Add comprehensive tests and optimizations for simulation and UI performance

- Introduced a new benchmark save script to create a stress test scenario with extreme values for simulation performance.
- Added a full UI benchmark script to measure frame rates and performance metrics during UI interactions.
- Implemented tests for coarse generations to ensure population transitions are handled correctly.
- Created tests for extra parameters to validate the loading and application of configuration settings.
- Developed simulation optimization tests to verify the efficiency of population drift and rounding mechanisms.
- Added split optimization tests to ensure accurate allocation and rounding behavior in population management.
- Included startup parameter tests to confirm the correct initialization of global parameters before scene readiness.
- Enhanced the audit rounding ledger to compare selective and full rounding results for consistency.

tests/test_batch_boundaries.gd

@@ -38,6 +38,43 @@ func dispose(world) -> void:
 
 func run() -> void:
     var world = fixture()
+    world.catalog.entities.N.lifespan = 100
+    world.batches.append_batch(world.state, "N", 2, 10, 10)
+    world.batches.append_batch(world.state, "N", 3, 10, 10)
+    check(world.state.batches.N.size() == 1 and E.eq(world.state.batches.N[0].amount, 5), "Repeated insertion merges using the cohort index")
+    world.batches.append_batch(world.state, "N", 1, 0, 0)
+    check(E.eq(world.state.batches.N[0].created_from, 0), "Earlier insertion preserves chronological order")
+    var replaced: Array = world.state.batches.N.duplicate(true)
+    world.state.batches.N = replaced
+    world.batches.append_batch(world.state, "N", 7, 10, 10)
+    check(E.eq(replaced[1].amount, 12), "Replacing cohort array invalidates cached references")
+    var separate: Dictionary = world.state.duplicate(true)
+    world.batches.append_batch(separate, "N", 9, 10, 10)
+    check(E.eq(separate.batches.N[1].amount, 21) and E.eq(world.state.batches.N[1].amount, 12), "Index is isolated between transaction states")
+    dispose(world)
+    world = fixture()
+    for speed in range(1, 7):
+        world.state.speed = speed
+        check(E.eq(world.batches.window_duration(world.state, 100), 2.5 if speed < 4 else pow(10, speed - 2)), "Windows follow selected speed")
+        check(E.eq(world.batches.window_duration(world.state, 5), 5), "Short explosions retain their timing")
+    var huge: Variant = E.of("10000000000000000000000000000000000000000")
+    world.catalog.entities.N.lifespan = 100
+    world.state.batches.N = [
+        {"amount": huge, "start_year": 100, "end_year": 110, "created_from": 0, "created_to": 10, "withdraw_remainder": 0.25},
+        {"amount": 7, "start_year": 120, "end_year": 130, "created_from": 20, "created_to": 30, "withdraw_remainder": 0.5}
+    ]
+    world.batches.coarsen(world.state)
+    check(world.state.batches.N.size() == 1, "High speed combines nearby cohorts")
+    check(E.eq(world.state.batches.N[0].amount, E.add(huge, 7)), "Coarsening preserves exact large whole counts")
+    check(E.eq(world.state.batches.N[0].withdraw_remainder, 0.75), "Coarsening preserves withdrawal carry")
+    var combined: Dictionary = world.state.batches.N[0].duplicate(true)
+    world.batches.coarsen(world.state)
+    check(world.state.batches.N[0] == combined, "Coarsening is idempotent")
+    world.state.speed = 1
+    world.batches.coarsen(world.state)
+    check(world.state.batches.N[0] == combined, "Slowing down does not invent finer history")
+    dispose(world)
+    world = fixture()
     world.state.batch_origins.LGRB = E.of("10357034.80000000074505806")
     var boundary: Variant = E.of("41215289.79999999701976776")
     for interval in [[E.subtract(boundary, E.of("2.5")), E.add(boundary, E.of("2.25"))], [boundary, E.add(boundary, 2)]]:
@@ -54,5 +91,23 @@ func run() -> void:
         check(E.eq(total, 100), "Boundary correction preserves all objects")
         check(E.le(world.state.batches.LGRB.size(), 7), "Finite number of windows")
     dispose(world)
+    world = fixture()
+    world.batches.append_batch(world.state, "N", 100, 100, 100)
+    var first: Dictionary = world.state.batches.N[0].duplicate(true)
+    world.batches.append_batch(world.state, "N", 7, 100, 100)
+    check(world.state.batches.N.size() == 1 and E.eq(world.state.batches.N[0].amount, 107), "Repeated births merge directly into one window")
+    check(E.eq(world.state.batches.N[0].start_year, first.start_year), "Direct merge preserves transition time")
+    check(world.batches.withdraw_batches(world.state, "N", 0).is_empty(), "Future cohorts are not withdrawn")
+    var untouched: Array = world.state.batches.N
+    check(world.batches.withdraw_batches(world.state, "N", 1).is_empty() and is_same(untouched, world.state.batches.N), "Readiness index skips future cohorts")
+    world.state.batches.N = [{"amount": 7, "start_year": 0, "end_year": 0, "created_from": 0, "created_to": 0}]
+    check(world.batches.withdraw_batches(world.state, "N", 1).size() == 1, "Replacing cohorts invalidates readiness index")
+    world.batches.append_batch(world.state, "N", 3, 100, 100)
+    check(E.eq(world.state.batches.N[0].amount, 3), "Replacing cohorts invalidates instant merge cache")
+    world.batches.withdraw_batches(world.state, "N", 0)
+    world.batches.scale_batches(world.state, "N", 0)
+    world.batches.withdraw_batches(world.state, "N", 1)
+    check(world.state.batches.N.is_empty(), "Scaling invalidates readiness and removes zero cohorts")
+    dispose(world)
     print(("Batch boundaries: %d checks, %d failures" % [checks, failures]))
     quit((0 if E.eq(failures, 0) else 1))