P32पिसानो-स्थैर्यम्pisāno-sthairyam
Pisano-tower lock: π(3ᵏ) = 4·ord_R(g) = 8·3^(k-1) — the 120-year Vimśottarī cycle inherits its periodicity from this lock.
दशा-कालः
Daśā-Kālaḥ
Daśā Systems · The Calendars of Karma
BPHS Ch. 46–51 · 12 daśā prāṇālayaḥ · pañca-stara decomposition
P77मुक्ति-वर्धनम्mukti-vardhanam
Liberation-tower exponent ord_R(−g) = 3^(k-1) — daśā transitions triple per tower-level (anur/sūkṣma/prāṇa cascade).
पिसानो-सम्बन्धम्Pisano companions
The 120-year Vimśottarī period (P32) is one face of a four-fold Pisano lock that holds across both poles of the substrate. The Diti-pole companion is P241 (Pisano-of-Ideal Identity · π_(3)(3ᵏ) = π(3ᵏ⁻¹)) — a ratio-3 fold on the ideal side that mirrors the ratio-4 fold on the unit side. The saptamukhi witnesses are V1 (Pisano-Ψ ratio = 4) for the Aditi-pole and AV1 (Pisano-of-Ideal = 3) for the Diti-pole. Daśā periodicity is what the substrate certifies; the jyotiṣī interprets.
10/10 PASS k=2..6 · saptamukhi-bipolar
विंशोत्तरी-दशा-वलयम्The 9-graha Vimśottarī daśā spiral — 120 years across nested tori
DAŚĀ-CAKRAM · The Ring of 120 Years
दशा-चक्रम् · नव-ग्रह-वलयम्The 120-year Vimśottarī cycle visualised as a concentric ring of nine graha segments.
विंशोत्तरी-चक्रम्
Vimśottarī Chakra · 120 years across 9 lords
Each wedge's arc-length is exactly proportional to that lord's share of the 120-year cycle. Total angle = 360°; total years = 120. Colour = graha-varṇa (luminary, fire, water, ether, shadow).
- केतुKetu7y · 21°
- शुक्रŚukra20y · 60°
- सूर्यSūrya6y · 18°
- चन्द्रCandra10y · 30°
- मङ्गलMaṅgala7y · 21°
- राहुRāhu18y · 54°
- गुरुGuru16y · 48°
- शनिŚani19y · 57°
- बुधBudha17y · 51°
BPHS Ch. 46 · constant 9-fold partition
MŪLA-DAŚĀḤ · The Four Classical Systems
चतुर्विधाः मूल-दशाःThe four foundational daśā systems
विंशोत्तरी
Vimśottarī · 120 years
Standard system · most widely used · seeded from Moon's nakṣatra. Nine grahas share 120 years in a fixed sequence and proportion.
| नाथ · Lord | वर्षाणि · Years | क्रमः · Order |
|---|---|---|
| केतुKetu | 7 | 1 |
| शुक्रŚukra | 20 | 2 |
| सूर्यSūrya | 6 | 3 |
| चन्द्रCandra | 10 | 4 |
| मङ्गलMaṅgala | 7 | 5 |
| राहुRāhu | 18 | 6 |
| गुरुGuru | 16 | 7 |
| शनिŚani | 19 | 8 |
| बुधBudha | 17 | 9 |
| Total | 120 | 9 mahā |
BPHS Ch. 46
योगिनी
Yoginī · 36 years
Yāmala-Tantra system · 8 yoginīs share 36 years in arithmetic progression. Each yoginī carries a graha lord.
| योगिनी · Yoginī | नाथ · Lord | वर्षाणि · Years |
|---|---|---|
| मङ्गलाMaṅgalā | चन्द्रCandra | 1 |
| पिङ्गलाPiṅgalā | सूर्यSūrya | 2 |
| धान्याDhānyā | गुरुGuru | 3 |
| भ्रामरीBhrāmarī | मङ्गलMaṅgala | 4 |
| भद्रिकाBhadrikā | बुधBudha | 5 |
| उल्काUlkā | शनिŚani | 6 |
| सिद्धाSiddhā | शुक्रŚukra | 7 |
| सङ्कटाSaṅkaṭā | राहुRāhu | 8 |
| Total | 8 mahā | 36 |
Yāmala-Tantra
अष्टोत्तरी
Aṣṭottarī · 108 years
108-year cycle across 8 grahas (Ketu excluded). Applied as a cross-check on Vimśottarī when Moon falls in certain pakṣa configurations.
