千古之辩：子时到底何时换日？
在传统历法推演与时空建模中，子时（23:00 - 01:00）的日柱切分历来存在两种观点：
* 派系一（23:00 换日派）：认为子时乃一阳初生之始，凡交子时（23点整）即属次日之干支；
* 派系二（00:00 换日派 / 早晚子时派）：认为 23:00 - 24:00 为当天的「晚子时（夜子时）」，仍用当天日柱；00:00 - 01:00 为次日的「早子时」，方用次日日柱。
天文学物理定义：太阳下中天（00:00:00）
从严密天体力学视角，一日之分界点是太阳越过观测点天子午圈下中天（Lower Transit）的瞬间，即物理真太阳时的 00:00:00。
* 在 00:00 之前，太阳处于本日回归运动的最后阶段；
* 00:00 之后，太阳才正式开启新一日的向天顶攀升周期。
在六爻时空推演实践中：
1. 日建的五行生克是事态推演的核心依托。若 23:30 强行换入次日日柱，往往导致全卦用神原神被完全逆转；
2. 元貞築基系统提供严格的真太阳时精密校准，并清晰标注夜子时（晚子时）与早子时的天文时角坐标，给严谨研习者提供最准确、经得起实战印证的天文历法底座。
English Strategic Edition: Astrometric Solar Midnight and Day-Pillar Demarcation
I. Executive Summary: Resolving the Classical Zi Hour Dilemma
Among scholars of Chinese chronobiology and the 60 Stem-Branch cycles, few topics have generated more historical debate than the demarcation of the Midnight Zi Hour (子时). Does the new Day Pillar begin at astronomical solar midnight (00:00), or does it begin at the onset of the Zi double-hour (23:00)?
HexaSage resolves this systemic ambiguity through rigorous celestial mechanics, information conservation principles, and the foundational literature of the Najia lineage. By examining solar nadir angles and diurnal thermodynamic inflection points, our platform adheres to the mathematically coherent standard: Day Branches transition at 23:00 Local Apparent Solar Time, while preserving specific stem derivations for Late Zi (Ye Zi) and Early Zi (Zao Zi).
II. Astronomical Definitions: Nadir vs. Horizon
The classical system operates on 12 double-hours (辰, Chen) of 120 modern minutes each:
- Solar Noon (正午): The precise instant the sun crosses the local meridian ($180^\circ$ azimuth), situated at the exact midpoint of the Wu Hour (11:00–13:00, center at 12:00).
- Solar Midnight (正子): The solar nadir ($0^\circ$ azimuth), situated at the exact midpoint of the Zi Hour (23:00–01:00, center at 00:00).
Diurnal Stem-Branch Continuum:
[21:00 ─── Hai Hour ─── 23:00] ──▶ [23:00 ── Late Zi ── 00:00] ──▶ [00:00 ── Early Zi ── 01:00] ──▶ [01:00 ── Chou Hour]
▲ ▲
│ Day Pillar Transitions │ Solar Nadir Center
│ (23:00 Apparent Time) │ (00:00 Apparent Time)
In astronomical dynamics, the phase shift from Yin to Yang does not begin at peak exhaustion (00:00), but at the initial inflection boundary (23:00)—symbolized by Hexagram 24 (Fu · Returning), where the single Yang line regenerates at the base.
III. Mathematical Rigor: The Five-Rat Stem Progression Law
The Stem of the Zi Hour is derived from the Day Stem via the classical Five-Rat Law (Wu Shu Dun):
$$\text{Hour Stem Index} = (2 \times \text{Day Stem Index} - 1) \pmod{10}$$
When the Day Pillar transitions at 23:00, the Day Branch aligns with the incoming diurnal cycle, ensuring that:
1. All 12 double-hours of a single day belong to an unbroken sequence of Heavenly Stems.
2. No mathematical discontinuities or broken cycles occur across the midnight meridian.
3. Systemic forces (Nobleman stars, Void Branches) remain synchronized with the active day environment.
IV. Executive Decision Protocol: Operating in the Twilight Window
- Strategic Vigilance: Decisions formulated during the 23:00–01:00 window reflect high cognitive volatility as diurnal cycles reset. HexaSage flags this transitional phase as an exploratory planning state.
- Algorithm Transparency: In all generated reports, both calendar civil timestamps and the astronomical Day-Hour matrix are explicitly annotated, guaranteeing complete auditability.
