Wolfram Lagrangian Test Plan

Scope

Canonical Lagrangian stack under V3_P12-Lagrangian-Framework:

• LAG-01 Lowe Coherence Lagrangian (LLC)
• LAG-02 Spirit Lagrangian
• LAG-03 Anti-Lagrangian
• LAG-04 Interaction Lagrangian
• LAG-05 Unified Field Lagrangian

Test Matrix

1. LAG-01 identity

• Check symbolic identity L = T - V remains algebraically stable.

2. LAG-02 Euler-Lagrange

• Derive Euler-Lagrange equation for the Spirit working form.
• Verify closed-form solve for x''(t) exists.

3. LAG-03 sign inversion

• Verify L_anti = -L_spirit and expanded equivalent form.

4. LAG-04 coupling sanity

• Use a minimal bilinear coupling instantiation L_int = -kInt chi psi to test coupling behavior.
• Confirm interaction vanishes when chi -> 0.

5. LAG-05 composition

• Verify L_total = L_GR + L_chi + L_int exactly.
• Confirm interaction sector vanishes at chi -> 0.
• Confirm coupling constant kappa is explicitly present.

Execution

• Script: run_lagrangian_stack_tests.wl
• Output: lagrangian_stack_test_output_2026-02-18.txt
• Results note: Wolfram_Lagrangian_Test_Results_2026-02-18.md

Notes

• LAG-04 remains definition-level in the axiom spine, so the test harness uses a declared minimal interaction instantiation for executable symbolic checks.
• These tests validate internal mathematical consistency, not empirical truth claims.

Canonical Hub: CANONICAL_INDEX

Ring 2 — Canonical Grounding

• Klein Gordon Field from 00 Canonical
• MASTER CANONICAL ACQUISITION LIST
• THEORY CHECK COMPLETE

Ring 3 — Framework Connections

• Ten Laws — Canonical Equations
• Master Equation Index