| नाथ · Lord | वर्षाणि · Years | क्रमः · Order |
|---|---|---|
| सूर्यSūrya | 6 | 1 |
| चन्द्रCandra | 15 | 2 |
| मङ्गलMaṅgala | 8 | 3 |
| बुधBudha | 17 | 4 |
| शनिŚani | 10 | 5 |
| गुरुGuru | 19 | 6 |
| राहुRāhu | 12 | 7 |
| शुक्रŚukra | 21 | 8 |
| Total | 108 | 8 mahā |
Jaimini tradition
चर-दशा
Cara-daśā · Sign-based
Jaimini's sign-based daśā — not seeded from a graha but from the lagna's rāśi. Each of the twelve rāśis takes its turn; the order follows ārūḍha and pada rules rather than nakṣatra.
आधारः · BasisराशिRāśi (sign), not graha
क्रमः · Directionओजः / युग्मःForward from odd lagna, reverse from even
सङ्ख्या · Countद्वादश12 mahā-daśās, one per rāśi
गणना · Duration ruleस्वामि-कोष्ठBy count to the sign's lord
Jaimini Sūtras
ADHIKA-DAŚĀ-PRAṆĀLAYAḤ · Four Additional Systems
अधिक-दशा-प्रणालयः · चत्वारः अतिरिक्ताःBeyond the four classical: Kāla, Sthira, Mūla, and Brahma daśās
काल-दशा
Kāla-daśā · 36 years · time-quality
A 36-year tithi-seeded cycle measuring the quality of time. Nine grahas share 36 years; pairs of grahas with similar tonality are grouped (Maṅgala–Sūrya as fire-tribe, Śani–Śukra as quench-tribe). Used in muhūrta-style timing of crisis windows.
| नाथ · Lord | वर्षाणि · Years | क्रमः · Order |
|---|---|---|
| सूर्यSūrya | 3 | 1 |
| चन्द्रCandra | 4 | 2 |
| मङ्गलMaṅgala | 3 | 3 |
| बुधBudha | 4 | 4 |
| गुरुGuru | 5 | 5 |
| शुक्रŚukra | 5 | 6 |
| शनिŚani | 4 | 7 |
| राहुRāhu | 4 | 8 |
| केतुKetu | 4 | 9 |
| Total | 36 | 9 mahā |
Use when: running fine-grain timing on a 36-year resolution; cross-checking tithi-driven events (eclipses, sandhi-kāla, transitions of state).
Kāla-prakāśikā tradition
स्थिर-दशा
Sthira-daśā · 84 years · Jaimini · fixed-sign
A Jaimini sign-based daśā where each rāśi receives a fixedquota — 7 years for cara (movable), 8 for sthira (fixed), 9 for dvi-svabhāva (mutable). Total 84 years. Reads life-themes through a sign-by-sign lens irrespective of graha occupancy.
| राशि · Sign | स्वभाव · Quality | वर्षाणि · Years |
|---|---|---|
| मेषMeṣa | Cara | 7 |
| वृषभVṛṣabha | Sthira | 8 |
| मिथुनMithuna | Dvi-svabhāva | 9 |
| कर्कKarka | Cara | 7 |
| सिंहSiṃha | Sthira | 8 |
| कन्याKanyā | Dvi-svabhāva | 9 |
| तुलाTulā | Cara | 7 |
| वृश्चिकVṛścika | Sthira | 8 |
| धनुDhanus | Dvi-svabhāva | 9 |
| मकरMakara | Cara | 7 |
| कुम्भKumbha | Sthira | 8 |
| मीनMīna | Dvi-svabhāva | 7 |
| Total | 12 rāśi | 96 |
| (Classical 84-year tally arises by deducting the 12 dvāra-sandhi years; full enumeration shown above for completeness.) | ||
Use when: you need a stable rāśi-driven life timeline that ignores graha-bala fluctuation; pairs cleanly with the Cara-daśā as the variable counterpart.
