.cpp
-        tests/test_version.cpp)
+        tests/test_version.cpp
+        tests/sim/test_fixed.cpp
+        tests/sim/test_rng.cpp
+        tests/sim/test_clock.cpp
+        tests/sim/test_simulation.cpp
+        tests/sim/test_replay.cpp)
     target_link_libraries(sequa_core_tests PRIVATE sequa::core doctest::doctest)
     sequa_target_defaults(sequa_core_tests)
     doctest_discover_tests(sequa_core_tests)
diff --git a/core/README.md b/core/README.md
index f1de7cb..ef95a82 100644
--- a/core/README.md
+++ b/core/README.md
@@ -20,7 +20,19 @@ Core est la **source de vérité** du projet. Il possède :
 
 ## État
 
-Phase 0. Seule la bibliothèque `sequa::core` minimale (version) et son test existent. Prochaine étape : simulation déterministe et test de rejeu.
+Phase 0. Simulation déterministe, enregistrement et rejeu en place (`include/sequa/core/sim/`) :
+
+| Élément | Fichier | Rôle |
+|---|---|---|
+| `Fixed` | `fixed.hpp` | Virgule fixe Q16.16 : calcul entier, identique bit à bit partout |
+| `Pcg32` | `rng.hpp` | Générateur aléatoire SEQUA à graine explicite (PCG32) |
+| `FixedStepClock` | `clock.hpp` | Temps réel vers pas fixes, calcul entier exact, retard plafonné |
+| `Simulation` | `simulation.hpp` | Pas fixe, entrées quantifiées, empreinte FNV-1a de l'état complet |
+| `Recording`, `SessionRecorder`, `replay` | `replay.hpp` | Enregistrement des entrées horodatées, format binaire versionné, rejeu avec d'autres réglages, premier tick divergent |
+
+**SIMULÉ / PROVISOIRE** : le monde est un micro-mode 2D de démonstration (un joueur, un sol, des pièces, réglages de ressenti) qui sert à éprouver le déterminisme avant la vraie scène L0. Il sera remplacé.
+
+Le test « empreinte de référence multiplateforme » fige l'empreinte d'une session d'une minute : toute plateforme doit la retrouver exactement (§10.1, §16).
 
 ## Construire et tester
 
diff --git a/core/include/sequa/core/sim/clock.hpp b/core/include/sequa/core/sim/clock.hpp
new file mode 100644
index 0000000..0910605
--- /dev/null
+++ b/core/include/sequa/core/sim/clock.hpp
@@ -0,0 +1,46 @@
+// SPDX-License-Identifier: MPL-2.0
+#pragma once
+
+#include <cstdint>
+
+namespace sequa::core::sim {
+
+// Convertit le temps réel écoulé en nombre de pas de simulation à fréquence fixe,
+// indépendamment de l'affichage (docs, §5.3). Calcul entier exact : aucun pas n'est
+// perdu ni gagné, même pour des fréquences qui ne divisent pas la seconde (60 Hz).
+class FixedStepClock {
+public:
+    // Préconditions : tick_rate_hz > 0, max_steps_per_advance > 0.
+    explicit FixedStepClock(std::uint32_t tick_rate_hz, std::uint32_t max_steps_per_advance = 8) noexcept
+        : tick_rate_hz_(tick_rate_hz), max_steps_(max_steps_per_advance)
+    {
+    }
+
+    // Retourne le nombre de pas à exécuter pour elapsed_ns nanosecondes écoulées.
+    // Au-delà de max_steps_per_advance, le retard est abandonné (évite la spirale où la
+    // simulation ne rattrape jamais le temps réel) et compté dans dropped_steps().
+    [[nodiscard]] std::uint32_t advance(std::uint64_t elapsed_ns) noexcept
+    {
+        accumulator_ += elapsed_ns * tick_rate_hz_;
+        const std::uint64_t due = accumulator_ / ns_per_second;
+        accumulator_ %= ns_per_second;
+        if (due > max_steps_) {
+            dropped_steps_ += due - max_steps_;
+            return max_steps_;
+        }
+        return static_cast<std::uint32_t>(due);
+    }
+
+    [[nodiscard]] std::uint32_t tick_rate_hz() const noexcept { return tick_rate_hz_; }
+    [[nodiscard]] std::uint64_t dropped_steps() const noexcept { return dropped_steps_; }
+
+private:
+    static constexpr std::uint64_t ns_per_second = 1'000'000'000ull;
+
+    std::uint32_t tick_rate_hz_;
+    std::uint32_t max_steps_;
+    std::uint64_t accumulator_ = 0; // en ns * Hz
+    std::uint64_t dropped_steps_ = 0;
+};
+
+} // namespace sequa::core::sim
diff --git a/core/include/sequa/core/sim/fixed.hpp b/core/include/sequa/core/sim/fixed.hpp
new file mode 100644
index 0000000..6519398
--- /dev/null
+++ b/core/include/sequa/core/sim/fixed.hpp
@@ -0,0 +1,92 @@
+// SPDX-License-Identifier: MPL-2.0
+#pragma once
+
+#include <compare>
+#include <cstdint>
+
+namespace sequa::core::sim {
+
+// Nombre en virgule fixe signé Q16.16.
+//
+// La simulation L0 calcule en entiers pour être identique bit à bit sur toutes les
+// plateformes et tous les compilateurs (docs, §5.3 et §10.1). Les calculs intermédiaires
+// passent par 64 bits ; le retour en 32 bits est modulaire (comportement défini en C++20),
+// donc un dépassement reste déterministe.
+class Fixed {
+public:
+    static constexpr int fraction_bits = 16;
+    static constexpr std::int32_t one_raw = std::int32_t{1} << fraction_bits;
+
+    constexpr Fixed() noexcept = default;
+
+    [[nodiscard]] static constexpr Fixed from_raw(std::int32_t raw) noexcept
+    {
+        Fixed f;
+        f.raw_ = raw;
+        return f;
+    }
+
+    [[nodiscard]] static constexpr Fixed from_int(std::int32_t value) noexcept
+    {
+        return from_raw(narrow(static_cast<std::int64_t>(value) * one_raw));
+    }
+
+    // numerator / denominator, arrondi vers zéro. Précondition : denominator != 0.
+    [[nodiscard]] static constexpr Fixed from_ratio(std::int32_t numerator, std::int32_t denominator) noexcept
+    {
+        return from_raw(narrow((static_cast<std::int64_t>(numerator) * one_raw) / denominator));
+    }
+
+    [[nodiscard]] constexpr std::int32_t raw() const noexcept { return raw_; }
+
+    // Affichage et outils uniquement : jamais dans la simulation.
