P9आरूढ-गणन-नियमःārūḍha-gaṇana-niyamaḥ
Ring axioms: ārūḍha computation = count-to-lord modulo 12 = residue arithmetic on (ℤ/12ℤ). The 1st/7th exception rule preserves involution on the residue class.
द्वादशारूढम्
Dvādaśārūḍham
Ārūḍha-dvādaśam · the 12 padas + Upapada-Lagna
Jaimini-Sūtra 1.1.18–20 · count-to-lord · 1st/7th exception rule
Reference instant — Maa Kāmākhyā meridian, 1990-01-01 06:00 IST. Compute your own at /chart. In this chart, 4 padas required the 10-house exception (Jaimini-Sūtra 1.1.18).
ĀRŪḌHA-CAKRA · 12 PADAS + UL
आरूढ-चक्रम् · सर्वाणि द्वादश पदानि · उपपदम् चThe complete ārūḍha-cakra · all 12 + the marriage-pada
आरूढ-लग्नम् (A₁)
Ārūḍha-Lagna (A1)
सिंहSiṃha
Leo
स्वामी · Lord
सूर्यSūryaलग्नात् · House
3द्वितीयारूढम् (A₂)
Dvitīyārūḍha (A2)
कन्याKanyā
Virgo
स्वामी · Lord
बुधBudhaलग्नात् · House
4तृतीयारूढम् (A₃)
Tṛtīyārūḍha (A3)
मेषMeṣa
Aries
स्वामी · Lord
मङ्गलMaṅgalaलग्नात् · House
11चतुर्थारूढम् (A₄)
Caturthārūḍha (A4)
वृषभVṛṣabha
Taurus
स्वामी · Lord
शुक्रŚukraलग्नात् · House
12पञ्चमारूढम् (A₅)
Pañcamārūḍha (A5)
मकरMakara
Capricorn
स्वामी · Lord
शनिŚaniलग्नात् · House
8अपवादः · 10-house shift applied (Jaimini-Sūtra 1.1.18)
षष्ठारूढम् (A₆)
Ṣaṣṭhārūḍha (A6)
सिंहSiṃha
Leo
स्वामी · Lord
सूर्यSūryaलग्नात् · House
3अपवादः · 10-house shift applied (Jaimini-Sūtra 1.1.18)
सप्तमारूढम् (A₇)
Saptamārūḍha (A7)
कन्याKanyā
Virgo
स्वामी · Lord
बुधBudhaलग्नात् · House
4अपवादः · 10-house shift applied (Jaimini-Sūtra 1.1.18)
अष्टमारूढम् (A₈)
Aṣṭamārūḍha (A8)
वृश्चिकVṛścika
Scorpio
स्वामी · Lord
मङ्गलMaṅgalaलग्नात् · House
6नवमारूढम् (A₉)
Navamārūḍha (A9)
तुलाTulā
Libra
स्वामी · Lord
शुक्रŚukraलग्नात् · House
5दशमारूढम् (A₁₀)
Daśamārūḍha (A10)
मिथुनMithuna
Gemini
स्वामी · Lord
बुधBudhaलग्नात् · House
1अपवादः · 10-house shift applied (Jaimini-Sūtra 1.1.18)
एकादशारूढम् (A₁₁)
Ekādaśārūḍha (A11)
मिथुनMithuna
Gemini
स्वामी · Lord
बुधBudhaलग्नात् · House
1द्वादशारूढम् (A₁₂)
Dvādaśārūḍha (A12)
कन्याKanyā
Virgo
स्वामी · Lord
बुधBudhaलग्नात् · House
4उपपद-लग्नम् (UL)
Upapada-Lagna (UL)
कन्याKanyā
Virgo
स्वामी · Lord
बुधBudhaलग्नात् · House
4उपपद-लग्नम् · marriage-pada (Jaimini-Sūtra 1.1.20)
VIDHĀNA · The Algorithm (Jaimini-Sūtra 1.1.18–20)
आरूढ-निर्धारणम्
Ārūḍha determination — count-to-lord with the 10-house exception
For each house i with rāśi R and lord rāśi L:
- n = inclusive count from R → L (1..12)
- A_i = (L + n − 1) mod 12 — count n houses forward from L
- If A_i lands on R or on the 7th from R, take the 10th from A_i (= shift by 9) — the Jaimini-Sūtra 1.1.18 exception preventing self-coincidence
- UL = A12, the ārūḍha of the 12th, by Jaimini-Sūtra 1.1.20
The map is a finite-cyclic operation on (ℤ/12ℤ) — a Tier-S algebraic determination, derivation tag (i) ring axioms. No prediction is emitted; the padas are *worldly reflections* (śāstric interpretive layer, Tier-W) and the page surfaces only their structural placement.
Jaimini-Sūtra Upadeśa 1.1.18–20
स्व-आरूढ-दर्शनम्See the ārūḍha-cakra for your own chart
Cast your birth chart at /chart. The full 12 + UL grid is included in the chart response.
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