Appendix I — Derivation 9: Strong and Weak Interactions from Modal Anchoring

Appendix I — Derivation 9: Strong & Weak Phenomena from Modal Anchoring

(Built on Foundations v1.0 – 2025-06-10)

No forces, no gauge bosons.
What the Standard Model calls SU(3) “colour” and SU(2) “weak” forces
arises in Phase-Biased Geometry from anchoring balance, saturation and
chirality-dependent cost.

1 Confinement = multi-sheet anchoring

See Appendix W - Colour Lagrangian Derivation for the three-sheet proton.

This reproduces: free quark absence, baryon colour-neutrality, meson
(doublet) stability.

2 Internal distortions = gluon analogue

Within a colour-neutral cluster the three sheets twist and retwist.
Those phase-derivative distortions are the dynamical variables that
appear in the SU(3) quartic term of
Appendix W - Colour Lagrangian Derivation.
Energy is stored as coherence curvature—no standalone gluon field.

3 Chirality cost and weak phenomena

[[Magnetic-Moment Structures]] shows handed phase windings.
A parity-bias term

δ∫ρL2BRd3x+cyclic

(Concept-v2 Stage D) gives lower anchoring cost for left-handed
envelopes. Consequences:

Observation PBG reading
Parity violation lower cost ⇒ L modes dominate interactions
β-decay handed sheet re-tiling in neutron core releases a minimal phase packet (mode ≡ ν̄ₑ)
V–A current chirality weighting in interference term, no separate gauge field

The single parameter δ is fixed once from neutron asymmetry; no new
couplings per flavour.

4 Modal decay channels

Decay happens when local saturation or chirality bias makes the current
configuration non-minimal. Allowed products must:

  1. Keep total winding & charge conserved (phase continuity).
  2. Individually anchor in the ambient field.
  3. Respect saturation exclusion (Pauli-type rule).

This reproduces observed selection rules without Feynman vertices.

5 What is already derived vs open

Feature Status Reference
SU(3) cost & bare gs Derived Appendix W - Colour Lagrangian Derivation
Asymptotic freedom sign Derived same appendix
Confinement criterion Qualitative FEM result colour appendix
Parity-bias δ Calibrated from Ae Concept-v2 Stage D
Full weak mixing matrix Open chirality programme

Bottom line

Strong and weak effects in PBG are not separate forces but
geometric responses of coherence sheets to anchoring pressure and
handed phase bias. Quantitative work continues, but no extra
fundamental constants have been introduced beyond
(α,β,γ) and one calibrated chirality factor δ.

Appendix H - Particle Statistics | [Index](./Appendix Master) | Appendix J - Casimir Pressure