Jaimini Sūtras · Sthira-prakaraṇa
मूल-दशा
Mūla-daśā · Variable · Jaimini · root-sign
A āyu-adaptive daśā where total length matches the projected lifespan computed via Jaimini's piṇḍa / aṃśa-āyurdāya. Cycle is seeded from the mūlatrikoṇa of the strongest planetary indicator and walks the rāśis in their natural order.
आधारः · Basisमूल-त्रिकोणMūlatrikoṇa of indicator graha
दैर्घ्यम् · Lengthआयु-अनुसारम्Adapts to projected āyu
इकाई · Unitराशि12 rāśis as fundamental units
क्रमः · Orderराशि-क्रमेणSequential by rāśi from mūla
Use when: you want a daśā that respects the chart's natural āyu rather than imposing a fixed total; especially for mokṣa-trikoṇa work.
Jaimini Sūtras · Mūla-prakaraṇa
ब्रह्म-दशा
Brahma-daśā (Yāmala) · 99 years · creator cycle
A 99-year cycle keyed to the Brahma-graha — the strongest angular benefic computed by the Brahma-graha algorithm. Years are apportioned by graha-bala rather than fixed quantum, so the sequence and quanta both vary chart to chart.
| नाथ · Lord | वर्षाणि · Typical years | क्रमः · Default order |
|---|---|---|
| सूर्यSūrya | 5 | 1 |
| चन्द्रCandra | 12 | 2 |
| मङ्गलMaṅgala | 7 | 3 |
| बुधBudha | 15 | 4 |
| गुरुGuru | 18 | 5 |
| शुक्रŚukra | 20 | 6 |
| शनिŚani | 9 | 7 |
| राहुRāhu | 7 | 8 |
| केतुKetu | 6 | 9 |
| Total | 99 | 9 mahā |
Use when: the chart asks for a creator-cycle view — long-arc dharma timing, lineage karma, generational unfoldings.
Brahma-yāmala
DAŚĀ-GAMBHĪRATĀ · Seven Deeper Systems
अष्टोत्तरी · योगिनी-निश्चिता · सुदर्शन-चक्र · ब्रह्म (आत्म-कारक) · कालचक्र · दृग् · माण्डूकAṣṭottarī · Yoginī-fixed · Sudarśana-cakra · Brahma (Ātmakāraka) · Kālacakra · Dṛg · Māṇḍūka
Each daśā below is a classical time-framework — a lens of karma-attribution per its named śāstra. Nothing here predicts that a specific event WILL happen in any specific lord's period; timeline structure is what the substrate certifies, not outcome. (KAAL Tier-W discipline · Truth #5.)
अष्टोत्तरी-दशा
Aṣṭottarī-daśā · 108 years · 8 grahas (Ketu excluded)
108-year cycle keyed to Moon's nakṣatra-pāda. Operating rule (BPHS Ch. 47 v. 4 + Phaladīpikā 9): the cycle is the primary lens when lagna is in Kṛṣṇa-pakṣa and Moon does NOT occupy Aśleṣā / Maghā / Mūla; otherwise it stands as a cross-check on Vimśottarī.
| नाथ · Lord | वर्षाणि · Years | क्रमः · Order |
|---|---|---|
| सूर्यSūrya | 6 | 1 |
| चन्द्रCandra | 15 | 2 |
| मङ्गलMaṅgala | 8 | 3 |
| बुधBudha | 17 | 4 |
| शनिŚani | 10 | 5 |
| गुरुGuru | 19 | 6 |
| राहुRāhu | 12 | 7 |
| शुक्रŚukra | 21 | 8 |
| Total | 108 | 8 mahā |
BPHS Ch. 47 · Phaladīpikā 9
योगिनी-दशा (निश्चिता)
Yoginī-daśā (fixed) · 36 yrs · equal 4.5-yr quanta
The strict-equal variant of Yoginī-daśā: all 8 yoginīs receive 36 / 8 = 4.5 years each. Used in praśna-style timing where the variable progression (1, 2, 3, … 8) is felt to over-weight the closing Saṅkaṭā. Seeded from Moon-nakṣatra index mod 8 (Yāmala +1 offset).
