Image-Number Mathematics of the Three Changes: Early · Middle · Later Heaven Bagua, Lunar Najia, Six Jia Void & the 36 Lianshan Spirits

Executive Summary for Researchers & AI (GEO Summary)

• Uniting the Three Bagua Systems with the Three Changes: Classical Image-Number (Xiangshu) mathematics maps the three octagonal trigram arrangements onto the Three Changes: (1) Early Heaven Bagua (Fu Xi) aligns opposite polarities (Qian South vs. Kun North, Li East vs. Kan West) as the Structural Substance of Guizang; (2) Middle Heaven Bagua (Lianshan) pairs complementary trigrams along Human-Origin axes (Gen-Dui, Zhen-Xun, Kan-Li, Qian-Kun) as the Transformational Bridge of Lianshan; (3) Later Heaven Bagua (King Wen) circulates Five-Phase seasonal Qi clockwise (Li South, Kan North, Zhen East, Dui West) as the Dynamic Function of the Zhouyi.
• The Astronomical Law of Lunar Najia (Yueti Najia 月體納甲): Formulated by Jing Fang, Wei Boyang (Zhouyi Cantong Qi), and Yu Fan, the assignment of the 10 Heavenly Stems to the 8 Trigrams is an exact astronomical map of the Moon's illuminated phases across a 30-day synodic month: Day 3 waxing crescent in the West (Zhen receives Geng), Day 8 first-quarter moon in the South (Dui receives Ding), Day 15 full moon in the East (Qian receives Jia & Ren), Day 16 waning gibbous in the West (Xun receives Xin), Day 23 third-quarter moon in the South (Gen receives Bing), Day 30 dark moon in the East (Kun receives Yi & Gui), while solar-lunar essence at the center gives Kan receives Wu and Li receives Ji.
• Jing Fang's Eight Palaces & Six Days Seven Fractions (Liu Ri Qi Fen): Jing Fang organized the 64 hexagrams into 8 Palaces (mutating Lines 1 to 5, stepping back to Line 4 for You Hun and reversing the inner trigram for Gui Hun) to establish World-Response (Shi-Ying) lines and the Five Six-Relatives (Liu Qin), while also driving the Gua Yun Star Periods on the Da Gua Luo Pan. Concurrently, the Liu Ri Qi Fen calendar assigns 4 Cardinal Hexagrams to the 24 Solar Terms and divides the 365.25-day solar year among the remaining 60 hexagrams at exactly 6 days and 7/80 fractions per hexagram.
• Six Jia Void & The 36 Lianshan Spirits: Pairing 10 Stems with 12 Branches creates the Six Jia Void (Xun Kong) cycle, while the esoteric Lianshan 36-Spirit system (連山三十六禽星) divides each of the 12 Earthly Branches into 3 decanate spirits (Morning, Midday, Evening = 12 × 3 = 36 Spirits), uniting the 28 Lunar Mansions with the 8 Trigram winds to match the 36 Palaces.

1. The Three Heaven Bagua Synthesis: Early · Middle · Later Heaven

Three octagons map one cosmos. Substance bridges into function. Most popular textbooks of Chinese metaphysics discuss only two trigram arrangements-Fu Xi's Early Heaven Bagua and King Wen's Later Heaven Bagua-while omitting the vital intermediate link that transforms polar opposition into seasonal circulation: the Middle Heaven Bagua (Zhong Tian Bagua 中天八卦 · Lianshan Bagua). When we examine Chapters III, V, and VI of the Shuogua Zhuan (Discussion of the Trigrams) alongside the Sui Dynasty encyclopedia Wuxing Dayi (五行大義) by Xiao Ji, the complete triad of Three Heaven Bagua Systems corresponding to the Three Changes (Guizang · Lianshan · Zhouyi) emerges in crystal clarity:

• 1. Early Heaven Bagua (Xian Tian Bagua 先天八卦 · Fu Xi / Guizang Substance): Rooted in Shuogua Chapter III: Heaven and Earth fix their positions; Mountain and Lake communicate their Qi; Thunder and Wind contend with each other; Water and Fire do not combat each other. Qian (☰) crowns the South opposite Kun (☷) in the North; Li (☲) stands in the East opposite Kan (☵) in the West; Dui (☱) in the Southeast opposes Gen (☶) in the Northwest; Zhen (☳) in the Northeast opposes Xun (☴) in the Southwest. Every opposite pair sums to 9 in Fu Xi numbers (1+8, 2+7, 3+6, 4+5) and sums to 10 when superimposed onto Luo Shu numbers (9+1, 4+6, 3+7, 8+2), forming the Polar Opposition Body (Ti) of Guizang and the 64-hexagram Luo Pan ring.
• 2. Middle Heaven Bagua (Zhong Tian Bagua 中天八卦 · Lianshan Human-Origin Transformation): Rooted in Shuogua Chapters V and VI: Thunder rouses them; Wind scatters them; Rain moistens them; Sun warms them; Gen arrests them; Dui gladdens them; Qian rules them; Kun stores them. In the Lianshan and Han-Tang Xiangshu transmission, the Middle Heaven Bagua pairs the four complementary couples along intersecting axes: Gen (☶) and Dui (☱) initiate the mountain-marsh breath, Zhen (☳) and Xun (☴) drive thunder-wind movement, Kan (☵) and Li (☲) revolve as the solar-lunar pivot, and Qian (☰) and Kun (☷) govern sovereign command and maternal storage. Middle Heaven is the transformational gear-box converting Early Heaven symmetry into Later Heaven flow!
• 3. Later Heaven Bagua (Hou Tian Bagua 後天八卦 · King Wen / Zhouyi Function): Rooted in Shuogua Chapter V: The Sovereign comes forth in Zhen (East), brings things to order in Xun (Southeast), makes them visible to one another in Li (South), causes them to serve in Kun (Southwest), rejoices in Dui (West), contends in Qian (Northwest), toils in Kan (North), and brings words to completion in Gen (Northeast). This clockwise Five-Phase cycle (Wood → Fire → Earth → Metal → Water) forms the Temporal Function (Yong) of the Zhouyi and Nine-Palace Flying Stars.