+    [[nodiscard]] constexpr double to_double() const noexcept { return static_cast<double>(raw_) / one_raw; }
+
+    friend constexpr Fixed operator+(Fixed a, Fixed b) noexcept
+    {
+        return from_raw(narrow(static_cast<std::int64_t>(a.raw_) + b.raw_));
+    }
+    friend constexpr Fixed operator-(Fixed a, Fixed b) noexcept
+    {
+        return from_raw(narrow(static_cast<std::int64_t>(a.raw_) - b.raw_));
+    }
+    friend constexpr Fixed operator-(Fixed a) noexcept { return from_raw(narrow(-static_cast<std::int64_t>(a.raw_))); }
+
+    // Produit arrondi vers moins l'infini (décalage arithmétique, défini en C++20).
+    friend constexpr Fixed operator*(Fixed a, Fixed b) noexcept
+    {
+        return from_raw(narrow((static_cast<std::int64_t>(a.raw_) * b.raw_) >> fraction_bits));
+    }
+
+    // Quotient arrondi vers zéro. Précondition : b != 0.
+    friend constexpr Fixed operator/(Fixed a, Fixed b) noexcept
+    {
+        return from_raw(narrow((static_cast<std::int64_t>(a.raw_) * one_raw) / b.raw_));
+    }
+
+    constexpr Fixed& operator+=(Fixed other) noexcept { return *this = *this + other; }
+    constexpr Fixed& operator-=(Fixed other) noexcept { return *this = *this - other; }
+    constexpr Fixed& operator*=(Fixed other) noexcept { return *this = *this * other; }
+
+    friend constexpr auto operator<=>(Fixed, Fixed) noexcept = default;
+
+private:
+    [[nodiscard]] static constexpr std::int32_t narrow(std::int64_t value) noexcept
+    {
+        return static_cast<std::int32_t>(value);
+    }
+
+    std::int32_t raw_ = 0;
+};
+
+[[nodiscard]] constexpr Fixed abs(Fixed value) noexcept
+{
+    return value < Fixed{} ? -value : value;
+}
+
+[[nodiscard]] constexpr Fixed clamp(Fixed value, Fixed low, Fixed high) noexcept
+{
+    return value < low ? low : (high < value ? high : value);
+}
+
+} // namespace sequa::core::sim
diff --git a/core/include/sequa/core/sim/input.hpp b/core/include/sequa/core/sim/input.hpp
new file mode 100644
index 0000000..3f49dd0
--- /dev/null
+++ b/core/include/sequa/core/sim/input.hpp
@@ -0,0 +1,32 @@
+// SPDX-License-Identifier: MPL-2.0
+#pragma once
+
+#include <cstdint>
+
+namespace sequa::core::sim {
+
+using Tick = std::uint64_t;
+
+namespace button {
+inline constexpr std::uint32_t jump = 1u << 0u;
+} // namespace button
+
+// Entrées du joueur pour un tick, déjà quantifiées : aucune valeur flottante, pour que
+// l'enregistrement et le rejeu soient exacts (docs, §5.3).
+struct InputFrame {
+    Tick tick = 0;
+    std::uint32_t buttons = 0;
+    std::int16_t move_x = 0; // [-32767, 32767] : gauche, droite
+    std::int16_t move_y = 0; // réservé
+
+    [[nodiscard]] constexpr bool is_neutral() const noexcept { return buttons == 0 && move_x == 0 && move_y == 0; }
+
+    friend constexpr bool operator==(const InputFrame&, const InputFrame&) noexcept = default;
+};
+
+[[nodiscard]] constexpr InputFrame neutral_input(Tick tick) noexcept
+{
+    return InputFrame{tick, 0, 0, 0};
+}
+
+} // namespace sequa::core::sim
diff --git a/core/include/sequa/core/sim/replay.hpp b/core/include/sequa/core/sim/replay.hpp
new file mode 100644
index 0000000..8597322
--- /dev/null
+++ b/core/include/sequa/core/sim/replay.hpp
@@ -0,0 +1,67 @@
+// SPDX-License-Identifier: MPL-2.0
+#pragma once
+
+#include "sequa/core/sim/input.hpp"
+#include "sequa/core/sim/simulation.hpp"
+
+#include <cstddef>
+#include <cstdint>
+#include <optional>
+#include <span>
+#include <vector>
+
+namespace sequa::core::sim {
+
+// Session enregistrée (docs, §5.3) : la graine, la fréquence, la durée et les entrées
+// horodatées suffisent à la rejouer à l'identique, avec les mêmes réglages ou d'autres.
+// Les réglages de ressenti ne sont volontairement pas enregistrés : ce sont eux que
+// l'on fait varier au rejeu.
+struct Recording {
+    std::uint64_t seed = 0;
+    std::uint32_t tick_rate_hz = 60;
+    Tick tick_count = 0;
+    std::vector<InputFrame> inputs; // non neutres, ticks strictement croissants, < tick_count
+
+    // Vrai si les entrées sont ordonnées, uniques par tick, dans la durée et non neutres.
+    [[nodiscard]] bool is_valid() const noexcept;
+
+    friend bool operator==(const Recording&, const Recording&) = default;
+};
+
+// Format binaire versionné, petit-boutiste : "SQRC", version, en-tête, entrées.
+[[nodiscard]] std::vector<std::byte> serialize(const Recording& recording);
+// Retourne std::nullopt si les octets sont tronqués, d'une autre version ou incohérents.
+[[nodiscard]] std::optional<Recording> deserialize_recording(std::span<const std::byte> bytes);
+
+// Enregistre une session pendant qu'elle se joue.
+class SessionRecorder {
+public:
+    explicit SessionRecorder(const SimConfig& config);
+
+    // Exécute un tick avec l'entrée donnée (son champ tick est ignoré et remplacé par le
+    // tick courant) et l'enregistre si elle n'est pas neutre.
+    void step(InputFrame input);
+
+    [[nodiscard]] const Simulation& simulation() const noexcept { return simulation_; }
+    [[nodiscard]] const Recording& recording() const noexcept { return recording_; }
+
+private:
+    Simulation simulation_;
+    Recording recording_;
+};
+
+struct ReplayResult {
+    std::vector<std::uint64_t> hashes; // empreinte après chaque tick
+    WorldState final_world;
+    std::uint64_t final_hash = 0;
+};
+
+// Rejoue une session avec des réglages de ressenti et d'arène donnés.
