Migrated from Method backlog

This issue was created from a legacy filesystem backlog card. GitHub Issues are now the live work tracker; repository docs remain Method evidence.

Source backlog: docs/method/backlog/cool-ideas/MATH_tumble-tower-stage-0-aabb.md
Original lane: cool-ideas
Original legend: MATH

Original backlog card

Milestone: Tumble Tower | Priority: P2

Status: active cool idea. Task DAG issue #231 is still open and blocks the
Tumble Tower physics ladder/course (#232, #235, #238). crates/warp-geom
already provides AABB geometry and deterministic broad-phase scaffolding, but
no Tumble Tower gravity/contact-resolution simulation or physics fingerprint
exists yet.

Stage 0: AABB

Issue: #231

User Story: As a learner studying deterministic physics, I want the simplest possible physics simulation (axis-aligned bounding boxes with gravity and stacking) so that I can understand deterministic collision detection from first principles.

Requirements

• R1: Implement 2D AABB (axis-aligned bounding box) representation: position, half-extents, velocity.
• R2: Implement gravity as a constant downward acceleration applied per tick.
• R3: Implement AABB-vs-AABB overlap detection (separating axis test on 2 axes).
• R4: Implement contact resolution: push overlapping boxes apart along the minimum penetration axis; zero out velocity along the contact normal.
• R5: Simulation arithmetic uses F32Scalar by default, with DFix64 as the
  fixed-point lane where the feature is enabled; avoid raw f32 in the
  authoritative update path.
• R6: Per-tick physics_fingerprint for determinism verification.

Acceptance Criteria

• AC1: A single box dropped from height settles on the ground plane within 60 ticks.
• AC2: A stack of 5 boxes remains stable for 200 ticks (no interpenetration, no drift).
• AC3: Two runs with identical initial conditions produce identical per-tick fingerprint sequences.
• AC4: Golden vector: specific 5-box stack scenario produces a known physics_fingerprint at tick 200.

Definition of Done

• Code reviewed and merged
• Tests pass (CI green)
• Documentation updated (if applicable)

Scope: AABB representation, gravity, overlap detection, contact resolution, fingerprinting.
Out of Scope: Rotation (Stage 1); friction/restitution (Stage 2); sleeping (Stage 3); networking.

Test Plan

• Goldens: Golden fingerprint sequence for a 5-box drop scenario over 200 ticks.
• Failures: Box with zero half-extents (degenerate AABB, rejected at construction); negative gravity (boxes fly up, simulation still valid).
• Edges: Two boxes landing simultaneously; box exactly touching ground (zero penetration); very high stack (20 boxes).
• Fuzz/Stress: Property test: random initial positions and velocities for 10 boxes, verify no interpenetration after 500 ticks of settling.

Blocked By: none in the task DAG; implementation is the first Tumble Tower
physics slice.
Blocking: stage-1-rotation, lockstep-harness, visualization

Est. Hours: 6h
Expected Complexity: ~450 LoC