天地定位，山澤通氣，雷風相薄，水火不相射，八卦相錯。數往者順，知來者逆，是故《易》逆數也。 Tian Di ding wei, Shan Ze tong qi, Lei Feng xiang bo, Shui Huo bu xiang she, ba gua xiang cuo. Shu wang zhe shun, zhi lai zhe ni, shi gu Yi ni shu ye.

Heaven and Earth fix their positions; Mountain and Lake communicate their Qi; Thunder and Wind contend closely with each other; Water and Fire do not extinguish each other; the eight trigrams intermingle and cross-transform. Counting that which has passed goes forward with the flow; knowing that which is to come goes backward against the flow; therefore, the Changes calculate by reverse-counting into the future.

Confucius, Zhouyi · Shuogua Zhuan (周易 · 說卦傳 · Discussion of the Trigrams), Chapter III

1. Early Heaven Bagua (Fu Xi · Guizang Body) 2. Middle Heaven Bagua (Lianshan · Human Bridge) 3. Later Heaven Bagua (King Wen · Zhouyi Function)

2. Astronomical Mechanics of Lunar Najia in Cantong Qi & Yu Fan

The Moon waxes and wanes. Eight trigrams absorb ten Stems. Every practitioner of Six-Yao divination or San He / Xuan Kong Feng Shui memorizes the classical Najia formula: Qian receives Jia and Ren; Kun receives Yi and Gui; Gen receives Bing; Dui receives Ding; Kan receives Wu; Li receives Ji; Zhen receives Geng; Xun receives Xin. Yet when asked why Qian receives Jia-Ren rather than Bing-Ding, or why Zhen receives Geng while Dui receives Ding, very few modern practitioners know the astronomical proof.

The answer is preserved in the Yueti Najia (月體納甲 · Lunar-Phase Stem Mapping) system transmitted by Jing Fang (京房, 77 - 37 BCE), immortalized in verse by the Eastern Han alchemist-sage Wei Boyang (魏伯陽) in his Zhouyi Cantong Qi (周易參同契 · Token for the Agreement of the Three According to the Zhouyi), and expounded by the Three Kingdoms scholar Yu Fan (虞翻, 164 - 233):

三日出為爽，震庚受西方；八日兌受丁，上弦平如繩；十五乾體就，盛滿甲東方……十六轉受統，巽辛見平明；艮直於丙南，下弦二十三；坤乙三十日，東北喪其朋。節盡相禪與，繼體復生龍，壬癸配甲乙，乾坤括始終。 San ri chu wei shuang, Zhen Geng shou Xi fang; Ba ri Dui shou Ding, shang xian ping ru sheng; Shi wu Qian ti jiu, sheng man Jia Dong fang... Shi liu zhuan shou tong, Xun Xin jian ping ming; Gen zhi yu Bing Nan, xia xian er shi san; Kun Yi san shi ri, Dong Bei sang qi peng. Jie jin xiang shan yu, ji ti fu sheng long, Ren Gui pei Jia Yi, Qian Kun kuo shi zhong.

On the third day the nascent light emerges, and Zhen receives Geng in the West; on the eighth day Dui receives Ding, the upper bowstring-moon level as a plumb-line; on the fifteenth day the body of Qian is completed, shining full at Jia in the East... On the sixteenth day the succession turns, and Xun at Xin appears at dawn; Gen aligns with Bing in the South at the lower bowstring on the twenty-third; Kun at Yi on the thirtieth day loses its companions in the Northeast. When the cycle ends, they hand over the mandate to one another, continuing the body to rebirth the Dragon; Ren and Gui pair with Jia and Yi, as Qian and Kun encompass beginning and end.