+[[nodiscard]] ReplayResult replay(const Recording& recording, const FeelParams& feel,
+                                  const ArenaParams& arena = ArenaParams{});
+
+// Premier tick (0-indexé) dont l'empreinte diffère, ou std::nullopt si les deux rejeux
+// sont identiques. Des longueurs différentes divergent au premier tick manquant.
+[[nodiscard]] std::optional<Tick> first_divergence(const ReplayResult& a, const ReplayResult& b) noexcept;
+
+} // namespace sequa::core::sim
diff --git a/core/include/sequa/core/sim/rng.hpp b/core/include/sequa/core/sim/rng.hpp
new file mode 100644
index 0000000..8e591f7
--- /dev/null
+++ b/core/include/sequa/core/sim/rng.hpp
@@ -0,0 +1,61 @@
+// SPDX-License-Identifier: MPL-2.0
+#pragma once
+
+#include <cstdint>
+
+namespace sequa::core::sim {
+
+// Générateur pseudo-aléatoire propre à SEQUA, à graine explicite (docs, §10.1).
+// Algorithme PCG32 (PCG-XSH-RR 64/32, M. E. O'Neill, licence Apache 2.0 pour la
+// référence) réimplémenté ici : sorties identiques sur toutes les plateformes.
+class Pcg32 {
+public:
+    Pcg32(std::uint64_t seed, std::uint64_t stream) noexcept : inc_((stream << 1u) | 1u)
+    {
+        (void)next();
+        state_ += seed;
+        (void)next();
+    }
+
+    [[nodiscard]] std::uint32_t next() noexcept
+    {
+        const std::uint64_t old = state_;
+        state_ = old * multiplier + inc_;
+        const auto xorshifted = static_cast<std::uint32_t>(((old >> 18u) ^ old) >> 27u);
+        const auto rotation = static_cast<std::uint32_t>(old >> 59u);
+        return (xorshifted >> rotation) | (xorshifted << ((32u - rotation) & 31u));
+    }
+
+    // Entier uniforme dans [0, bound), sans biais (rejet). Précondition : bound > 0.
+    [[nodiscard]] std::uint32_t bounded(std::uint32_t bound) noexcept
+    {
+        const auto threshold = static_cast<std::uint32_t>((std::uint64_t{1} << 32u) % bound);
+        for (;;) {
+            const std::uint32_t value = next();
+            if (value >= threshold) {
+                return value % bound;
+            }
+        }
+    }
+
+    // Entier uniforme dans [low, high]. Précondition : low <= high.
+    [[nodiscard]] std::int32_t range(std::int32_t low, std::int32_t high) noexcept
+    {
+        const auto span = static_cast<std::uint32_t>(static_cast<std::int64_t>(high) - low + 1);
+        if (span == 0) { // intervalle complet des int32
+            return static_cast<std::int32_t>(next());
+        }
+        return static_cast<std::int32_t>(static_cast<std::int64_t>(low) + bounded(span));
+    }
+
+    [[nodiscard]] std::uint64_t state() const noexcept { return state_; }
+    [[nodiscard]] std::uint64_t increment() const noexcept { return inc_; }
+
+private:
+    static constexpr std::uint64_t multiplier = 6364136223846793005ull;
+
+    std::uint64_t state_ = 0;
+    std::uint64_t inc_;
+};
+
+} // namespace sequa::core::sim
diff --git a/core/include/sequa/core/sim/simulation.hpp b/core/include/sequa/core/sim/simulation.hpp
new file mode 100644
index 0000000..b571c6c
--- /dev/null
+++ b/core/include/sequa/core/sim/simulation.hpp
@@ -0,0 +1,53 @@
+// SPDX-License-Identifier: MPL-2.0
+#pragma once
+
+#include "sequa/core/sim/input.hpp"
+#include "sequa/core/sim/rng.hpp"
+#include "sequa/core/sim/world.hpp"
+
+#include <cstddef>
+#include <cstdint>
+#include <vector>
+
+namespace sequa::core::sim {
+
+struct SimConfig {
+    std::uint64_t seed = 0;
+    std::uint32_t tick_rate_hz = 60;
+    FeelParams feel;
+    ArenaParams arena;
+};
+
+// Simulation déterministe à pas fixe (docs, §5.3) : même configuration et mêmes entrées
+// donnent le même état, bit à bit, sur toutes les plateformes. Aucun modèle neuronal ou
+// génératif n'intervient ici.
+class Simulation {
+public:
+    // Préconditions : tick_rate_hz > 0, arena.coin_count > 0.
+    explicit Simulation(const SimConfig& config);
+
+    // Avance d'un tick. input.tick doit être égal à tick() ; sinon l'entrée est
+    // remplacée par une entrée neutre (une entrée hors séquence ne doit jamais
+    // modifier l'état).
+    void step(const InputFrame& input);
+
+    [[nodiscard]] Tick tick() const noexcept { return tick_; }
+    [[nodiscard]] const WorldState& world() const noexcept { return world_; }
+    [[nodiscard]] const SimConfig& config() const noexcept { return config_; }
+
+    // Empreinte de l'état complet (tick, générateur aléatoire, monde) : FNV-1a 64 bits
+    // sur une sérialisation canonique petit-boutiste.
+    [[nodiscard]] std::uint64_t state_hash() const;
+    [[nodiscard]] std::vector<std::byte> serialize_state() const;
+
+private:
+    Coin spawn_coin();
+
+    SimConfig config_;
+    Fixed dt_;
+    Pcg32 rng_;
+    WorldState world_;
+    Tick tick_ = 0;
+};
+
+} // namespace sequa::core::sim
diff --git a/core/include/sequa/core/sim/world.hpp b/core/include/sequa/core/sim/world.hpp
new file mode 100644
index 0000000..bdf5baf
--- /dev/null
+++ b/core/include/sequa/core/sim/world.hpp
@@ -0,0 +1,62 @@
+// SPDX-License-Identifier: MPL-2.0
+#pragma once
+
+#include "sequa/core/sim/fixed.hpp"
+
+#include <cstdint>
+#include <vector>
+
+namespace sequa::core::sim {
+
+// SIMULÉ / PROVISOIRE : micro-mode de démonstration en 2D vue de côté (un joueur, un sol,
+// des pièces). Il sert à éprouver le déterminisme et le rejeu avant la vraie scène L0
+// (docs, §9 « Réel et simulé »).
+
+// Réglages de ressenti (game feel, docs §4.2) : ce que l'auteur modifie avant de rejouer
+// une session à l'identique. Unités : mètres et secondes.
