For the avian_3d_character example the same code (disabling sleeps and warm start) seems to completely mess up the simulation (at least with the 1 second replication interval that I'm testing with).

I tried additionally syncing the Collisions resource like this, but to no avail:

        // in protocol.rs
        app.register_resource::<CollisionInternals>(ChannelDirection::ServerToClient);
        app.add_systems(FixedPreUpdate, write_collisions_to_actual_collisions);
        app.add_systems(FixedPostUpdate, store_collisions);
        app.insert_resource(CollisionInternals(IndexMap::with_hasher(fxhash::FxBuildHasher::default()))); // needs `cargo add fxhash`
// [...]

#[derive(Serialize, Deserialize, Debug, Resource)] // needs `cargo add indexmap --features serde`
struct CollisionInternals(IndexMap<(Entity, Entity), Contacts, fxhash::FxBuildHasher>);

fn write_collisions_to_actual_collisions(
    collision_internals: Res<CollisionInternals>,
    mut collisions: ResMut<Collisions>,
) {
    *collisions.get_internal_mut() = collision_internals.0.clone();
}

fn store_collisions(
    collision_internals: ResMut<CollisionInternals>,
    collisions: Res<Collisions>,
) {
    collision_internals.into_inner().0 = collisions.get_internal().clone();
}

the cubes are still teleporting a bit every replication interval

For the avian_3d_character example the same code (disabling sleeps and warm start) seems to completely mess up the simulation (at least with the 1second replication interval that I'm testing with).

I tried syncing additional the Collisions resource like this, but to no avail:

        // in protocol.rs
        app.register_resource::<CollisionInternals>(ChannelDirection::ServerToClient);
        app.add_systems(FixedPreUpdate, write_collisions_to_actual_collisions);
        app.add_systems(FixedPostUpdate, store_collisions);
        app.insert_resource(CollisionInternals(IndexMap::with_hasher(fxhash::FxBuildHasher::default()))); // needs `cargo add fxhash`
// [...]

#[derive(Serialize, Deserialize, Debug, Resource)] // needs `cargo add indexmap --features serde`
struct CollisionInternals(IndexMap<(Entity, Entity), Contacts, fxhash::FxBuildHasher>);

fn write_collisions_to_actual_collisions(
    collision_internals: Res<CollisionInternals>,
    mut collisions: ResMut<Collisions>,
) {
    *collisions.get_internal_mut() = collision_internals.0.clone();
}

fn store_collisions(
    collision_internals: ResMut<CollisionInternals>,
    collisions: Res<Collisions>,
) {
    collision_internals.into_inner().0 = collisions.get_internal().clone();
}

the cubes are still teleporting a bit every replication interval

Thanks for trying this!
The avian 2d seems to have fewer rollbacks, so it might be something else; maybe a problem with the 3d example itself?

Probably this is missing an implementation of MapEntities, however even with a app.add_map_entities::<CollisionInternals>(); that implementation is not called. It appears that there's a ComponentRegistry and a MessageRegistry but no ResourceRegistry that takes care of resources?

        app.register_resource::<CollisionInternals>(ChannelDirection::ServerToClient);
        app.add_map_entities::<CollisionInternals>();
        app.add_systems(FixedPreUpdate, write_collisions_to_actual_collisions);
        app.add_systems(FixedPostUpdate, store_collisions);
        app.insert_resource(CollisionInternals(None));
// [...]
#[derive(Serialize, Deserialize, Debug, Resource, Clone)]
struct CollisionInternals(Option<IndexMap<(Entity, Entity), Contacts, fxhash::FxBuildHasher>>);

impl MapEntities for CollisionInternals {
    fn map_entities<M: EntityMapper>(&mut self, entity_mapper: &mut M) {
        panic!("Nice! MapEntities was called!");
        let mut new_map = IndexMap::with_capacity_and_hasher(
            self.0.as_ref().map_or(0, |x| x.len()),
            fxhash::FxBuildHasher::default(),
        );
        if let Some(inner) = self.0.take() {
            for ((e1, e2), value) in inner.into_iter() {
                new_map.insert(
                    (entity_mapper.map_entity(e1), entity_mapper.map_entity(e2)),
                    value,
                );
            }
            self.0 = Some(new_map);
        }
    }
}

fn write_collisions_to_actual_collisions(
    collision_internals: Res<CollisionInternals>,
    mut collisions: ResMut<Collisions>,
) {
    if let Some(collision_internals) = &collision_internals.0 {
        *collisions.get_internal_mut() = collision_internals.clone();
    }
}

fn store_collisions(collision_internals: ResMut<CollisionInternals>, collisions: Res<Collisions>) {
    collision_internals.into_inner().0 = Some(collisions.get_internal().clone());
}

Resources are replicated as messages, so they are part of the MessageRegistry: https://github.com/cBournhonesque/lightyear/blob/main/lightyear/src/protocol/message.rs#L312

But rolling back resources is not supported currently

EDIT: actually it is in main: #622