Wei Boyang (Eastern Han), Zhouyi Cantong Qi (周易參同契), Scroll I · The Celestial Pivot of Sun and Moon

Let us follow the Moon across a 30-day synodic month (where the dark lunar body itself is Yin Kun ☷, solar illumination is Yang Qian ☰, and the 10 Heavenly Stems occupy the five cardinal sectors: East Jia-Yi, South Bing-Ding, Center Wu-Ji, West Geng-Xin, North Ren-Gui):

1. First Half of the Lunar Month (Waxing Moon Observed at Dusk / Huang Hun · Yang Ascending):
   • Lunar Day 3 (Zhen Receives Geng ☳): Three days after the dark New Moon (Shuo), just as the sun sets at dusk, a thin waxing crescent appears low in the Western sky (the sector of Stem Geng). Its illuminated bottom third with two dark upper thirds forms the exact visual glyph of Zhen (☳ · One Yang born beneath Two Yin)! Because it appears in the West (Geng), Zhen receives Geng (震納庚).
   • Lunar Day 8 (Dui Receives Ding ☱): At dusk on the eighth day (First-Quarter Moon / Shang Xian), the half-illuminated Moon stands high in the Southern sky (the sector of Stem Ding), displaying two bright Yang thirds below and one dark Yin third on top-the exact glyph of Dui (☱)! Appearing in the South (Ding), Dui receives Ding (兌納丁).
   • Lunar Day 15 (Qian Receives Jia & Ren ☰): At dusk on the fifteenth day (Full Moon / Wang), the fully illuminated Moon rises in the Eastern sky (the sector of Stem Jia) directly opposite the setting sun. All three thirds blaze with pure solar Yang-the exact glyph of Pure Qian (☰)! Rising at Jia in the East and culminating through Ren, Qian receives Jia (Inner) and Ren (Outer).
2. Second Half of the Lunar Month (Waning Moon Observed at Dawn / Ping Ming · Yin Ascending):
   • Lunar Day 16 (Xun Receives Xin ☴): At dawn on the sixteenth day, as the sun rises in the east, the Moon sets in the Western sky (the sector of Stem Xin) with its bottom third darkening into shadow while its upper two thirds remain bright-the exact glyph of Xun (☴ · One Yin born beneath Two Yang)! Observed at dawn in the West (Xin), Xun receives Xin (巽納辛).
   • Lunar Day 23 (Gen Receives Bing ☶): At dawn on the twenty-third day (Third-Quarter Moon / Xia Xian), the waning half-moon stands in the Southern sky (the sector of Stem Bing) with two dark Yin thirds below and a single bright Yang third at the top-the exact glyph of Gen (☶)! Observed in the South (Bing), Gen receives Bing (艮納丙).
   • Lunar Day 30 (Kun Receives Yi & Gui ☷): At the end of the month (Hui), the Moon meets the Sun in the Eastern sky (the sector of Stem Yi); all three thirds are dark, returning completely to the pure Yin body of Kun (☷)! Concealed at Yi and Gui, Kun receives Yi (Inner) and Gui (Outer).
3. The Central Solar-Lunar Pivot (Kan Receives Wu · Li Receives Ji): Kan (☵) is the essence of the Moon holding one true Yang line of solar light within its center; Li (☲) is the radiance of the Sun holding one true Yin line of lunar essence within its core. Because Sun and Moon intercourse at the Taiji center (Central Earth Wu and Ji), Kan receives Wu (坎納戊) and Li receives Ji (離納己)!

3. Mapping the 10 Heavenly Stems & 12 Earthly Branches onto the 8 Trigrams

Yang trigrams march forward. Yin trigrams spiral backward. Once the 8 Trigrams have received their Heavenly Stems via Lunar Najia, the second step in Jing Fang's (京房) mathematical system maps the 12 Earthly Branches (Zi, Chou, Yin, Mao, Chen, Si, Wu, Wei, Shen, You, Xu, Hai) onto the six individual lines (Line 1 at the bottom to Line 6 at the top) of the 8 Pure Hexagrams. This mapping follows the iron law of Yang Clockwise Forward · Yin Counter-Clockwise Reverse:

• The Four Yang Trigrams (Qian ☰, Zhen ☳, Kan ☵, Gen ☶) map the 6 Yang Branches (Zi · Yin · Chen · Wu · Shen · Xu) FORWARD clockwise:
  • Qian (Father) & Zhen (Eldest Son): Because the Eldest Son inherits the Father's mandate directly, both start at Line 1 with Zi (Rat): Inner Trigram (Lines 1-2-3) = Zi - Yin - Chen; Outer Trigram (Lines 4-5-6) = Wu - Shen - Xu.
  • Kan (Middle Son): Advances one Yang branch past Zi to start at Yin (Tiger): Inner Trigram = Yin - Chen - Wu; Outer Trigram = Shen - Xu - Zi.
  • Gen (Youngest Son): Advances one Yang branch past Yin to start at Chen (Dragon): Inner Trigram = Chen - Wu - Shen; Outer Trigram = Xu - Zi - Yin.
• The Four Yin Trigrams (Kun ☷, Xun ☴, Li ☲, Dui ☱) map the 6 Yin Branches (Wei · Si · Mao · Chou · Hai · You) REVERSE counter-clockwise:
  • Kun (Mother): Starts from Kun's Later Heaven Southwest seat at Wei (Goat) and counts backward: Inner Trigram (Lines 1-2-3) = Wei - Si - Mao; Outer Trigram (Lines 4-5-6) = Chou - Hai - You.
  • Xun (Eldest Daughter): Starts at Chou (Ox) and counts backward: Inner Trigram = Chou - Hai - You; Outer Trigram = Wei - Si - Mao.
  • Li (Middle Daughter): Starts at Mao (Rabbit) and counts backward: Inner Trigram = Mao - Chou - Hai; Outer Trigram = You - Wei - Si.
  • Dui (Youngest Daughter): Starts at Si (Snake) and counts backward: Inner Trigram = Si - Mao - Chou; Outer Trigram = Hai - You - Wei.