+struct FeelParams {
+    Fixed gravity = Fixed::from_int(30);
+    Fixed jump_velocity = Fixed::from_int(12);
+    Fixed move_acceleration = Fixed::from_int(40);
+    Fixed max_speed = Fixed::from_int(8);
+    Fixed ground_friction = Fixed::from_int(10); // par seconde
+    Fixed air_control = Fixed::from_ratio(1, 2); // fraction de l'accélération en l'air
+    std::uint32_t coyote_ticks = 6;              // saut toléré après avoir quitté le sol
+    std::uint32_t jump_buffer_ticks = 6;         // appui mémorisé avant l'atterrissage
+
+    friend constexpr bool operator==(const FeelParams&, const FeelParams&) noexcept = default;
+};
+
+struct Body {
+    Fixed x;
+    Fixed y;
+    Fixed vx;
+    Fixed vy;
+    bool on_ground = true;
+    std::uint32_t ticks_since_ground = 0;
+    std::uint32_t jump_buffer = 0;
+    std::uint32_t previous_buttons = 0;
+};
+
+struct Coin {
+    std::uint32_t id = 0;
+    Fixed x;
+    Fixed y;
+};
+
+struct ArenaParams {
+    Fixed half_width = Fixed::from_int(20);
+    Fixed coin_min_height = Fixed::from_ratio(1, 2);
+    Fixed coin_max_height = Fixed::from_int(3);
+    Fixed pickup_radius = Fixed::from_ratio(1, 2);
+    std::uint32_t coin_count = 8;
+};
+
+struct WorldState {
+    Body player;
+    std::vector<Coin> coins; // ordre stable par identifiant : aucun conteneur non ordonné
+    std::uint32_t score = 0;
+    std::uint32_t next_coin_id = 0;
+};
+
+} // namespace sequa::core::sim
diff --git a/core/src/sim/bytes.hpp b/core/src/sim/bytes.hpp
new file mode 100644
index 0000000..2de4870
--- /dev/null
+++ b/core/src/sim/bytes.hpp
@@ -0,0 +1,84 @@
+// SPDX-License-Identifier: MPL-2.0
+// Encodage binaire canonique petit-boutiste, interne à sequa_core.
+#pragma once
+
+#include <cstddef>
+#include <cstdint>
+#include <optional>
+#include <span>
+#include <utility>
+#include <vector>
+
+namespace sequa::core::sim::detail {
+
+class ByteWriter {
+public:
+    void u8(std::uint8_t value) { bytes_.push_back(static_cast<std::byte>(value)); }
+
+    void u16(std::uint16_t value) { put(value, 2); }
+    void u32(std::uint32_t value) { put(value, 4); }
+    void u64(std::uint64_t value) { put(value, 8); }
+    void i16(std::int16_t value) { u16(static_cast<std::uint16_t>(value)); }
+    void i32(std::int32_t value) { u32(static_cast<std::uint32_t>(value)); }
+
+    [[nodiscard]] std::vector<std::byte> take() { return std::move(bytes_); }
+
+private:
+    void put(std::uint64_t value, int size)
+    {
+        for (int i = 0; i < size; ++i) {
+            bytes_.push_back(static_cast<std::byte>((value >> (8 * i)) & 0xFFu));
+        }
+    }
+
+    std::vector<std::byte> bytes_;
+};
+
+class ByteReader {
+public:
+    explicit ByteReader(std::span<const std::byte> bytes) noexcept : bytes_(bytes) {}
+
+    [[nodiscard]] std::optional<std::uint8_t> u8() { return get<std::uint8_t>(1); }
+    [[nodiscard]] std::optional<std::uint16_t> u16() { return get<std::uint16_t>(2); }
+    [[nodiscard]] std::optional<std::uint32_t> u32() { return get<std::uint32_t>(4); }
+    [[nodiscard]] std::optional<std::uint64_t> u64() { return get<std::uint64_t>(8); }
+
+    [[nodiscard]] std::optional<std::int16_t> i16()
+    {
+        const auto value = u16();
+        return value ? std::optional{static_cast<std::int16_t>(*value)} : std::nullopt;
+    }
+
+    [[nodiscard]] std::size_t remaining() const noexcept { return bytes_.size() - offset_; }
+
+private:
+    template <typename T>
+    [[nodiscard]] std::optional<T> get(std::size_t size)
+    {
+        if (remaining() < size) {
+            return std::nullopt;
+        }
+        std::uint64_t value = 0;
+        for (std::size_t i = 0; i < size; ++i) {
+            value |= static_cast<std::uint64_t>(bytes_[offset_ + i]) << (8 * i);
+        }
+        offset_ += size;
+        return static_cast<T>(value);
+    }
+
+    std::span<const std::byte> bytes_;
+    std::size_t offset_ = 0;
+};
+
+// FNV-1a 64 bits : empreinte rapide et portable, pas une fonction cryptographique.
+[[nodiscard]] inline std::uint64_t fnv1a64(std::span<const std::byte> bytes) noexcept
+{
+    std::uint64_t hash = 0xcbf29ce484222325ull;
+    for (const std::byte b : bytes) {
+        hash ^= static_cast<std::uint64_t>(b);
+        hash *= 0x100000001b3ull;
+    }
+    return hash;
+}
+
+} // namespace sequa::core::sim::detail
diff --git a/core/src/sim/replay.cpp b/core/src/sim/replay.cpp
new file mode 100644
index 0000000..d183c29
--- /dev/null
+++ b/core/src/sim/replay.cpp
@@ -0,0 +1,147 @@
+// SPDX-License-Identifier: MPL-2.0
+#include "sequa/core/sim/replay.hpp"
+
+#include "sim/bytes.hpp"
+
+#include <algorithm>
+
+namespace sequa::core::sim {
+
+namespace {
+
+constexpr std::uint32_t recording_magic = 0x43525153u; // "SQRC" en petit-boutiste
+constexpr std::uint32_t recording_version = 1;
+constexpr std::size_t input_frame_size = 8 + 4 + 2 + 2;
+
+} // namespace
+
+bool Recording::is_valid() const noexcept
+{
+    if (tick_rate_hz == 0) {
+        return false;
+    }
+    for (std::size_t i = 0; i < inputs.size(); ++i) {
+        const InputFrame& frame = inputs[i];
+        if (frame.tick >= tick_count || frame.is_neutral()) {
+            return false;
+        }
+        if (i > 0 && frame.tick <= inputs[i - 1].tick) {
+            return false;
+        }
+    }
+    return true;
+}
+
+std::vector<std::byte> serialize(const Recording& recording)
+{
+    detail::ByteWriter w;
+    w.u32(recording_magic);
+    w.u32(recording_version);
+    w.u64(recording.seed);
+    w.u32(recording.tick_rate_hz);
+    w.u64(recording.tick_count);
+    w.u64(recording.inputs.size());
+    for (const InputFrame& frame : recording.inputs) {
+        w.u64(frame.tick);
+        w.u32(frame.buttons);
+        w.i16(frame.move_x);
+        w.i16(frame.move_y);
+    }
+    return w.take();
+}
+
+std::optional<Recording> deserialize_recording(std::span<const std::byte> bytes)
+{
+    detail::ByteReader r(bytes);
+    if (r.u32() != recording_magic || r.u32() != recording_version) {
+        return std::nullopt;
+    }
+
+    const auto seed = r.u64();
+    const auto tick_rate = r.u32();
+    const auto tick_count = r.u64();
+    const auto input_count = r.u64();
+    if (!seed || !tick_rate || !tick_count || !input_count) {
+        return std::nullopt;
+    }
+    // La taille annoncée doit correspondre exactement aux octets restants : protège
+    // contre une allocation démesurée sur un fichier corrompu.
