3D dynamical pair-annihilation: capture to breather to vacuum evolution

[xrodz]

Goal

Run the full 3D dynamical pair-annihilation of a ± hedgehog pair in the M5 field, the capture → breather → vacuum-decay evolution, and confirm that topology cancellation releases the stored field energy as outgoing waves.

Why now

On the antimatter / annihilation row the accounting is already settled, but it is accounting, not dynamics:

Piece	Status
Charge ledger	✅ single ±1 → Q ≈ ±1; the enclosing sphere of a ± pair → Q = 0 (additive) (m5_8_2v_pair_annihilation_budget.py)
Energy ledger	✅ pair rest energy ≈ 2× H_static, balances
1+1D principle trail	✅ SG kink + antikink → breather → vacuum, Q = 0 throughout (sine_gordon_annihilation.py)
3D dynamical capture → breather → vacuum	🚧 open, this issue

m5_8_2v is a budget ledger (it sums charges and energies of a placed configuration); it does not evolve the pair. The missing piece is an EOM-driven 3D run where the two defects actually approach, capture, ring down through a breather, and decay to vacuum.

Scope

• Initialize a +1 / −1 hedgehog pair at separation d in the M5 matrix field.
• Evolve under the M5 equation of motion (the same integrator as the molten-clock runs).
• Track over time: topological charge Q(t) (should stay ≈ 0 for the enclosing volume and resolve the two unit charges into the cancellation), total energy H(t) partitioned into bound vs radiated, and the outgoing-wave flux through a far sphere.
• Confirm the released energy ≈ the pair rest energy (2× H_static) leaves as radiation, and that the late state is vacuum (or a decaying breather), matching the 1+1D trail in 3D.

Acceptance

A single headless script + plot showing Q(t), the bound/radiated energy split, and the far-sphere flux for at least one separation, demonstrating capture → breather → vacuum with the energy ledger closing dynamically.

Physics-only, headless. Builds directly on m5_8_2v and sine_gordon_annihilation.py.

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RENDERING DELIVERABLE (the annihilation demo, 2026-06-17)

The annihilation dynamic demo lives here (not in the M5-demos umbrella): render the capture → breather → vacuum evolution of a ± pair on screen, with the charge ledger (Q: ±1 → 0) and the energy ledger (pair rest energy released as outgoing waves) shown live. Demo-only / headless-first (the physics is validated headless; the render is for seeing it). Use the existing rendering stack (WAVE_MENU charge + energy channels, the E/B glyphs); see 4b_rendering_features.md. A short 4b as-built note when it lands.

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Antimatter + annihilation — detail moved from the MODELS.md coverage cell (2026-06-19)

The MODELS.md "Antimatter + annihilation" cell (M5 column) was condensed to a summary; its prior full descriptive text is preserved here:

Q → −Q under reflection; annihilation = topology-cancellation releasing stored field energy as outgoing waves (natural for topological soliton models, starting with sine-Gordon). Gauss law + (topological, Gauss-Bonnet) charge quantization permit charge destruction ONLY by annihilation with the opposite charge, releasing the integrated-Hamiltonian energy (the particle's mass); stopping the clock cannot destroy charge. Principle-level trail run: SG kink + antikink pass through in the integrable limit, and with radiation losses capture → breather → vacuum decay, Q = 0 throughout. On the production matrix the accounting is settled: the charge ledger is validated (single ±1 → Q ≈ ±1, the enclosing sphere of a ± pair → Q = 0, additive) and the energy ledger balances (pair rest energy ≈ 2× H_static, released as outgoing waves); the remaining piece is the full 3D dynamical capture → breather → vacuum evolution.