Appendix AD — Derivation 29: Chiral Anchoring and Structural Parity Asymmetry

Overview

Parity violation in the Standard Model is introduced through:

Handed spinor couplings
Explicit chiral Lagrangians
Weak interaction asymmetry imposed algebraically

In PBG, there are no spinors or gauge fields.
Parity asymmetry instead emerges geometrically—from the anchoring conditions of structured, phase-winding modes in asymmetric coherence gradients.

This appendix shows:

How chirality arises from structural anchoring geometry
Why certain modal configurations exhibit preferred helicity
How parity violation is not imposed—but anchoring-favoured

1. Phase-Winding Modes and Anchoring Asymmetry

Let a mode have helical structure:

ψ (x) = ρ (x) e^{i (\vec{k} \cdot \vec{x} + θ (\vec{x}))}

where $θ (\vec{x})$ contains a handed phase twist—e.g. circular or spiral phase winding.

Anchoring cost depends on:

Phase gradient: $\nabla ϕ$
Direction of coherence field gradient: $\nabla B$

We define the anchoring directional tension:

T = \int ρ^{2} (\nabla ϕ \cdot \nabla B) d^{3} x

If $\nabla ϕ$ aligns with $\nabla B$ , anchoring is efficient.
If $\nabla ϕ$ opposes it, anchoring cost increases.

Thus, mirror-image phase structures can anchor differently, even in symmetric geometry.

2. Geometric Parity Asymmetry

Under spatial inversion:

\vec{x} \to - \vec{x}, \nabla ϕ \to - \nabla ϕ, \nabla B \to - \nabla B

So their dot product $\nabla ϕ \cdot \nabla B$ remains unchanged.

But the internal structure of $ψ (x)$ , including phase helicity, may change sign.
The asymmetry arises when:

The coherence field $B (x)$ is not spherically symmetric (e.g. due to external sources)
Modal structure is helically wound
Anchoring gradients favour one phase rotation direction

This breaks mirror symmetry dynamically—not algebraically.

3. Anchoring Cost Difference for Left/Right Helicity

Let $ψ_{L}$ and $ψ_{R}$ be left- and right-handed versions of a structured mode.

Define the anchoring asymmetry:

Δ C = C [ψ_{L}] - C [ψ_{R}]

If $Δ C \neq 0$ , then one handedness anchors more stably—leading to:

Asymmetric survival in thermal turnover
Biased interaction probabilities
Parity-violating dynamics

This effect strengthens in:

Coherence gradients with directional curvature
Structured environments (e.g. early-universe coherence shells)

4. Interaction Asymmetry and Weak Analogue

Weak interaction phenomena in the SM:

Only couple to left-handed fermions
Exhibit maximal parity violation

In PBG, this is reinterpreted as:

Only modes with anchoring-favoured chirality can participate in certain coherence-structured interactions.

This aligns with:

Chiral neutrino anchoring suppression
Spin-aligned coherence preference
Directional asymmetries in modal interference zones

No field coupling is required—only structural geometry.

5. Observable Consequences

Polarisation asymmetries in early-universe radiation (e.g. CMB TE correlations)
Neutrino helicity bias arising from coherence class–anchoring tension
Chiral decay pathways for anchored composite structures
Directional anchoring delay in spiral-mode propagators

These all follow from geometric anchoring asymmetry, not parity-violating Lagrangians.

Conclusion

Parity violation is not imposed in PBG—it emerges from anchoring structure geometry.

Modes with helical phase structure experience asymmetric anchoring cost
This defines a preferred chirality under coherence gradients
Weak interaction behaviour is reinterpreted as chiral anchoring asymmetry

Appendix AC | [Index](./Appendix Master) | Appendix AE