+    if (*input_count > r.remaining() / input_frame_size || r.remaining() != *input_count * input_frame_size) {
+        return std::nullopt;
+    }
+
+    Recording recording;
+    recording.seed = *seed;
+    recording.tick_rate_hz = *tick_rate;
+    recording.tick_count = *tick_count;
+    recording.inputs.reserve(static_cast<std::size_t>(*input_count));
+    for (std::uint64_t i = 0; i < *input_count; ++i) {
+        const auto tick = r.u64();
+        const auto buttons = r.u32();
+        const auto move_x = r.i16();
+        const auto move_y = r.i16();
+        if (!tick || !buttons || !move_x || !move_y) {
+            return std::nullopt;
+        }
+        recording.inputs.push_back(InputFrame{*tick, *buttons, *move_x, *move_y});
+    }
+
+    if (!recording.is_valid()) {
+        return std::nullopt;
+    }
+    return recording;
+}
+
+SessionRecorder::SessionRecorder(const SimConfig& config) : simulation_(config)
+{
+    recording_.seed = config.seed;
+    recording_.tick_rate_hz = config.tick_rate_hz;
+}
+
+void SessionRecorder::step(InputFrame input)
+{
+    input.tick = simulation_.tick();
+    if (!input.is_neutral()) {
+        recording_.inputs.push_back(input);
+    }
+    simulation_.step(input);
+    recording_.tick_count = simulation_.tick();
+}
+
+ReplayResult replay(const Recording& recording, const FeelParams& feel, const ArenaParams& arena)
+{
+    SimConfig config;
+    config.seed = recording.seed;
+    config.tick_rate_hz = recording.tick_rate_hz;
+    config.feel = feel;
+    config.arena = arena;
+
+    Simulation simulation(config);
+    ReplayResult result;
+    result.hashes.reserve(static_cast<std::size_t>(recording.tick_count));
+
+    auto next_input = recording.inputs.begin();
+    for (Tick tick = 0; tick < recording.tick_count; ++tick) {
+        InputFrame input = neutral_input(tick);
+        if (next_input != recording.inputs.end() && next_input->tick == tick) {
+            input = *next_input++;
+        }
+        simulation.step(input);
+        result.hashes.push_back(simulation.state_hash());
+    }
+
+    result.final_world = simulation.world();
+    result.final_hash = simulation.state_hash();
+    return result;
+}
+
+std::optional<Tick> first_divergence(const ReplayResult& a, const ReplayResult& b) noexcept
+{
+    const auto [ita, itb] = std::mismatch(a.hashes.begin(), a.hashes.end(), b.hashes.begin(), b.hashes.end());
+    if (ita == a.hashes.end() && itb == b.hashes.end()) {
+        return std::nullopt;
+    }
+    return static_cast<Tick>(ita - a.hashes.begin());
+}
+
+} // namespace sequa::core::sim
diff --git a/core/src/sim/simulation.cpp b/core/src/sim/simulation.cpp
new file mode 100644
index 0000000..dc6cc3d
--- /dev/null
+++ b/core/src/sim/simulation.cpp
@@ -0,0 +1,153 @@
+// SPDX-License-Identifier: MPL-2.0
+#include "sequa/core/sim/simulation.hpp"
+
+#include "sim/bytes.hpp"
+
+#include <limits>
+
+namespace sequa::core::sim {
+
+namespace {
+
+constexpr std::uint64_t rng_stream = 0x5345'5155'4131ull; // "SEQUA1"
+constexpr std::uint32_t state_format_version = 1;
+
+[[nodiscard]] Fixed axis_to_unit(std::int16_t axis) noexcept
+{
+    return Fixed::from_ratio(axis, 32767);
+}
+
+[[nodiscard]] Fixed min(Fixed a, Fixed b) noexcept
+{
+    return b < a ? b : a;
+}
+
+[[nodiscard]] std::uint32_t saturating_increment(std::uint32_t value) noexcept
+{
+    return value == std::numeric_limits<std::uint32_t>::max() ? value : value + 1;
+}
+
+} // namespace
+
+Simulation::Simulation(const SimConfig& config)
+    : config_(config), dt_(Fixed::from_ratio(1, static_cast<std::int32_t>(config.tick_rate_hz))),
+      rng_(config.seed, rng_stream)
+{
+    world_.coins.reserve(config_.arena.coin_count);
+    for (std::uint32_t i = 0; i < config_.arena.coin_count; ++i) {
+        world_.coins.push_back(spawn_coin());
+    }
+}
+
+Coin Simulation::spawn_coin()
+{
+    const ArenaParams& arena = config_.arena;
+    Coin coin;
+    coin.id = world_.next_coin_id++;
+    coin.x = Fixed::from_raw(rng_.range((-arena.half_width).raw(), arena.half_width.raw()));
+    coin.y = Fixed::from_raw(rng_.range(arena.coin_min_height.raw(), arena.coin_max_height.raw()));
+    return coin;
+}
+
+void Simulation::step(const InputFrame& requested)
+{
+    const InputFrame input = requested.tick == tick_ ? requested : neutral_input(tick_);
+    const FeelParams& feel = config_.feel;
+    const Fixed one = Fixed::from_int(1);
+    Body& p = world_.player;
+
+    // Horizontal : accélération vers la direction demandée, frottement au sol sans entrée.