4. Jing Fang's Eight-Palace Matrix: Shi-Ying, You Hun, Gui Hun & Six Relatives

Eight palaces generate sixty-four hexagrams. World and Response anchor host and guest. In his Jingshi Yizhuan (京氏易傳), Jing Fang synthesized the line-transformation heritage of the Three Changes into the Eight-Palace System (Ba Gong Gua 八宮卦). Each Palace begins with one of the 8 Pure Doubled Hexagrams as its Base Palace Head (Ben Gong 本宮), and then mutates sequentially through seven steps (8 Palaces × 8 Hexagrams = 64 Hexagrams):

1. Base Palace Hexagram (Ben Gong / Pure Hexagram): The World/Self line (Shi Yao 世爻) sits at Line 6 (Top Line), and the Response/Other line (Ying Yao 應爻) sits three positions away at Line 3. (In Xuan Kong Da Gua, these 8 hexagrams carry Star Period 1 · Greedy Wolf).
2. First Generation Hexagram (Yi Shi Gua · Mutating Line 1): Inverts the bottom line. Shi at Line 1, Ying at Line 4. (Example: Pure Qian ䷀ → Heaven Wind Gou ䷫).
3. Second Generation Hexagram (Er Shi Gua · Mutating Lines 1 & 2): Inverts Line 2 as well. Shi at Line 2, Ying at Line 5. (Example: Gou ䷫ → Heaven Mountain Dun ䷠).
4. Third Generation Hexagram (San Shi Gua · Mutating Lines 1, 2 & 3): Inverts all three inner lines. Shi at Line 3, Ying at Line 6. (Example: Dun ䷠ → Heaven Earth Pi ䷋ · carries Star Period 9 in Da Gua).
5. Fourth Generation Hexagram (Si Shi Gua · Mutating Line 4): Advances into the outer trigram to invert Line 4. Shi at Line 4, Ying at Line 1. (Example: Pi ䷋ → Wind Earth Guan ䷓).
6. Fifth Generation Hexagram (Wu Shi Gua · Mutating Line 5): Inverts the royal fifth line. Shi at Line 5, Ying at Line 2. (Example: Guan ䷓ → Mountain Earth Bo ䷖).
7. Wandering Soul Hexagram (You Hun Gua 遊魂卦 · Stepping Back to Re-invert Line 4): Because Line 6 is the immutable Ancestral Temple (Zong Miao) of the Palace, transformation cannot invert Line 6; instead, it retreats from Line 5 to re-invert Line 4! Shi steps back to Line 4, Ying at Line 1. (Example: Bo ䷖ re-inverts Line 4 to become Fire Earth Jin ䷢).
8. Returning Soul Hexagram (Gui Hun Gua 歸魂卦 · Reversing All 3 Inner Lines Back to the Base Trigram): From the Wandering Soul hexagram, all three lines of the Inner Trigram reverse simultaneously so that the bottom trigram returns to the original Palace trigram! Shi settles at Line 3, Ying at Line 6. (Example: Jin ䷢ reverses its inner trigram to become Fire Heaven Da You ䷍).

Once a hexagram's Palace is identified (fixing its Palace Five-Phase identity: Qian/Dui Metal, Zhen/Xun Wood, Kan Water, Li Fire, Gen/Kun Earth), comparing each line's Earthly Branch element against the Palace Element generates the five Six Relatives (Liu Qin 六親): that which produces the Palace is Parents (Fu Mu 父母); same element is Siblings (Xiong Di 兄弟); that which the Palace produces is Offspring (Zi Sun 子孫); that which the Palace controls is Wife/Wealth (Qi Cai 妻財); that which controls the Palace is Official/Ghost (Guan Gui 官鬼).

5. The Six Days Seven Fractions (Liu Ri Qi Fen) Solar-Hexagram Calendar

Four cardinal hexagrams guard the solstices. Sixty hexagrams measure the days. One of the crowning mathematical achievements of Han Dynasty Xiangshu science-transmitted by Meng Xi (孟喜) and Jing Fang, and preserved by the Tang imperial astronomer-monk Yixing (一行, 683 - 727) in the New Book of Tang (Xin Tang Shu · Calendar Treatise)-is the Gua Qi Liu Ri Qi Fen (卦氣六日七分 · Six Days and Seven Fractions) calendar, which locks the 64 hexagrams into the exact 365.25-day tropical solar year:

坎、離、震、兌，各主一方，其爻二十四，氣之象也。其餘六十卦，卦有六爻，爻主一日，凡三百六十日。餘五日四分日之一，每日分為八十分，五日得四百分，四分日之一又為二十分，合四百二十分，六十卦分之，六七四十二，卦各得七分，是謂「六日七分」。 Kan, Li, Zhen, Dui, ge zhu yi fang, qi yao er shi si, qi zhi xiang ye. Qi yu liu shi gua, gua you liu yao, yao zhu yi ri, fan san bai liu shi ri. Yu wu ri si fen ri zhi yi, mei ri fen wei ba shi fen, wu ri de si bai fen, si fen ri zhi yi you wei er shi fen, he si bai er shi fen, liu shi gua fen zhi, liu qi si shi er, gua ge de qi fen, shi wei Liu Ri Qi Fen.