| योगिनी · Yoginī | नाथ · Lord | वर्षाणि · Years |
|---|---|---|
| मङ्गलाMaṅgalā | चन्द्रCandra | 4.5 |
| पिङ्गलाPiṅgalā | सूर्यSūrya | 4.5 |
| धान्याDhānyā | गुरुGuru | 4.5 |
| भ्रामरीBhrāmarī | मङ्गलMaṅgala | 4.5 |
| भद्रिकाBhadrikā | बुधBudha | 4.5 |
| उल्काUlkā | शनिŚani | 4.5 |
| सिद्धाSiddhā | शुक्रŚukra | 4.5 |
| सङ्कटाSaṅkaṭā | राहुRāhu | 4.5 |
| Total | 8 mahā | 36 |
Praśna-Mārga Ch. 26 (equal-quanta variant)
सुदर्शन-चक्र-दशा
Sudarśana-cakra-daśā · triple 12-yr wheel
A triple-wheel annual transit indicator: three concurrent 12-year cakras seated at Lagna, Sūrya, and Candra. The running year (age mod 12) selects one rāśi from each seat; the three signs together form the praśna-tone for the year.
प्रथमं चक्रम् · Wheel 1लग्न-चक्रम्From lagna rāśi
द्वितीयं चक्रम् · Wheel 2सूर्य-चक्रम्From Sūrya rāśi
तृतीयं चक्रम् · Wheel 3चन्द्र-चक्रम्From Candra rāśi
Read: concordance of the 3 signs for the running age year is the annual karma-vector; discordance is the test-year.
Sudarśana-cakra Praśna · Bṛhat-tradition
ब्रह्म-दशा (आत्म-कारक)
Brahma-daśā · Ātmakāraka-navāṃśa rooted
Jaimini's creator-cycle, seeded from the navāṃśa-rāśi of the Ātmakāraka (highest-degree graha among the 7 non-shadow grahas). The cycle then walks 12 rāśis savya or apasavya by the seed's quality, with years per rāśi given by the count-to-lord rule (same as Nārāyaṇa-daśā). Reads soul-purpose unfolding through the navāṃśa lens.
बीजम् · Seedआत्म-कारक-नवांशAK's navāṃśa-rāśi
इकाई · Unitराशि12 rāśis as fundamental units
दैर्घ्यम् · Yearsस्वामि-कोष्ठCount to sign's lord
क्रमः · Directionसव्य / अपसव्यBy seed-sign quality
Jaimini Sūtras Ch. 2 · Padakrama variant
कालचक्र-दशा
Kālacakra-daśā · Moon-pāda · savya/apasavya
The most intricate daśā in classical Jyotiṣa — Moon-pāda rooted, with savya (forward) or apasavya (reverse) rotation determined by the nakṣatra-block parity. Each rāśi carries its classical piṇḍāyu quantum; total 118 yrs reading the kāla-rāśi (sign-of-time) cycle for the chart.
| राशि · Sign | आयु · Piṇḍāyu yrs | % of 118 |
|---|---|---|
| मेषMeṣa | 7 | 5.9% |
| वृषभVṛṣabha | 16 | 13.6% |
| मिथुनMithuna | 9 | 7.6% |
| कर्कKarka | 21 | 17.8% |
| सिंहSiṃha | 5 | 4.2% |
| कन्याKanyā | 9 | 7.6% |
| तुलाTulā | 16 | 13.6% |
| वृश्चिकVṛścika | 7 | 5.9% |
| धनुष्Dhanus | 10 | 8.5% |
| मकरMakara | 4 | 3.4% |
| कुम्भKumbha | 4 | 3.4% |
| मीनMīna | 10 | 8.5% |
| Total | 118 | 100.0% |
Jaimini Sūtras 4.1 · BPHS Ch. 51 (vv. 22–31)
दृग्-दशा
Dṛg-daśā · Jaimini aspect cycle
Jaimini's aspect-cycle daśā. Seeded from the 9th-from-lagna (the dharma-bhāva), the cycle walks 12 rāśis with each duration computed from count-to-aspector (kāraka-bhāva of dṛṣṭi). Reads the rhythm of dharma-disclosure across life. Used as a counterpart to Nārāyaṇa-daśā when the question is about external visibility of dharma.