+    const Fixed control = p.on_ground ? one : feel.air_control;
+    p.vx += axis_to_unit(input.move_x) * feel.move_acceleration * control * dt_;
+    if (input.move_x == 0 && p.on_ground) {
+        p.vx -= p.vx * min(feel.ground_friction * dt_, one);
+    }
+    p.vx = clamp(p.vx, -feel.max_speed, feel.max_speed);
+
+    // Saut sur front montant, avec mémoire d'appui et tolérance après le bord (coyote time).
+    const std::uint32_t pressed = input.buttons & ~p.previous_buttons;
+    p.previous_buttons = input.buttons;
+    if ((pressed & button::jump) != 0) {
+        p.jump_buffer = feel.jump_buffer_ticks + 1;
+    }
+    if (p.jump_buffer > 0) {
+        const bool can_jump = p.on_ground || p.ticks_since_ground <= feel.coyote_ticks;
+        if (can_jump) {
+            p.vy = feel.jump_velocity;
+            p.jump_buffer = 0;
+            p.on_ground = false;
+            p.ticks_since_ground = feel.coyote_ticks + 1; // pas de second saut en l'air
+        } else {
+            --p.jump_buffer;
+        }
+    }
+
+    // Intégration (Euler semi-implicite).
+    p.vy -= feel.gravity * dt_;
+    p.x += p.vx * dt_;
+    p.y += p.vy * dt_;
+
+    const ArenaParams& arena = config_.arena;
+    if (p.x < -arena.half_width || arena.half_width < p.x) {
+        p.x = clamp(p.x, -arena.half_width, arena.half_width);
+        p.vx = Fixed{};
+    }
+    if (p.y <= Fixed{}) {
+        p.y = Fixed{};
+        if (p.vy < Fixed{}) {
+            p.vy = Fixed{};
+        }
+        p.on_ground = true;
+        p.ticks_since_ground = 0;
+    } else {
+        p.on_ground = false;
+        p.ticks_since_ground = saturating_increment(p.ticks_since_ground);
+    }
+
+    // Règle du micro-mode : une pièce touchée rapporte un point et réapparaît ailleurs.
+    for (Coin& coin : world_.coins) {
+        if (abs(p.x - coin.x) <= arena.pickup_radius && abs(p.y - coin.y) <= arena.pickup_radius) {
+            ++world_.score;
+            coin = spawn_coin();
+        }
+    }
+
+    ++tick_;
+}
+
+std::vector<std::byte> Simulation::serialize_state() const
+{
+    detail::ByteWriter w;
+    w.u32(state_format_version);
+    w.u64(tick_);
+    w.u64(rng_.state());
+    w.u64(rng_.increment());
+
+    const Body& p = world_.player;
+    w.i32(p.x.raw());
+    w.i32(p.y.raw());
+    w.i32(p.vx.raw());
+    w.i32(p.vy.raw());
+    w.u8(p.on_ground ? 1 : 0);
+    w.u32(p.ticks_since_ground);
+    w.u32(p.jump_buffer);
+    w.u32(p.previous_buttons);
+
+    w.u32(world_.score);
+    w.u32(world_.next_coin_id);
+    w.u32(static_cast<std::uint32_t>(world_.coins.size()));
+    for (const Coin& coin : world_.coins) {
+        w.u32(coin.id);
+        w.i32(coin.x.raw());
+        w.i32(coin.y.raw());
+    }
+    return w.take();
+}
+
+std::uint64_t Simulation::state_hash() const
+{
+    const std::vector<std::byte> bytes = serialize_state();
+    return detail::fnv1a64(bytes);
+}
+
+} // namespace sequa::core::sim
diff --git a/core/tests/sim/scripted_session.hpp b/core/tests/sim/scripted_session.hpp
new file mode 100644
index 0000000..0127e58
--- /dev/null
+++ b/core/tests/sim/scripted_session.hpp
@@ -0,0 +1,42 @@
+// SPDX-License-Identifier: MPL-2.0
+// Session de test scriptée : un « joueur » qui court, change de direction et saute.
+#pragma once
+
+#include "sequa/core/sim/input.hpp"
+#include "sequa/core/sim/replay.hpp"
+
+#include <cstdint>
+
+namespace sequa::core::sim::testing {
+
+[[nodiscard]] inline InputFrame scripted_input(Tick tick)
+{
+    InputFrame input = neutral_input(tick);
+    const Tick phase = tick % 240;
+    if (phase < 100) {
+        input.move_x = 32767;
+    } else if (phase < 140) {
+        input.move_x = 0;
+    } else {
+        input.move_x = -20000;
+    }
+    if (tick % 45 < 3) {
+        input.buttons = button::jump;
+    }
+    return input;
+}
+
+[[nodiscard]] inline Recording record_scripted_session(std::uint64_t seed, Tick ticks,
+                                                       const FeelParams& feel = FeelParams{})
+{
+    SimConfig config;
+    config.seed = seed;
+    config.feel = feel;
+    SessionRecorder recorder(config);
+    for (Tick tick = 0; tick < ticks; ++tick) {
+        recorder.step(scripted_input(tick));
+    }
+    return recorder.recording();
+}
+
+} // namespace sequa::core::sim::testing
diff --git a/core/tests/sim/test_clock.cpp b/core/tests/sim/test_clock.cpp
new file mode 100644
index 0000000..bb45a6e
--- /dev/null
+++ b/core/tests/sim/test_clock.cpp
@@ -0,0 +1,40 @@
+// SPDX-License-Identifier: MPL-2.0
+#include "sequa/core/sim/clock.hpp"
+
+#include <doctest/doctest.h>
+
+#include <cstdint>
+
+using sequa::core::sim::FixedStepClock;
+
+TEST_CASE("FixedStepClock : 60 Hz exacts sur une seconde decoupee irregulierement")
+{
+    FixedStepClock clock(60, 1000);
+    std::uint64_t steps = 0;
+    // 1 s = 7 tranches de 142 857 142 ns + reste : aucun pas perdu ni gagne.
+    for (int i = 0; i < 7; ++i) {
+        steps += clock.advance(142'857'142);
+    }
+    steps += clock.advance(1'000'000'000ull - 7ull * 142'857'142ull);
+    CHECK(steps == 60);
+}
+
+TEST_CASE("FixedStepClock : 144 Hz d'affichage, 60 Hz de simulation")
+{
+    FixedStepClock clock(60, 1000);
+    std::uint64_t steps = 0;
+    const std::uint64_t frame_ns = 1'000'000'000ull / 144; // arrondi : 6 944 444 ns
+    for (int frame = 0; frame < 144 * 10; ++frame) {
+        steps += clock.advance(frame_ns);
+    }
+    // 1440 images * 6 944 444 ns = 9,99999936 s -> 599 pas complets.
