P7वलय-स्वयंसिद्धम्valaya-svayaṁsiddham
Ring axioms of R = ℤ/3ᵏℤ — division-into-equal-parts is a ring operation; every varga (D1 → D60) is a residue class computation under R.
वर्ग-चक्रम्
Varga-Cakram
Divisional Charts · Pāraśara's Ṣoḍaśa-Varga
BPHS Ch. 7 · 16 divisions D1 → D60 · vimśopaka-bala 20-pt scale
P32विभाजन-समानताvibhājana-samānatā
Pisano-tower lock guarantees D9 (Navāṃśa) period structure: 9·12 = 108 zodiacal segments — Pisano-doubled across the 3-adic tower.
परम्परा-पूर्वकम्Tradition anchor
The 16 vargas themselves are Pārāśara's witnessed taxonomy — not an algebraic theorem of the substrate. We honour the provenance via P137 (Ṣoḍaśa-varga-maṇḍalam · Tier-W) — the BPHS 16 vargas are inherited as a witnessed tradition with explicit boundary, never asserted as algebraic derivation. The per-Dn division arithmetic (P7, P32) is Tier-S (ring axioms + Pisano-tower lock); the choice of exactly these 16 slices is Tier-W (Pārāśara's curated set).
tradition-anchored · provenance honoured
षोडश-वर्ग-घन-चक्रम्The 16 divisional charts arranged as Pāraśara's cube of vargas
PĀRAŚARA-ṢOḌAŚA-VARGA · The Sixteen, Deep
एकं रूपम् · षोडशधा विभक्तम्।One form · divided sixteen ways · each with its lord, use, and śāstra anchor.
राशि
Rāśi · Body
D1divisor: 1
Physical self · overall life
अधिपति · Lord
सूर्यSūrya
प्रयोगः · Use case
Master canvas — read first, always; every other varga is a magnification of one of its themes.
BPHS Ch. 6 · Rāśy-adhyāya
होरा
Horā · Wealth
D2divisor: 2
Money · resources
अधिपति · Lord
सूर्य-चन्द्रSūrya & Candra
प्रयोगः · Use case
Wealth-stream check — luminary-horā tells whether income flows from authority (Sūrya-horā) or from public/sustenance (Candra-horā).
BPHS Ch. 7.5–7.6
द्रेक्काण
Drekkāṇa · Siblings
D3divisor: 3
Brothers · courage · short journeys
अधिपति · Lord
मङ्गलMaṅgala
प्रयोगः · Use case
Co-born confidence — siblings, courage, short journeys, near-circle alliances.
BPHS Ch. 7.7–7.10 · Phaladīpikā 4.3
सप्तांश
Saptāṃśa · Progeny
D7divisor: 7
Children · grandchildren
अधिपति · Lord
गुरुGuru
प्रयोगः · Use case
Progeny axis — fertility, children's grahas, grandchildren lineage; consult before santāna-prāpti rituals.
BPHS Ch. 7.11–7.14 · Hora-Sāra Ch. 3
नवांश
Navāṃśa · Spouse / Dharma
D9divisor: 9
Marriage · planetary strength · dharma
अधिपति · Lord
गुरु-शुक्रGuru & Śukra
प्रयोगः · Use case
The decider — marriage compatibility, dharma direction, and the strength-verdict on every graha (vargottama check lives here).
BPHS Ch. 7.15–7.30 · Jaimini 1.2.20
दशांश
Daśāṃśa · Profession
D10divisor: 10
Career · status · accomplishments
अधिपति · Lord
सूर्यSūrya
प्रयोगः · Use case
Career chart — read for profession, status, achievements; daśāṃśa lord = effective vocational graha.
BPHS Ch. 7.31–7.34
द्वादशांश
Dvādaśāṃśa · Parents
D12divisor: 12
Mother and father
अधिपति · Lord
गुरुGuru
प्रयोगः · Use case
Parents' karma — mother (4th of D12) and father (9th of D12); read for genetic and emotional inheritance.