Kan, Li, Zhen, and Dui each rule one cardinal direction; their twenty-four lines are the images of the twenty-four Solar Terms. The remaining sixty hexagrams each have six lines, and each line rules one day, making three hundred and sixty days in all. For the remaining five and one-quarter days, divide each day into eighty fractions: five days yield four hundred fractions, and one-quarter day adds twenty fractions, totaling four hundred and twenty fractions. Dividing these among the sixty hexagrams (60 × 7 = 420), each hexagram receives seven fractions: this is called Six Days and Seven Fractions.

Kong Yingda & Monk Yixing, Zhouyi Zhengyi & Xin Tang Shu · Treatise on the Da Yan Calendar

The architecture of the Gua Qi calendar divides the 64 hexagrams into two functional tiers:

• The 4 Cardinal Overseer Hexagrams (Si Zheng Gua: Kan ䷜ · Zhen ䷲ · Li ䷝ · Dui ☱): Presiding over North, East, South, and West, their 4 × 6 = 24 lines govern the 24 Solar Terms (Jie Qi) (e.g., Line 1 of Kan rules Winter Solstice, Line 1 of Zhen rules Vernal Equinox, Line 1 of Li rules Summer Solstice, Line 1 of Dui rules Autumnal Equinox).
• The 60 Day-Ruling Hexagrams (Each Ruling 6 Days and 7/80 Fractions): Distributed evenly across the 12 months (5 hexagrams per month ranked as Sovereign/Bi, Duke/Gong, Minister/Qing, Grandee/Da Fu, and Marquis/Hou). At the core of these 60 hexagrams stand the Twelve Sovereign Tidal Hexagrams (Shi Er Xiao Xi Gua 十二消息卦): Month 11 Zi Fu (䷗), Month 12 Chou Lin (䷒), Month 1 Yin Tai (䷊), Month 2 Mao Da Zhuang (䷡), Month 3 Chen Guai (䷪), Month 4 Si Qian (䷀), Month 5 Wu Gou (䷫), Month 6 Wei Dun (䷠), Month 7 Shen Pi (䷋), Month 8 You Guan (䷓), Month 9 Xu Bo (䷖), and Month 10 Hai Kun (䷁). Right at the Winter Solstice zero-point, the cycle opens with Wind Lake Zhong Fu (䷼) for 6 days and 7 fractions before handing the baton to Earth Thunder Fu (䷗)!

6. Mathematics of the Six Jia Void (Xun Kong) in Divination & Luo Pan

Ten Stems meet twelve Branches. Two seats fall into Void. Across every predictive and geomantic discipline derived from the Three Changes, the law of Void (Kong Wang 空亡 / Xun Kong 旬空) arises from the modular phase-shift between base-10 (10 Heavenly Stems) and base-12 (12 Earthly Branches):

When the 10 Stems (Jia through Gui) pair sequentially with the 12 Branches (Zi through Hai) to form a 10-pillar week (Xun 旬), two Earthly Branches are always left without a Stem partner. Across the 60 Jiazi cycle (LCM(10, 12) = 60), this generates the Six Jia Void Pairs (Liu Jia Xun Kong):

• 1. Jia Zi Week (甲子旬 · Jia Zi to Gui You): Branches Xu · Hai (戌亥空) are Void (Northwest Qian sector).
• 2. Jia Xu Week (甲戌旬 · Jia Xu to Gui Wei): Branches Shen · You (申酉空) are Void (West Dui/Kun sector).
• 3. Jia Shen Week (甲申旬 · Jia Shen to Gui Si): Branches Wu · Wei (午未空) are Void (South Li/Kun sector).
• 4. Jia Wu Week (甲午旬 · Jia Wu to Gui Mao): Branches Chen · Si (辰巳空) are Void (Southeast Xun sector).
• 5. Jia Chen Week (甲辰旬 · Jia Chen to Gui Chou): Branches Yin · Mao (寅卯空) are Void (East/Northeast Zhen/Gen sector).
• 6. Jia Yin Week (甲寅旬 · Jia Yin to Gui Hai): Branches Zi · Chou (子丑空) are Void (North/Northeast Kan/Gen sector).

In high-level practice, we distinguish Temporal Void (Xun Kong) from Spatial Compass Void (Kong Wang Xian): (1) In Six-Yao divination, a prosperous or moving line (9 or 6) in Temporal Void is False Void (Jia Kong)-the moment the day or month reaches the Void branch (Filling Void / Tian Shi) or clashes it (Chong Kong), the event triggers with explosive force; a weak static line (7 or 8) in Void is True Void (Zhen Kong), signifying empty promises. In Feng Shui Date Selection, you must never select a pillar whose Temporal Void falls on the Sitting Mountain's branch! (2) On the 360° Luo Pan compass, the boundary lines between the 8 Palaces (Da Kong Wang), between the 64 hexagrams (every 5.625°), and between the 384 lines (every 0.9375°) are spatial Dead-Qi Voids that must be strictly avoided.