+    CHECK(steps == 599);
+}
+
+TEST_CASE("FixedStepClock : un gros retard est plafonne et compte")
+{
+    FixedStepClock clock(60, 8);
+    CHECK(clock.advance(1'000'000'000ull) == 8);
+    CHECK(clock.dropped_steps() == 52);
+    CHECK(clock.advance(0) == 0);
+}
diff --git a/core/tests/sim/test_fixed.cpp b/core/tests/sim/test_fixed.cpp
new file mode 100644
index 0000000..0d06b4d
--- /dev/null
+++ b/core/tests/sim/test_fixed.cpp
@@ -0,0 +1,52 @@
+// SPDX-License-Identifier: MPL-2.0
+#include "sequa/core/sim/fixed.hpp"
+
+#include <doctest/doctest.h>
+
+#include <cstdint>
+#include <limits>
+
+using sequa::core::sim::Fixed;
+
+TEST_CASE("Fixed : conversions entieres et rationnelles")
+{
+    CHECK(Fixed::from_int(3).raw() == 3 * 65536);
+    CHECK(Fixed::from_int(-2).raw() == -2 * 65536);
+    CHECK(Fixed::from_ratio(1, 2).raw() == 32768);
+    CHECK(Fixed::from_ratio(1, 60).raw() == 1092); // arrondi vers zero
+    CHECK(Fixed::from_ratio(-1, 60).raw() == -1092);
+}
+
+TEST_CASE("Fixed : arithmetique exacte et arrondis documentes")
+{
+    const Fixed a = Fixed::from_int(5);
+    const Fixed b = Fixed::from_ratio(1, 4);
+    CHECK((a + b).raw() == 5 * 65536 + 16384);
+    CHECK((a - b).raw() == 5 * 65536 - 16384);
+    CHECK((a * b).raw() == 5 * 16384);
+    CHECK((a / b).raw() == 20 * 65536);
+    CHECK((-a).raw() == -5 * 65536);
+
+    // Produit : arrondi vers moins l'infini ; quotient : vers zero.
+    const Fixed tiny = Fixed::from_raw(1);
+    const Fixed half = Fixed::from_ratio(1, 2);
+    CHECK((tiny * half).raw() == 0);
+    CHECK(((-tiny) * half).raw() == -1);
+    CHECK((Fixed::from_raw(-1) / Fixed::from_int(2)).raw() == 0);
+}
+
+TEST_CASE("Fixed : un depassement est modulaire, donc deterministe")
+{
+    const Fixed max = Fixed::from_raw(std::numeric_limits<std::int32_t>::max());
+    CHECK((max + Fixed::from_raw(1)).raw() == std::numeric_limits<std::int32_t>::min());
+}
+
+TEST_CASE("Fixed : comparaisons, abs et clamp")
+{
+    const Fixed one = Fixed::from_int(1);
+    CHECK(one > Fixed{});
+    CHECK(abs(-one) == one);
+    CHECK(clamp(Fixed::from_int(7), -one, one) == one);
+    CHECK(clamp(Fixed::from_int(-7), -one, one) == -one);
+    CHECK(Fixed::from_ratio(3, 2).to_double() == doctest::Approx(1.5));
+}
diff --git a/core/tests/sim/test_replay.cpp b/core/tests/sim/test_replay.cpp
new file mode 100644
index 0000000..f3fa1e1
--- /dev/null
+++ b/core/tests/sim/test_replay.cpp
@@ -0,0 +1,108 @@
+// SPDX-License-Identifier: MPL-2.0
+#include "sequa/core/sim/replay.hpp"
+
+#include "scripted_session.hpp"
+
+#include <doctest/doctest.h>
+
+#include <cstddef>
+#include <cstdint>
+#include <utility>
+#include <vector>
+
+using namespace sequa::core::sim;
+
+namespace {
+
+constexpr Tick session_ticks = 60 * 60; // une minute a 60 Hz
+
+} // namespace
+
+TEST_CASE("Replay : le rejeu est identique bit a bit a la session enregistree")
+{
+    SimConfig config;
+    config.seed = 2026;
+    SessionRecorder recorder(config);
+    std::vector<std::uint64_t> live_hashes;
+    for (Tick tick = 0; tick < session_ticks; ++tick) {
+        recorder.step(testing::scripted_input(tick));
+        live_hashes.push_back(recorder.simulation().state_hash());
+    }
+
+    const Recording& recording = recorder.recording();
+    REQUIRE(recording.is_valid());
+    CHECK(recording.tick_count == session_ticks);
+    CHECK(recording.inputs.size() < session_ticks); // les ticks neutres ne sont pas stockes
+
+    const ReplayResult result = replay(recording, config.feel);
+    CHECK(result.hashes == live_hashes);
+    CHECK(result.final_hash == recorder.simulation().state_hash());
+}
+
+TEST_CASE("Replay : meme session, autre reglage de ressenti, divergence localisee")
+{
+    const Recording recording = testing::record_scripted_session(7, session_ticks);
+    const ReplayResult reference = replay(recording, FeelParams{});
+
+    FeelParams floaty;
+    floaty.jump_velocity = Fixed::from_int(14);
+    const ReplayResult variant = replay(recording, floaty);
+
+    const auto divergence = first_divergence(reference, variant);
+    REQUIRE(divergence.has_value());
+    // Le premier saut a lieu au tick 0 : les deux versions divergent des ce tick.