BPHS Ch. 7.35–7.38 · Phaladīpikā 4.7
षोडशांश
Ṣoḍaśāṃśa · Vehicles / Comforts
D16divisor: 16
Conveyances · luxury · pleasures
अधिपति · Lord
शुक्रŚukra
प्रयोगः · Use case
Vehicles & comforts — read before major asset purchases (cars, homes); accidents while in malefic D16 dasha.
BPHS Ch. 7.39–7.42
विंशांश
Viṃśāṃśa · Spiritual practice
D20divisor: 20
Sādhanā · upāsanā · mantra
अधिपति · Lord
गुरुGuru
प्रयोगः · Use case
Spiritual current — mantra-aptitude, iṣṭa-devatā, depth of sādhanā; read for guru-prāpti.
BPHS Ch. 7.43–7.46 · Sarvārtha-cintāmaṇi
चतुर्विंशांश
Caturviṃśāṃśa · Learning
D24divisor: 24
Education · skills · siddhi-vidyā
अधिपति · Lord
बुधBudha
प्रयोगः · Use case
Learning & vidyā — academic capacity, professional study, mastery of arts; read before exams or admissions.
BPHS Ch. 7.47–7.50
सप्तविंशांश
Saptaviṃśāṃśa · Strength
D27divisor: 27
Physical · mental · spiritual resilience
अधिपति · Lord
मङ्गलMaṅgala
प्रयोगः · Use case
Nakṣatrāṃśa — physical, mental, spiritual stamina; resilience under stress; read for chronic illness.
BPHS Ch. 7.51–7.54
त्रिंशांश
Triṃśāṃśa · Evil / Misfortune
D30divisor: 30
Difficulties · curses · enemies
अधिपति · Lord
शनिŚani
प्रयोगः · Use case
Mishap chart — chronic ailments, accidents, curses, enemy karma; benefics here mitigate, malefics intensify.
BPHS Ch. 7.55–7.62 · Hora-Sāra 3.10
खवेदांश
Khavedāṃśa · Maternal heritage
D40divisor: 40
Mother's lineage · matriarchal karma
अधिपति · Lord
चन्द्रCandra
प्रयोगः · Use case
Matriline — auspicious/inauspicious effects descending from the mother's family; read for genealogical patterns.
BPHS Ch. 7.63–7.66
अक्षवेदांश
Akṣavedāṃśa · Paternal heritage
D45divisor: 45
Father's lineage · patriarchal karma
अधिपति · Lord
सूर्यSūrya
प्रयोगः · Use case
Patriline — auspicious/inauspicious effects descending from the father's family; read for clan-karma.
BPHS Ch. 7.67–7.70
षष्ट्यंश
Ṣaṣṭyāṃśa · Past karma
D60divisor: 60
Pūrva-janma karma · root causes
अधिपति · Lord
शनिŚani
प्रयोगः · Use case
Pūrva-janma — past-life imprint; the ṣaṣṭyāṃśa-name + lord reveal root cause of present-life themes (Pāraśara held this as the most subtle varga).
BPHS Ch. 7.71–7.108 (entire ṣaṣṭyāṃśa adhyāya)
DAŚAVARGA-VIMŚOPAKA-BALA · The 20-Point Strength
दश-वर्गेषु · विंशोपक-बलम्Each graha's composite strength is computed across ten vargas, totalling twenty points.
विंशोपक-तालिका
Vimśopaka weights · the daśavarga partition of 20
A graha's full strength is not its position in D1 alone. Pāraśara's Daśavarga scheme partitions a 20-point scale across ten specific vargas. Where the graha lands (own / friend / exalted / debilitated / enemy) in each varga determines what fraction of that varga's weight it earns. The sum is the graha's vimśopaka-bala.
