Circadian Rhythm

The circadian rhythm is a τ-categorical Poincaré orbit on the life sector with a 24-hour period: a stable closed loop in the cellular state-space whose phase is entrained to the diurnal solar cycle. It is the τ-categorical realization of biological time.

Categorical invariant. Poincaré orbit (VI.T17) of period τ ≈ 24h on the life-sector phase space, instantiated as a τ¹-rotation (VI.P09) of cellular gene-expression and metabolic states.

Primary registry anchor: VI.T17

Supporting items: VI.P09, VI.D27, VI.D70, VI.D25

1. I.K0 — Universe Postulate
2. VI.D15 — Life Sector
3. VI.D25 — Temporal Stability Predicate — life requires stable temporal structure
4. VI.D27 — Temporal Lemniscate — closed temporal loop class
5. VI.P09 — 24-Hour Cycle as τ¹ Rotation
6. VI.T17 — Circadian Rhythm as Poincaré Orbit — canonical theorem

Biomarker: Core clock genes BMAL1, CLOCK, PER1/2/3, CRY1/2 expression cycling; melatonin pulse; cortisol awakening response; body temperature 0.5-1°C diurnal swing; suprachiasmatic nucleus (SCN) firing rate.

Measurable range: Period 23.5-24.5h (free-running); entrained to 24.0h by light cycle; phase shift ~1h per day max under jet lag; complete shift requires ~7-10 days.

Observation method: Actigraphy, polysomnography (sleep/wake), salivary melatonin assay (DLMO), continuous body temperature, RNA-seq time-series, single-cell luciferase reporters of clock genes.

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

Anchor chain:

1. VI.L18 chirality channel
2. stereospecificity of clock-protein folding (L-amino acids)
3. homochirality of melatonin (pineal D-tryptophan derivative)

Manuscript reference: manuscript-sources/book-06/part02/ch15-circadian-rhythms.tex

Status: Planned

Related glossary entries

• LG-Y02-kinetic-pseudoscalar-channel Kinetic Pseudoscalar Channel
• LG-S01-cell The Cell

Referenced by

• LG-M03-sleep-repair Sleep Repair Function
• LG-T02-cell-cycle Cell Cycle
• LG-T03-sleep-cycle Sleep Cycle (NREM/REM)
• LG-T07-circadian-master-clock Circadian Master Clock (SCN-anchored)
• LG-T08-lemniscate-extended Extended Lemniscate