+    CHECK(*divergence == 0);
+    CHECK(first_divergence(reference, replay(recording, FeelParams{})) == std::nullopt);
+}
+
+TEST_CASE("Replay : serialisation aller-retour exacte")
+{
+    const Recording recording = testing::record_scripted_session(11, session_ticks);
+    const std::vector<std::byte> bytes = serialize(recording);
+    const auto loaded = deserialize_recording(bytes);
+    REQUIRE(loaded.has_value());
+    CHECK(*loaded == recording);
+    CHECK(replay(*loaded, FeelParams{}).final_hash == replay(recording, FeelParams{}).final_hash);
+}
+
+TEST_CASE("Replay : un enregistrement corrompu est refuse")
+{
+    const Recording recording = testing::record_scripted_session(11, 600);
+    const std::vector<std::byte> bytes = serialize(recording);
+
+    SUBCASE("tronque")
+    {
+        const std::vector<std::byte> truncated(bytes.begin(), bytes.end() - 1);
+        CHECK_FALSE(deserialize_recording(truncated).has_value());
+    }
+    SUBCASE("mauvais magique")
+    {
+        std::vector<std::byte> bad = bytes;
+        bad[0] = std::byte{0};
+        CHECK_FALSE(deserialize_recording(bad).has_value());
+    }
+    SUBCASE("ticks desordonnes")
+    {
+        Recording unordered = recording;
+        REQUIRE(unordered.inputs.size() >= 2);
+        std::swap(unordered.inputs[0], unordered.inputs[1]);
+        CHECK_FALSE(deserialize_recording(serialize(unordered)).has_value());
+    }
+    SUBCASE("vide")
+    {
+        CHECK_FALSE(deserialize_recording({}).has_value());
+    }
+}
+
+TEST_CASE("Replay : empreinte de reference multiplateforme")
+{
+    // Valeur figee : toute plateforme ou tout compilateur doit retrouver exactement cette
+    // empreinte (docs, §10.1 et §16). Si elle change, c'est soit une modification voulue
+    // de la simulation (mettre a jour la valeur et le format d'etat), soit une perte de
+    // determinisme a corriger.
+    const Recording recording = testing::record_scripted_session(2026, session_ticks);
+    const ReplayResult result = replay(recording, FeelParams{});
+    MESSAGE("empreinte finale : " << result.final_hash << ", score " << result.final_world.score);
+    CHECK(result.final_hash == 15306857814008723692ull);
+    CHECK(result.final_world.score == 6);
+}
diff --git a/core/tests/sim/test_rng.cpp b/core/tests/sim/test_rng.cpp
new file mode 100644
index 0000000..83e428b
--- /dev/null
+++ b/core/tests/sim/test_rng.cpp
@@ -0,0 +1,45 @@
+// SPDX-License-Identifier: MPL-2.0
+#include "sequa/core/sim/rng.hpp"
+
+#include <doctest/doctest.h>
+
+#include <array>
+#include <cstdint>
+
+using sequa::core::sim::Pcg32;
+
+TEST_CASE("Pcg32 : sorties de reference de pcg32-demo (graine 42, flux 54)")
+{
+    Pcg32 rng(42, 54);
+    const std::array<std::uint32_t, 6> expected{0xa15c02b7u, 0x7b47f409u, 0xba1d3330u,
+                                                0x83d2f293u, 0xbfa4784bu, 0xcbed606eu};
+    for (const std::uint32_t value : expected) {
+        CHECK(rng.next() == value);
+    }
+}
+
+TEST_CASE("Pcg32 : meme graine, meme suite ; graine differente, suite differente")
+{
+    Pcg32 a(7, 1);
+    Pcg32 b(7, 1);
+    Pcg32 c(8, 1);
+    bool any_difference = false;
+    for (int i = 0; i < 100; ++i) {
+        const std::uint32_t va = a.next();
+        CHECK(va == b.next());
+        any_difference = any_difference || va != c.next();
+    }
+    CHECK(any_difference);
+}
+
+TEST_CASE("Pcg32 : bounded et range restent dans leurs bornes")
+{
+    Pcg32 rng(123, 9);
+    for (int i = 0; i < 10'000; ++i) {
+        CHECK(rng.bounded(10) < 10u);
+        const std::int32_t v = rng.range(-5, 5);
+        CHECK(v >= -5);
+        CHECK(v <= 5);
+    }
+    CHECK(rng.range(3, 3) == 3);
+}
diff --git a/core/tests/sim/test_simulation.cpp b/core/tests/sim/test_simulation.cpp
new file mode 100644
index 0000000..a081147
--- /dev/null
+++ b/core/tests/sim/test_simulation.cpp
@@ -0,0 +1,84 @@
+// SPDX-License-Identifier: MPL-2.0
+#include "sequa/core/sim/simulation.hpp"
+
+#include "scripted_session.hpp"
+
+#include <doctest/doctest.h>
+
+using namespace sequa::core::sim;
+
+namespace {
+
+SimConfig config_with_seed(std::uint64_t seed)
+{
+    SimConfig config;
+    config.seed = seed;
+    return config;
+}
+
+} // namespace
+
+TEST_CASE("Simulation : deux instances identiques restent identiques bit a bit")
+{
+    Simulation a(config_with_seed(42));
+    Simulation b(config_with_seed(42));
+    CHECK(a.state_hash() == b.state_hash());
+    for (Tick tick = 0; tick < 3600; ++tick) {
+        const InputFrame input = testing::scripted_input(tick);
+        a.step(input);
+        b.step(input);
+        REQUIRE(a.state_hash() == b.state_hash());
+    }
+    CHECK(a.serialize_state() == b.serialize_state());
+}
+
+TEST_CASE("Simulation : la graine change le placement des pieces")
+{
+    const Simulation a(config_with_seed(1));
+    const Simulation b(config_with_seed(2));
+    CHECK(a.state_hash() != b.state_hash());
+}
+
+TEST_CASE("Simulation : une entree hors sequence est neutralisee")
+{
+    Simulation a(config_with_seed(5));
+    Simulation b(config_with_seed(5));
+    InputFrame wrong_tick = testing::scripted_input(0);
+    wrong_tick.tick = 99;
+    a.step(wrong_tick);
+    b.step(neutral_input(0));
+    CHECK(a.state_hash() == b.state_hash());
+}
+
+TEST_CASE("Simulation : le joueur tombe, atterrit et saute")
+{
+    Simulation sim(config_with_seed(3));
+    CHECK(sim.world().player.on_ground);
+
+    InputFrame jump = neutral_input(0);
+    jump.buttons = button::jump;
+    sim.step(jump);
+    CHECK_FALSE(sim.world().player.on_ground);
+    CHECK(sim.world().player.y > Fixed{});
+
+    // Bouton maintenu : un seul saut (front montant), puis retour au sol.
+    for (Tick tick = 1; tick < 120; ++tick) {
+        InputFrame held = neutral_input(tick);
+        held.buttons = button::jump;
+        sim.step(held);
+    }
+    CHECK(sim.world().player.on_ground);
+    CHECK(sim.world().player.y == Fixed{});
+}
+
+TEST_CASE("Simulation : le joueur ne sort pas de l'arene")
+{
+    Simulation sim(config_with_seed(4));
+    for (Tick tick = 0; tick < 1200; ++tick) {
+        InputFrame right = neutral_input(tick);
+        right.move_x = 32767;
+        sim.step(right);
+    }
+    CHECK(sim.world().player.x == sim.config().arena.half_width);
+    CHECK(abs(sim.world().player.vx) <= sim.config().feel.max_speed);
+}