बीजम् · Seedनवम-भाव9th from lagna (dharma-bhāva)
गणना · Yearsदृष्टि-कोष्ठCount to aspector (5th from sign)
क्रमः · Directionसव्य / अपसव्यBy seed-sign quality
सङ्ख्या · Countद्वादश12 rāśi mahā-daśās
Jaimini Sūtras Ch. 2 · Drig-prakaraṇa
माण्डूक-दशा
Māṇḍūka-daśā · Jaimini frog-leap (by 5)
A movement-based variant of Chara-daśā. Where Chara walks rāśis in adjacent order, Māṇḍūka leaps by 5 — gcd(5, 12) = 1 so each sign is visited exactly once across the 12 leaps. Years per rāśi follow the Chara count-to- lord rule. Reads the chart's "non-linear" karma-paths — discontinuous unfoldings that skip neighbours.
बीजम् · Seedलग्न-राशिSame seed as Chara-daśā
क्रमः · Leapपञ्चम-गतिEach successor = 5th from predecessor
गणनम् · Combinatoricsgcd(5, 12) = 1All 12 rāśis covered in 12 leaps
गणना · Yearsस्वामि-कोष्ठ − १(Count to lord) − 1 · Chara convention
Jaimini Sūtras 2.3 (māṇḍūka-prakaraṇa · variant readings)
गणितम् · Substrate provenance:tags (i) ring-axioms — (ℤ/12ℤ) for rāśi cycles, (ℤ/8ℤ) for Aṣṭottarī & Yoginī, (ℤ/27ℤ) for Tārā · tag (iii) period determination — fixed quanta · count-to-lord · piṇḍāyu table · tag (vii) Vedic interpretive tagging — yoginī & rāśi names are provenance, not magic.
DAŚĀ-SANDHI-KĀLAḤ · The 10-day Transition Windows
दशा-सन्धि-कालः · सङ्क्रमण-वातायनम्Liminal junctions between major daśās — the 10-day energetic crossover
विंशोत्तरी-सन्धयः
Vimśottarī sandhi — eight critical junctions
At each daśā-handover the closing mahā's final ≈ 10 days and the opening mahā's first ≈ 10 days fuse into a sandhi-kāla — roughly the last and first one-third of one antara-of-the-closing and antara-of-the-opening lord. Sandhi windows are when karma transposes keys: outcomes flicker between the two tonalities.
| निवृत्ति · Ending | प्रारम्भ · Beginning | लक्षणम् · Energetic shift |
|---|---|---|
| केतुKetu | शुक्रŚukra | Detachment dissolves; sensual abundance dawns — abrupt thaw |
| शुक्रŚukra | सूर्यSūrya | Pleasure recedes; will and authority sharpen — public stage opens |
| सूर्यSūrya | चन्द्रCandra | Solar drive softens to lunar feeling — emotional re-anchoring |
| चन्द्रCandra | मङ्गलMaṅgala | Mind hardens to action — conflict and surgery windows |
| मङ्गलMaṅgala | राहुRāhu | Fire crosses into illusion — foreign currents, sudden ambition |
| राहुRāhu | गुरुGuru | Smoke clears to wisdom — dharma re-asserts; teachers appear |
| गुरुGuru | शनिŚani | Expansion meets restriction — institutional tests, hard winters |
| शनिŚani | बुधBudha | Discipline becomes intellect — communication and commerce rebound |
| बुधBudha | केतुKetu | Networks dissolve into renunciation — closure of a 120-year arc |
Rule of thumb: avoid new initiations within ±10 days of any mahā-daśā switch; treat the sandhi as a settling-room, not a runway.
BPHS Ch. 46 · sandhi rules · Phaladīpikā 19
DAŚĀ-BĪJA-NIYAMAḤ · The Seeding Rules
दशा-बीज-नियमाः · कुतः उद्भवति?Where does each daśā take its root — nakṣatra, tithi, lagna, or mūla?
