Stem-Branch System (干支)

The foundational combinatorial system of Chinese metaphysics. Ten Heavenly Stems and twelve Earthly Branches combine into a 60-pair sexagenary cycle used for counting years, months, days, and hours. Each stem and branch carries an elemental association; the Five Elements generative and conquering cycles govern their interactions. The 納音 (cycle elements) layer assigns a poetic element-name to each of the 60 pairs.

Stems and Branches (天干地支)

Export	Description
STEMS	['甲','乙','丙','丁','戊','己','庚','辛','壬','癸']
BRANCHES	['子','丑','寅','卯','辰','巳','午','未','申','酉','戌','亥']
STEM_ELEMENT	Record<Stem, Element> (甲乙=木, 丙丁=火, ...)
BRANCH_ELEMENT	Record<Branch, Element>
stemByIndex(n)	Get stem by index (mod 10)
branchByIndex(n)	Get branch by index (mod 12)
stemPolarity(stem)	'陽' or '陰'
branchPolarity(branch)	'陽' or '陰'

Sexagenary Cycle (六十甲子)

Export	Description
makeStemBranch(stem, branch)	Build a StemBranch string
stemBranchByCycleIndex(n)	Get pair at position n in the 60-cycle
stemBranchCycleIndex(stem, branch)	Reverse lookup (returns -1 for invalid parity)
parseStemBranch(str)	Parse two-character string into stem + branch
allSixtyStemBranch()	All 60 valid pairs in cycle order

Five Elements (五行)

Export	Description
GENERATIVE_CYCLE	金→水→木→火→土→金
CONQUERING_CYCLE	金→木→土→水→火→金
ELEMENT_ORDER	['金','木','水','火','土']
getElementRelation(from, to)	Returns '生', '剋', '被生', '被剋', or '比和'

Cycle Elements (納音)

Export	Description
CYCLE_ELEMENTS	Full 60-pair lookup table with element and poetic name
getCycleElement(sb)	納音 element for a stem-branch pair
getCycleElementName(sb)	納音 poetic name (e.g. 海中金, 爐中火)

Types

type Stem = '甲' | '乙' | '丙' | '丁' | '戊' | '己' | '庚' | '辛' | '壬' | '癸';
type Branch = '子' | '丑' | '寅' | '卯' | '辰' | '巳' | '午' | '未' | '申' | '酉' | '戌' | '亥';
type StemBranch = `${Stem}${Branch}`;
type Element = '金' | '木' | '水' | '火' | '土';
type ElementRelation = '生' | '剋' | '被生' | '被剋' | '比和';
type Strength = '旺' | '相' | '休' | '囚' | '死';
interface HiddenStem { stem: Stem; proportion: number; }