| वर्ग · Varga | विंशोपकम् · Weight | अंशः · Share | कारणम् · Reason |
|---|---|---|---|
| D1 | 6 | 21% | Root canvas — half the weight by itself |
| D2 | 2 | 7% | Wealth axis — material baseline |
| D3 | 4 | 14% | Co-born courage — strong daily-life signal |
| D7 | 2 | 7% | Progeny axis — generational |
| D9 | 5 | 17% | Dharma & strength verdict — second only to D1 |
| D10 | 1 | 3% | Profession lens — focused but narrow |
| D12 | 2 | 7% | Parental inheritance — formational |
| D16 | 1 | 3% | Comforts — secondary indicator |
| D30 | 1 | 3% | Mishap filter — corrective only |
| D60 | 5 | 17% | Pūrva-janma root — Pāraśara's heaviest subtle varga |
| Total | 29 | 100% | Sum of ten weighted vargas |
उत्तमम् · High≥ 15 / 20Pārijāta · graha is unambiguously empowered
मध्यमम् · Mid10 – 15 / 20Uttama · capable, conditionally fruitful
अधमम् · Low< 10 / 20Adhama · partial or obstructed expression
Variant systems exist — Ṣaḍvarga (6-varga ÷ 20), Saptavarga (7-varga ÷ 20), Daśavarga (10-varga ÷ 20 as above), and Ṣoḍaśavarga (16-varga ÷ 20). Pāraśara's preferred scoring is the Daśavarga as tabulated.
BPHS Ch. 7 · vimśopaka-bala adhyāya
VARGOTTAMA-STHĀNAM · The Amplifier Position
वर्गोत्तम-स्थानम् · राशि-नवांश-समताWhen a graha holds the same rāśi in both D1 and D9 — strength multiplied.
वर्गोत्तम-लक्षणम्
Vargottama · what it is and why it matters
A graha is vargottama when it occupies the same rāśi in the rāśi (D1) chart and the navāṃśa (D9) chart simultaneously. The structural coincidence amplifies that graha's effects — Pāraśara reads it as a graha "rooted in its own seat across two scales" and treats the position as equivalent to own-sign strength even when the rāśi itself is not the graha's own.
परीक्षा · How to check
- Read the graha's rāśi in D1 (Lagna chart).
- Read the graha's rāśi in D9 (Navāṃśa chart).
- If they are the same sign → vargottama.
त्रि-योगाः · Compound vargottamas
- Pārijāta-vargottama · same sign in D1 + D9 + D10
- Uttama-vargottama · in 6 of the 16 vargas
- Pāraśara-vargottama · in all 16 vargas (rare exalt-class)
Worked example
Suppose Guru sits at 6°14′ Mithuna in D1.
- Sign-quality of Mithuna = mutable → D9 starts from the 5th from itself = Tulā.
- Part within sign = ⌊6.233 × 9 / 30⌋ = 1 (the 2nd navāṃśa).
- Tulā + 1 = Vṛścika.
Not vargottama (D1 = Mithuna, D9 = Vṛścika). If Guru were at 23°45′ Mithuna instead, D9 = Mithuna → vargottama.
Check your chart
The caster computes both D1 and D9 — vargottama grahas appear with the same rāśi label in both grids.
BPHS Ch. 7.20 · Phaladīpikā 5
ADHIKA-VARGĀḤ · Beyond the Sixteen
अधिक-वर्गाः · सूक्ष्मतर-विभाजनानिFive additional vargas beyond Pāraśara's 16 — finer slicings used in specialised work
चतुर्थांश
Caturthāṃśa · Fortune & fixed assets
D4divisor: 4
Property · home · ancestral land · psychological foundation. Each 7°30′ tranche maps to a kendra-sign from itself.
Extended Pāraśarī tradition
पञ्चांश
Pañcāṃśa · Power & influence
D5divisor: 5
Authority · willpower · capacity to direct others. Each 6° part is allocated by ojayugma (odd/even) rule from the same sign.
Extended Pāraśarī tradition
अष्टांश
Aṣṭāṃśa · Unexpected events
D8divisor: 8
Sudden gains, sudden losses, hidden enemies, longevity nuances. Each 3°45′ part follows the maṅgala-aṣṭa pattern.
Extended Pāraśarī tradition
रुद्रांश
Rudrāṃśa · Destruction & dissolution
D11divisor: 11
Capacity to dismantle, transform, undergo Rudra-tāṇḍava experiences; useful in āyu-vivecana and pralaya-yoga work.