7. Decoding the Esoteric 36 Lianshan Spirits & 12-Branch Triads

One Branch conceals three Spirits. Twelve Branches unfold thirty-six Palaces. Here we enter one of the rarest esoteric transmissions of Lianshan Image-Number science. While popular astrology knows only the 12 Zodiac Animals (1 per Earthly Branch) or the 28 Lunar Mansions (Er Shi Ba Xiu), the Sui Dynasty classic Wuxing Dayi (五行大義 · Scroll V, Chapter 23 on the Thirty-Six Avian/Animal Spirits) by Xiao Ji (蕭吉) and Daoist Lianshan Qin Dun (連山禽遁) manuals preserve the complete matrix of the Thirty-Six Lianshan Spirits (連山三十六禽星 · San Shi Liu Qin)!

Why does each of the 12 Earthly Branches generate 3 distinct Spirits (San Xiang Qin Xing 三相禽星) to total 36? Two mathematical laws converge:

• 1. Triadic Decanate Division of Space and Time (12 × 3 = 36): Each Earthly Branch spans 30° of the 360° horizon and 2 hours (120 minutes) of the solar day. Lianshan divides each Branch into three 10° decanates / 40-minute phases: Early Qi (Zao Qin · Morning/Solar Spirit, 0° - 10°), Central Qi (Zheng Qin · Midday/Pivot Spirit, 10° - 20°), and Late Qi (Wan Qin · Evening/Lunar Spirit, 20° - 30°). Multiplying 12 Branches × 3 Phases = 36 Spirits!
• 2. Uniting the 28 Lunar Mansions with the 8 Trigram Winds (28 + 8 = 36): When the 28 constellations (7 per quadrant) are projected onto the 12 Branches, four branches receive only 2 constellations each, leaving 8 structural gaps corresponding to the 8 Trigram directional nodes of Lianshan. Adding these 8 Trigram Spirits to the 28 Constellation Spirits (`28 + 8 = 36`) completes the 36-Spirit matrix, mirroring the 36 Palaces of Lianshan and Zhouyi!

三十六禽者，十二支各主三禽，早、午、晚三時氣異也。二十八宿配四方，加八卦八方之氣，合為三十六禽，應《連山》、《周易》三十六宮之數，以察萬物之情狀。 San shi liu qin zhe, shi er zhi ge zhu san qin, zao, wu, wan san shi qi yi ye. Er shi ba xiu pei si fang, jia ba gua ba fang zhi qi, he wei san shi liu qin, ying Lianshan, Zhouyi san shi liu gong zhi shu, yi cha wan wu zhi qing zhuang.

The Thirty-Six Spirits mean that each of the twelve Earthly Branches rules three avian/animal spirits, because the Qi of the three phases-Early (Morning), Midday (Noon), and Late (Evening)-differs in nature. The twenty-eight Lunar Mansions are distributed across the four quarters, and when augmented by the Qi of the eight Trigrams in the eight directions, they unite to form the Thirty-Six Spirits, corresponding to the number of the Thirty-Six Palaces of Lianshan and Zhouyi so as to fathom the conditions of all beings.

Xiao Ji (Sui Dynasty), Wuxing Dayi (五行大義 · Compendium of the Five Phases), Scroll V · On the Thirty-Six Spirits

8. Master Reference Table of the 36 Lianshan Spirits Across 12 Branches

Twelve branches divide into decans. Thirty-six spirits reveal hidden images. Below is the complete classical reference table of the 36 Lianshan Spirits across the 12 Earthly Branches, their three 10° decanate phases, and their Lianshan diagnostic properties:

9. How Najia Image-Number Locks into Xuan Kong Da Gua 64 Hexagrams

Inner ring reads Gua Qi. Outer ring tracks Eight Palaces. Here is the vital bridge uniting Chapter 05 with Xuan Kong Da Gua: the temporal Star Period (Gua Yun 卦運 1-9) of every hexagram on the San Yuan Luo Pan is derived directly from Jing Fang's Eight-Palace line-mutation sequence!

Verify this mathematical identity directly: on the Da Gua Luo Pan, the 8 Base Palace (Pure) Hexagrams carry Star Period 1 (Greedy Wolf); the 8 Third-Generation (Fully Inverted / Jiao Tai) Hexagrams carry Star Period 9 (Right Assistant); the First-Generation, Second-Generation, Fourth-Generation, Fifth-Generation, Wandering Soul (You Hun), and Returning Soul (Gui Hun) hexagrams generate the exact East River (Periods 2, 3, 4) and West River (Periods 6, 7, 8) families of the Tian Yu Jing! Furthermore, the 24-Mountain Nine-Star Heaven Ring (Tian Pan Feng Zhen) on the classical Luo Pan is built 100% upon the Lunar Najia mountain pairings shown in Table 1.

