Polarity Functional

The Polarity Functional is the τ-categorical map P_S: End(S) → 2_τ that tests whether a holonomy sector S carries intrinsic parity asymmetry. It is trivial for EM, strong, and gravitational sectors and non-trivially realized exclusively for the weak sector — making the weak sector the unique parity-asymmetric input to the Life Sector.

Categorical invariant. Map P_S: End(S) → 2_τ on the endomorphism object of a holonomy sector S; the weak sector is the unique sector where P_S is non-trivial.

Primary registry anchor: VI.D01

Supporting items: VI.D02, VI.D03, VI.T01, VI.L01

1. I.K0 — Universe Postulate establishes the categorical kernel τ
2. VI.D01 — Polarity Functional — tests intrinsic parity asymmetry of a holonomy sector
3. VI.L01 — Weak-sector uniqueness — only the weak sector carries non-trivial P_S
4. VI.T01 — Parity Bridge Theorem — P_S non-triviality is the structural bridge into τ-life

Biomarker: Parity violation in β-decay (Wu 1957): asymmetric electron emission relative to ⁶⁰Co nuclear spin axis. Biological echo: L-amino-acid preference (>99.99% ee) and D-sugar preference, which inherit from P_weak being the only non-trivial sector polarity.

Measurable range: Wu experiment asymmetry parameter A ≈ −0.4 (electron preferentially anti-aligned with nuclear spin); weak-sector parity-violation seed ~10⁻¹⁷ relative; biological enantiomeric excess ee ≈ 1.0 after K_χ amplification; EM/strong/GR parity asymmetry compatible with zero (current bounds: |A_strong| < 10⁻⁷, |A_EM| < 10⁻¹⁰).

Observation method: Polarized β-decay (Wu-class experiments); atomic parity-violation measurements (cesium PNC, ~10⁻¹¹ amplitude); muonium spectroscopy; biomolecular polarimetry and CD spectroscopy as the downstream parity-shadow signal.

Calibration anchor: LG-Y02-kinetic-pseudoscalar-channel

Anchor chain:

1. VI.D01 — categorical polarity functional
2. VI.L01 weak-sector uniqueness — P_S is non-trivial only on the weak sector
3. VI.L18 K_χ — the τ-categorical operator that propagates this polarity into biology

Manuscript reference: manuscript-sources/book-06/part01/ch03-parity-bridge.tex

Status: Planned

Related glossary entries

• LG-Y01-life-sector Life Sector
• LG-Y02-kinetic-pseudoscalar-channel Kinetic Pseudoscalar Channel
• LG-Y03-tau-distinction τ-Distinction

Referenced by

• LG-Y03-tau-distinction τ-Distinction