Life Cascade — K_χ multi-branch tree

Unlike physics’s linear cascade, the life calibration cascade is a multi-branch tree rooted at one structural anchor: the Kinetic Pseudoscalar Channel (LG-Y02, registry VI.L18).

The K_χ channel breaks parity at the weak-sector level and amplifies the seed (~10⁻¹⁷ relative chirality bias) into biological-scale homochirality (ee ≈ 1.0). Every life-sector empirical correlate inherits its observable signature from this anchor.

The cascade architecture (multi-branch tree)

┌──────────────────────────────────────────────────────────────────────┐
│  Layer 0: τ-categorical kernel (I.K0)                                │
└────────────────────────────────┬─────────────────────────────────────┘
                                 ▼
┌──────────────────────────────────────────────────────────────────────┐
│  Layer 1: Life Sector (VI.D15) emerges as one of the τ-sectors       │
└────────────────────────────────┬─────────────────────────────────────┘
                                 ▼
┌──────────────────────────────────────────────────────────────────────┐
│  Layer 2: Kinetic Pseudoscalar Channel — LG-Y02 (VI.L18)             │
│    Parity-odd, time-even operator on weak × EM tensor product        │
│    Amplifies weak-sector chirality (10⁻¹⁷) → biological ee ≈ 1.0     │
└────┬───────────┬──────────────┬─────────────┬─────────────┬──────────┘
     │           │              │             │             │
     ▼           ▼              ▼             ▼             ▼
┌─────────┐ ┌─────────┐  ┌─────────────┐ ┌──────────┐ ┌────────────┐
│Chirality│ │ Energy  │  │ Information │ │ Temporal │ │ Phenomenal │
│branch   │ │ branch  │  │ branch      │ │ branch   │ │ branch     │
└─────────┘ └─────────┘  └─────────────┘ └──────────┘ └────────────┘

The five branches

Chirality branch (the canonical anchor branch)

• Anchor: LG-Y02 K_χ channel (VI.L18)
• Outputs: L-amino-acid dominance in proteins (ee ≈ 1.0); D-sugar dominance in nucleic acids
• Observation: polarimetry, circular dichroism, chiral chromatography, CISS experiments (Paltiel et al. 2026-04-22)
• Glossary entries: LG-S01-cell, LG-S02..S15 (15 structures)

Energy branch

• Branches from: K_χ → stereospecific enzyme binding
• Outputs: ATP/ADP cycle at 10:1 ratio; respiration; photosynthesis; electron transport
• Observation: ³¹P NMR; luciferase assay; Seahorse extracellular flux
• Glossary entries: LG-E01-atp through LG-E09 (9 entries)

Information branch

• Branches from: K_χ → DNA D-ribose chirality preserved
• Outputs: Genetic code as BSD motivic structure; epigenetic state propagation
• Observation: sequencing, ribosome profiling, epigenetic mark assays
• Glossary entries: LG-I01..LG-I11 (11 entries)

Temporal branch

• Branches from: K_χ → asymmetric circadian protein folding
• Outputs: Circadian rhythm; cell cycle; generation time
• Observation: transcriptomics over time; behavioural assays
• Glossary entries: LG-T01..LG-T09 (9 entries)

Phenomenal branch

• Branches from: K_χ → neural-defect asymmetry
• Outputs: sleep; consciousness; cognition; sensory experience
• Observation: fMRI, EEG, behavioural psychophysics
• Glossary entries: LG-M01..LG-M09 (9 entries)

Glossary anchor

Lean formalization

Life-sector formalization is planned for v0.5 of TauLib. Current Lean formalization is concentrated in the physics cascade (Books I–V); the life cascade depends on those mathematical/physical primitives plus VI-sector lemmas not yet in TauLib.

Read next

• Life glossary — all 78 entries across 7 categories
• Calibration Cascade — the linear physics analog
• Metaphysics architecture — the categorical-only architecture for Book VII

Provenance

This is a Jekyll surface of the canonical corpus document at corpus/life-glossary/calibration-cascade.md. The corpus version is the source of truth; this page is a curated rendering for the public-facing site.