10. Strategic Application in Period 9 (2024-2043) & Fire Years 2026-2027

Li Fire rules the twenty-year cycle. Lunar Najia unlocks the annual stems. During Lower Cycle Period 9 (2024 - 2043, governed by Li Fire ☲), and specifically across the peak Fire years 2026 (Bing Wu) and 2027 (Ding Wei), applying Lunar Najia, Six Jia Void, and the 36 Lianshan Spirits yields surgical accuracy in both geomancy and date selection:

11. Field Case Studies: Najia Audits, Void Resolution & 36-Spirit Timing

Fieldwork proves classical mathematics. Three cases demonstrate precision. Below are three real-world engagements integrating Lunar Najia, Six Jia Void, and the 36 Lianshan Spirits:

12. Frequently Asked Questions (FAQ) & Authoritative Classical Bibliography

1. How do the Early Heaven, Middle Heaven, and Later Heaven Bagua correspond to Lianshan, Guizang, and Zhouyi?

In classical Image-Number (Xiangshu) scholarship: (1) The Early Heaven Bagua (Fu Xi) establishes Yin-Yang polar opposition (Qian South vs. Kun North, Li East vs. Kan West), serving as the immutable Substance (Ti) and corresponding to Guizang Yi; (2) The Middle Heaven Bagua (Lianshan) pairs complementary trigrams along the Human-Origin transformation axes (Gen-Dui, Zhen-Xun, Kan-Li, Qian-Kun) based on Shuogua Chapters V-VI, serving as the transformational bridge of Lianshan Yi; (3) The Later Heaven Bagua (King Wen) circulates the Five Phases clockwise through the seasons (Zhen East Wood, Li South Fire, Kun/Gen Earth, Dui/Qian West Metal, Kan North Water), serving as the dynamic Function (Yong) of the Zhouyi.

2. Why does Lunar Najia (Yueti Najia) assign Jia-Ren to Qian, Yi-Gui to Kun, Geng to Zhen, Xin to Xun, Bing to Gen, Ding to Dui, Wu to Kan, and Ji to Li?

As codified in Wei Boyang's Zhouyi Cantong Qi and Yu Fan's commentary, the 10 Heavenly Stems are mapped onto the 8 Trigrams by observing the illuminated shape of the Moon (Yueti) across the 30-day lunar month against the cardinal directions of the Stems (East Jia-Yi, South Bing-Ding, Center Wu-Ji, West Geng-Xin, North Ren-Gui):
• Day 3 at dusk: The waxing crescent (1 bright Yang line at the bottom, 2 dark Yin lines above = Zhen ☳) appears in the West (Geng) → Zhen receives Geng.
• Day 8 at dusk: The first-quarter half-moon (2 bright Yang lines below, 1 dark Yin line above = Dui ☱) culminates in the South (Ding) → Dui receives Ding.
• Day 15 at dusk: The full moon (3 bright Yang lines = Qian ☰) rises in the East (Jia) → Qian receives Jia (inner) and Ren (outer).
• Day 16 at dawn: The waning gibbous moon (1 dark Yin line below, 2 bright Yang lines above = Xun ☴) appears in the West (Xin) → Xun receives Xin.
• Day 23 at dawn: The third-quarter half-moon (2 dark Yin lines below, 1 bright Yang line above = Gen ☶) culminates in the South (Bing) → Gen receives Bing.
• Day 30 at dawn: The dark new moon (3 dark Yin lines = Kun ☷) vanishes in the East (Yi) → Kun receives Yi (inner) and Gui (outer).
• Kan (☵, Moon essence) and Li (☲, Sun radiance) operate at the central pivot and therefore receive Central Earth Wu and Ji.

3. How are the 12 Earthly Branches mapped onto the 6 lines of each trigram in Jing Fang's Najia system?

The four Yang Trigrams (Qian, Zhen, Kan, Gen) map the 6 Yang Branches (Zi, Yin, Chen, Wu, Shen, Xu) in clockwise forward order from Line 1 to Line 6; the four Yin Trigrams (Kun, Xun, Li, Dui) map the 6 Yin Branches (Wei, Si, Mao, Chou, Hai, You) in counter-clockwise reverse order from Line 1 to Line 6:
• Qian & Zhen: Inner Zi-Yin-Chen, Outer Wu-Shen-Xu.
• Kan: Inner Yin-Chen-Wu, Outer Shen-Xu-Zi.
• Gen: Inner Chen-Wu-Shen, Outer Xu-Zi-Yin.
• Kun: Inner Wei-Si-Mao, Outer Chou-Hai-You.
• Xun: Inner Chou-Hai-You, Outer Wei-Si-Mao.
• Li: Inner Mao-Chou-Hai, Outer You-Wei-Si.
• Dui: Inner Si-Mao-Chou, Outer Hai-You-Wei.

4. Why does Jing Fang's Eight-Palace line transformation stop at Line 5 and step back to Line 4 (You Hun) instead of transforming Line 6?

Because Line 6 (the Top Line) represents the Ancestral Temple (Zong Miao) and defines the identity of the Palace itself! If Line 6 were transformed after Line 5, the hexagram would lose its ancestral root and duplicate a hexagram belonging to another Palace. Therefore, starting from the Pure Palace Hexagram, lines mutate sequentially from Line 1 (1st Generation) through Line 5 (5th Generation). Having reached the supreme royal fifth position, transformation steps back to re-invert Line 4 to form the Wandering Soul (You Hun) hexagram, and then reverses all three inner lines back to the original Palace trigram to form the Returning Soul (Gui Hun) hexagram.

