What (One-liner)

From a w-history, compute velocity / acceleration / trend-persistence / xyz-divergence → 4-tier risk (low/medium/high/critical) + estimated steps to fracture + Chinese warning text. The Canvas renders warning_message verbatim.

How to use

reflexivity_4d_ode (w trajectory) → reflexivity_detector_v1 → bear_agent / risk_management
                                    → risk_level="high"
                                    → warning_message="w 加速发散..."
                                    → estimated_steps_to_fracture=5

Core formulas

See frontmatter formula. Key points:

1. Second differences: velocity = diff(w)/dt, acceleration = diff(velocity)/dt
2. Trend persistence: count same-sign velocities backward from the end
3. Scoring: accumulate over velocity / acceleration / persistence / |w|
4. Fracture decision: score≥8 OR |w|>5 → critical + fracture_detected
5. Early warning: medium/high AND NOT fracture_detected → early_warning

Assumptions & applicability

Assumptions: the w series was produced by reflexivity_4d_ode / run_multi_step, and thresholds are Pangura internal calibration constants.

Applies to: early warning of w collapse through macro regime transitions; Canvas cross-asset fragility signal source.

Does not apply to: intraday trading, hedging sizing, non-reflexivity series.

Known limitations

See frontmatter limitations. Six key items: hard-coded thresholds / hard-coded Chinese warning / xyz_divergence only at the endpoint / single dt / rough est_steps / short-data fallback to low.

References

• Soros (1987) Alchemy of Finance — reflexivity philosophy
• Pangura Research Note 2026-03 (pending) — threshold calibration

Golden Test

tests/golden/fixtures/tier4/reflexivity_detector/ — numpy_manual (independent numpy re-implementation of the rule scoring), 1e-12 tolerance. 10 tests:

6 Scenarios

• low_risk_flat / medium_risk_rising / high_risk_accelerating / critical_past_threshold
• with_xyz_background (exercises xyz_divergence)
• too_short (n<3 fallback)

4 Contract tests

• result_structure (top-level + signal key set)
• mutually_exclusive_flags (fracture_detected XOR early_warning)
• determinism (5 reruns byte-identical)
• from_trajectory_equivalence (pipeline API matches direct call)

Changelog

• 1.0.0 (2026-04-21) — First Active (Tier 4 batch 2.1)