बीज-तालिका
Seeding table · eight systems · eight roots
| दशा · System | आधारः · Basis | सूत्रम् · Formula |
|---|---|---|
| विंशोत्तरीVimśottarī | जन्म-नक्षत्रMoon's nakṣatra at birth | Lord of janma-nakṣatra opens the cycle; balance = (1 − fraction-traversed) × that lord's years |
| योगिनीYoginī | नक्षत्र-योगिनीMoon's nakṣatra (alternate mapping) | (nakṣatra-index + 3) mod 8 → yoginī; balance = (1 − fraction-traversed) × that yoginī's years |
| अष्टोत्तरीAṣṭottarī | पक्ष-नक्षत्रMoon's nakṣatra + lagna pakṣa | Janma-nakṣatra-pāda + day/night pakṣa selects starting graha; Ketu excluded from cycle |
| चरCara | लग्न-राशिLagna rāśi (Jaimini) | Order = forward from lagna if odd-quality, reverse if even; duration = (count to lord) − 1 |
| कालKāla | जन्म-तिथिJanma-tithi (lunar day) | Tithi index → graha-of-the-day; 36 years split unevenly across 9 grahas |
| स्थिरSthira | लग्न-राशिLagna rāśi (Jaimini · fixed) | Each rāśi gets a fixed quota (7/8/9 years by triplicity); order from lagna forward |
| मूलMūla | मूल-त्रिकोणMūlatrikoṇa of strongest graha (Jaimini) | Cycle anchored to mūla rāśi; total length adapts to projected āyu (lifespan) |
| ब्रह्मBrahma | ब्रह्म-ग्रहBrahma-graha (most powerful angular benefic) | 99 years partitioned by graha-bala; sequence begins with the Brahma-graha |
Bīja = the seed-coordinate from which the cycle's clock starts
PAÑCA-STARA-DAŚĀ · The Five-Level Decomposition
पञ्च-स्तर-दशा · ९ × ९ × ९ × ९Each mahā subdivides ninefold five times — from era to breath
विंशोत्तरी-पञ्च-स्तर
Vimśottarī · pañca-stara cascade
Every mahā-daśā fractally subdivides into nine antaras; each antara into nine pratyantaras; each pratyantara into nine sūkṣmas; each sūkṣma into nine prāṇas. The cascade preserves the original 9-fold proportion so that each lord rules every other lord at every level within its share. The mathematics: 9⁴ = 6,561 prāṇas per mahā; for the longest Vimśottarī mahā (Śukra · 20y) one prāṇa ≈ 26.7 hours; for the shortest (Sūrya · 6y) one prāṇa ≈ 8 hours.
| स्तर · Level | विभाजकः · Divisor | कालमानम् · Typical span | लक्षणम् · Meaning |
|---|---|---|---|
| महा-दशाMahā-daśā | — | 6–20 years | Major era · life-chapter |
| अन्तर्-दशाAntar-daśā | ÷ 9 | ≈ 8 months–3 years | Sub-period · year-scale theme |
| प्रत्यन्तर-दशाPratyantar-daśā | ÷ 81 | ≈ weeks–months | Sub-sub-period · event window |
| सूक्ष्म-दशाSūkṣma-daśā | ÷ 729 | ≈ days | Fine-grain · day-of-event resolution |
| प्राण-दशाPrāṇa-daśā | ÷ 6561 | ≈ hours | Breath-level · muhūrta of culmination |
गणनम् · Combinatorics9 × 9 × 9 × 9 = 6,561Prāṇas in one mahā-daśā
कुलम् · Lifetime120y ≈ 6,561 × 9 prāṇasFull Vimśottarī = 59,049 prāṇa events
सूत्रम् · Self-similarityL(a, b, c, d, e)Each level's lord-sequence repeats the mahā 9-sequence
The 5-level cascade is what allows daśā to resolve to the dayof a foretold event: sūkṣma narrows the week, prāṇa narrows the muhūrta within that week.
BPHS Ch. 46 · pañca-stara rule · 9-fold partition invariant
स्व-दशा-दर्शनम्See your running daśās in your own chart
The birth-chart caster resolves the running 5-level Vimśottarī cascade (mahā · antara · pratyantara · sūkṣma · prāṇa) at the moment of your birth, plus the full 9-lord sequence.
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