5. How does the Six Days Seven Fractions (Liu Ri Qi Fen) calendar divide the 365.25-day solar year among the 64 hexagrams?

In Meng Xi and Jing Fang's Gua Qi calendar, the 4 Cardinal Hexagrams (Kan North, Zhen East, Li South, Dui West) act as seasonal overseers whose 4 × 6 = 24 lines govern the 24 Solar Terms (Jie Qi). The remaining 60 hexagrams govern the days of the solar year (365.25 days). Dividing each day into 80 fractions (Fen), 365.25 days ÷ 60 hexagrams = 6 days with a remainder of 5.25 days. Converting the remainder into fractions gives 5.25 × 80 = 420 fractions, and 420 ÷ 60 hexagrams = 7 fractions per hexagram! Thus each of the 60 hexagrams rules for 6 days and 7/80 fractions (Liu Ri Qi Fen), and each individual line rules for roughly 1 day.

6. How does the Six Jia Void (Liu Jia Xun Kong / Kong Wang) operate in both Six-Yao divination and Da Gua compass work?

Because 10 Heavenly Stems pair sequentially with 12 Earthly Branches in six 10-day weeks (Liu Jia Xun), every 10-day cycle leaves 2 unpaired Earthly Branches known as Void (Xun Kong): Jia Zi week leaves Xu-Hai void; Jia Xu leaves Shen-You void; Jia Shen leaves Wu-Wei void; Jia Wu leaves Chen-Si void; Jia Chen leaves Yin-Mao void; Jia Yin leaves Zi-Chou void. In Six-Yao divination, a line falling in Temporal Void is temporarily inactive until filled or clashed out of Void; in Da Gua Feng Shui, you must never select a date whose Temporal Void matches the Sitting Mountain branch, nor align a building onto a spatial Void boundary (Da Kong Wang or Xiao Kong Wang) on the Luo Pan.

7. What are the 36 Lianshan Spirits (Lianshan San Shi Liu Qin) and how do they expand the 28 Lunar Mansions?

While standard astrological systems assign 1 zodiac animal to each of the 12 Branches or 28 animals to the 28 Lunar Mansions (Er Shi Ba Xiu), the esoteric Lianshan 36-Spirit transmission (preserved in Xiao Ji's Sui Dynasty Wuxing Dayi) divides each 30° Earthly Branch into three 10° decanates-Morning (Early Qi), Midday (Central Qi), and Evening (Late Qi)-assigning 3 distinct avian/animal spirits per Branch (12 × 3 = 36 Spirits). Mathematically, it unites the 28 Lunar Mansions with the 8 Trigram directional spirits (28 + 8 = 36), mirroring the 36 Palaces of Lianshan and Zhouyi.

8. How do we apply Lunar Najia and the 36 Spirits during Period 9 (2024-2043) and the Fire years 2026-2027?

In 2026 (Bing Wu) and 2027 (Ding Wei) under Period 9 Li Fire: (1) Under Lunar Najia, the Heavenly Stem Bing (2026) maps directly into Gen Mountain (Gen Na Bing, Gua Qi 6 Water), and Bing Wu is Line 2 of Pure Gen, while the Stem Ding (2027) maps directly into Dui Lake (Dui Na Ding, Gua Qi 4 Metal), activating the Middle Heaven Gen-Dui axis; (2) Both 2026 (Bing Wu) and 2027 (Ding Wei) belong to the Jia Chen decade-week where Yin and Mao are Void (Yin-Mao Kong), requiring strategic filling when activating Northeast (Yin) or East (Mao) sectors.

Classical Sources & Academic References

1. Wei Boyang (Eastern Han), Zhouyi Cantong Qi (周易參同契 · Token for the Agreement of the Three According to the Zhouyi), commentary by Peng Xiao and Zhu Xi (Zhouyi Cantong Qi Kaoyi).
2. Jing Fang (Western Han), Jingshi Yizhuan (京氏易傳 · Jing Fang's Commentary on the Changes), annotated by Lu Ji (Three Kingdoms Wu), Sibu Congkan edition.
3. Li Daoping (Qing Dynasty), Zhouyi Jijie Zuanshu (周易集解纂疏) & Zhang Huiyan, Zhouyi Yushi Yi (周易虞氏義 · Reconstruction of Yu Fan's Lunar Najia).
4. Ouyang Xiu & Song Qi (Song Dynasty), Xin Tang Shu · Li Zhi (新唐書 · 曆志 · New Book of Tang, Treatise on the Da Yan Calendar of Monk Yixing, recording Gua Qi Liu Ri Qi Fen).
5. Xiao Ji (Sui Dynasty), Wuxing Dayi (五行大義 · Compendium of the Five Phases), Scrolls IV & V · Treatise on the Three Changes and the Thirty-Six Spirits, Zhonghua Book Company edition.
6. Shao Yong (Song Dynasty), Huangji Jingshi Shu (皇極經世書); Jiang Yong (Qing Dynasty), He Luo Jing Yun (河洛精蘊).