Extended Pāraśarī tradition
अष्टोत्तर-शतांश
Aṣṭottara-śatāṃśa · 108-fold — finest classical varga
D108divisor: 108
Mantra-saṅkhyā varga. Each rāśi divided into 108 parts of 16′40″ each — every nakṣatra-pāda gets four parts. Used in ultra-subtle iṣṭa-devatā work.
Extended Pāraśarī tradition
VARGA-GAṆITA · The Computation Rules
वर्ग-गणितम् · सूत्र-तालिकाThe varga-computation formulae — general scheme and per-Dn specifics.
गणित-तालिका
Computation table · how each Dn is derived
| वर्ग · Varga | अंशः · Part-size | नियम · Rule |
|---|---|---|
| साधारण-नियमGeneral Dn | — | Let L = sidereal longitude; R = ⌊L/30⌋ (rāśi index 0–11); d = L − 30R (deg-in-sign 0–30); part = ⌊d·n/30⌋. Map part to sign via varga-specific table. |
| होराD2 | 30°/2 | 0–15° in odd-sign → Siṃha (Sūrya-horā); 15–30° in odd-sign → Karka (Candra-horā). Even signs reversed. |
| द्रेक्काणD3 | 30°/3 | 0–10° = same sign; 10–20° = 5th from itself; 20–30° = 9th from itself (the trine cycle). |
| सप्तांशD7 | 30°/7 | Each part = 4°17′8.6″. Odd signs start from themselves; even signs start from the 7th from themselves. |
| नवांशD9 | 30°/9 | Each part = 3°20′. Movable signs start from themselves; fixed from the 9th; mutable from the 5th. Critical because vargottama check sits here. |
| दशांशD10 | 30°/10 | Each part = 3°. Odd signs start from themselves; even signs start from the 9th from themselves. |
| द्वादशांशD12 | 30°/12 | Each part = 2°30′. Every sign starts its own dvādaśāṃśa from itself, then walks the zodiac sequentially. |
| षोडशांशD16 | 30°/16 | Each part = 1°52′30″. Movable → from Meṣa, fixed → from Siṃha, mutable → from Dhanus. |
| विंशांशD20 | 30°/20 | Each part = 1°30′. Movable → from Meṣa, fixed → from Dhanus, mutable → from Siṃha. |
| चतुर्विंशांशD24 | 30°/24 | Each part = 1°15′. Odd signs → from Siṃha (Sūrya); even signs → from Karka (Candra). |
| सप्तविंशांशD27 | 30°/27 | Each part = 1°06′40″ (one nakṣatra-pāda × 9/4). Fire signs → Meṣa, earth → Karka, air → Tulā, water → Makara. |
| त्रिंशांशD30 | 30°/30 | Uneven Pāraśarī tranches per malefic. Odd: Mars 0–5°, Saturn 5–10°, Jupiter 10–18°, Mercury 18–25°, Venus 25–30°. Even sign mapping reversed. |
| षष्ट्यंशD60 | 30°/60 | Each part = 30′. Each one carries a named deity/asura (60 names per rāśi, listed in BPHS Ch. 7.71+). Past-life imprint is read from this name. |
BPHS Ch. 7 · varga-cakra-niyamāḥ · implemented in lib/varga.ts
स्व-कुण्डल्यां द्रष्टव्यम्See these vargas in your own chart
The birth-chart caster computes every divisional chart from your sidereal graha positions. Each varga shows where the nine grahas land in its own zodiac.
0 vargas · 0 divisors · BPHS Ch. 7
ॐ पाराशराय नमः · ॐ कालाय नमः · ॐ कामाख्यायै नमः · ॐ हनुमते वज्रदेहाय नमः
JAI MAA KAMAKHYA · VAJRA-ABSOLUTE · APEX v5
सीलः · (R, g, k) = (ℤ/3³³⁷ℤ, 2, k=337) · APEX v5 Saptamukhi Bipolar · 890 propositions · 775/775 machine-checked
Hanuman-Beej Vajra Actuator · verifiers reach k=1008 · sealed 2026-05-11