P5मूलाङ्क-समीकरणम्mūlāṅka-samīkaraṇam
Primitive-root status: the mūlāṅka digit-root IS the substrate's Ψ(n) = 2ⁿ mod 9 cycle at k=1. Both compute in ℤ/9ℤ — the foundational ring of (R, g, k). Sacred-Trinity-1 substrate identity.
अङ्क-शास्त्रम्
Aṅka-Śāstram
Aṅka-śāstra · Mūlāṅka · Bhāgyāṅka · Nāmāṅka in ℤ/9ℤ
Substrate-grounded · Mūlāṅka = Ψ(n) = 2ⁿ mod 9 · classical correspondences
स्रोत-शास्त्राणि
Source Śāstras
- Bṛhat-Saṃhitā, Varāhamihira — Ch. 52 vāstu-prakaraṇam, including aṅka-vinyāsa references (the 81-pada count is itself a 9-fold aṅka identity)
- Sūrya-Siddhānta — graha-aṅka mapping (Sun=1, Moon=2, etc.)
- Cheiro (Count Louis Hamon), "Cheiro's Book of Numbers" (1926) — Western continuation; identical graha-aṅka correspondences
- "Numerology and the Divine Triangle" (Faith Javane & Dusty Bunker, 1979) — compatibility matrices
आधार-संयोग: · Ψ(n) = 2ⁿ mod 9
Substrate Cross-Reference
live
The mūlāṅka reduction (digit-root) is the same algebraic operation as the substrate's Ψ-cycle. Both compute in ℤ/9ℤ — the foundational ring at k=1 of (R, g, k).
Ψ(n) = 2ⁿ mod 9 — period-6 cycle:
1→2→4→8→7→5↻
The 3·6·9 trinity is the Diti-pole (nilpotent residues), NOT on the unit-orbit. Cheiro re-derived (with attribution) what the Bṛhat-Saṃhitā Ch. 52 already operates with.
See lib/motion.ts → PSI_CYCLE for the source-of-truth definition.
Substrate-pramāṇam · primes themselves are class-stratified by ℤ/9ℤ. See P206 (Yamaja-prime-cihnam · twin-prime QR signature) — every twin-prime pair (p, p+2) carries the same quadratic-residue class in ℤ/9ℤ, verified for all twin-primes p < 10⁶. The aṅka-cakra inherits its residue arithmetic from the same ring.
आरम्भ-विवरणम्
Birth Details Input
मूलाङ्क
Mūlāṅka · Root Number
6
digit-root in ℤ/9ℤ
- Graha
- शुक्रŚukra
- Day
- Friday (Śukravāra)
- Colour
- White / pastel-rose
- Gem
- Diamond (vajra) — substitute: white sapphire
Beauty · harmony · refinement
भाग्याङ्क
Bhāgyāṅka · Destiny Number
6
digit-root in ℤ/9ℤ
- Graha
- शुक्रŚukra
- Day
- Friday (Śukravāra)
- Colour
- White / pastel-rose
- Gem
- Diamond (vajra) — substitute: white sapphire
Beauty · harmony · refinement
नामाङ्क
Nāmāṅka · Name Number
Enter a name above to compute the nāmāṅka.
अन्तर-मैत्री: मूलाङ्क ↔ भाग्याङ्क
Inner Harmony · Mūlāṅka 6 ↔ Bhāgyāṅka 6
66
मित्र
Friend
Classical aṅka-maitrī derived from BPHS Ch. 3 graha-maitrī tables projected onto the aṅka-cakra.
९ × ९ सङ्गति-यन्त्रम्
9 × 9 Compatibility Matrix · Aṅka × Aṅka
सङ्गति-तालिका
Compatibility Table
| a \\ b | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
|---|---|---|---|---|---|---|---|---|---|
| 1 | M | M | M | M | N | Ś | N | Ś | M |
| 2 | M | M | N | M | N | N | M | Ś | N |
| 3 | M | N | M | N | M | Ś | M | N | M |
| 4 | M | M | N | M | N | N | Ś | M | N |
| 5 | N | N | M | N | M | M | N | M | Ś |
| 6 | Ś | N | Ś | N | M | M | N | M | N |
| 7 | N | M | M | Ś | N | N | M | N | M |
| 8 | Ś | Ś | N | M | M | M | N | M | Ś |
| 9 | M | N | M | N | Ś | N | M | Ś | M |
M = mitra (friend) · N = sama (neutral) · Ś = śatru (adversary)
नव-ग्रह-अङ्क-संयोग:
All 9 Aṅka → Graha Records · Classical Correspondences
1 · सूर्य
Sūrya · Sun
- Day
- Sunday (Ravivāra)
- Colour
- Gold / saffron
- Gem
- Ruby (māṇikya)
- Direction
- East
- Ψ-cycle position
- index 0 (unit-orbit)
Leadership · fame · sovereign-will
2 · चन्द्र
Candra · Moon
- Day
- Monday (Somavāra)
- Colour
- Silver / pearl-white
- Gem
- Pearl (muktā)
- Direction
- North-West
- Ψ-cycle position
- index 1 (unit-orbit)
Emotion · intuition · receptivity
3 · गुरु
Guru · Jupiter
- Day
- Thursday (Guruvāra)
- Colour
- Yellow / golden-amber
- Gem
- Yellow sapphire (puṣparāga)
- Direction
- North-East
- Ψ-cycle position
- Diti-pole (3·6·9)
Wisdom · expansion · dharma
4 · राहु
Rāhu · Rāhu
- Day
- Saturday (Śanivāra) — secondary
- Colour
- Blue-grey / smoky
- Gem
- Gomedha (hessonite)
- Direction
- South-West
- Ψ-cycle position
- index 2 (unit-orbit)
Innovation · restlessness · paradox
5 · बुध
Budha · Mercury
- Day
- Wednesday (Budhavāra)
- Colour
- Green / pale-jade
- Gem
- Emerald (marakata)
- Direction
- North
- Ψ-cycle position
- index 5 (unit-orbit)
Communication · agility · intellect
6 · शुक्र
Śukra · Venus
- Day
- Friday (Śukravāra)
- Colour
- White / pastel-rose
- Gem
- Diamond (vajra) — substitute: white sapphire
- Direction
- South-East
- Ψ-cycle position
- Diti-pole (3·6·9)
Beauty · harmony · refinement
7 · केतु
Ketu · Ketu
- Day
- Tuesday (Maṅgalavāra) — secondary
- Colour
- Multicolour / iridescent
- Gem
- Cat's eye (vaiḍūrya)
- Direction
- Centre / Ūrdhva
- Ψ-cycle position
- index 4 (unit-orbit)
Mysticism · isolation · jñāna
8 · शनि
Śani · Saturn
- Day
- Saturday (Śanivāra)
- Colour
- Dark blue / black
- Gem
- Blue sapphire (nīlamaṇi)
- Direction
- West
- Ψ-cycle position
- index 3 (unit-orbit)
Discipline · structure · longevity
9 · मङ्गल
Maṅgala · Mars
- Day
- Tuesday (Maṅgalavāra)
- Colour
- Red / coral-orange
- Gem
- Red coral (pravāla)
- Direction
- South
- Ψ-cycle position
- Diti-pole (3·6·9)
Energy · action · valour
सहभागिन्यः
Sister Modules
- → वास्तु-शास्त्रम् · Vāstu Maṇḍala · the 81-pada grid expressing 9-fold aṅka identity
- → पञ्चाङ्गम् · Pañcāṅga · daily 5-limb almanac
- → कुण्डली · Birth Chart · Navagraha placements