What (One-liner)

Library primitive: scipy solve_ivp (RK45) solves the Pangura 4D reflexivity ODE (rate / investment / inflation / confidence). Not in the Canvas picker — serves as the base algorithm layer for upper-layer reflexivity nodes.

How to use

Not a Canvas UI. Access via:

• Python directly: from services.reflexivity import solve_4d_ode
• REST endpoint: POST /reflexivity/simulate
• Indirect upstream: reflexivity_agent_simulate.step_agent uses _rk4_step (distinct from this operator's solve_ivp — single-step RK4)

Core formulas

See frontmatter. Four coupled ODE equations:

• dx/dt = z + (y − a)x + m1·w
• dy/dt = 1 − b·y − x² + m2·w
• dz/dt = −x − c·z + m3·w
• dw/dt = −x·y·z + m4·w

Assumptions & applicability

Assumptions: scipy ≥ 1.10, ODE non-stiff, physically reasonable parameters.

Applies to: base algorithm layer for upper reflexivity nodes, paper reproduction, teaching.

Does not apply to: Canvas end users, stiff ODEs, custom equations.

Known limitations

See frontmatter limitations. Six key items: library primitive / hard-coded equations / RK45 not stiff-optimal / scipy version drift (<1e-7) / n_points not precision / error-field contract.

References

• Soros (1987) Alchemy of Finance — reflexivity
• Pangura Research Note 2026-03 (pending) — 4D ODE specification

Golden Test

tests/golden/fixtures/tier4/reflexivity_4d_ode/ — captured_snapshot (pinned scipy), 1e-6 tolerance. 10 tests:

5 Scenarios

• default_stable_short / default_stable_medium / high_coupling_divergent / damped_fast / negative_w_start

5 Contract tests

• result_structure / t_monotonic / determinism / y0_initial_condition / params_echoed

Changelog

• 1.0.0 (2026-04-21) — First Active (Tier 4 batch 2.3)