SHADBALA & ASHTAKAVARGA (BALA-06 · CLASSICAL CODEX)Trikona & Ekadhipatya Shodhana (Ashtakavarga Reductions) (Trikoṇa & Ekādhipatya Śodhana)
In classical Sanskrit horoscopy, Trikona & Ekadhipatya Shodhana (Ashtakavarga Reductions) (Trikoṇa & Ekādhipatya Śodhana — Two-Stage Matrix Reduction, Rashi/Graha Multipliers & Shodya Pinda) governs Algorithmic Bindu Reduction, Shodya Pinda Potency & Ashtakavarga Ayurdaya. Within the vectorized reference corpus (jyotish_corpus_core_v3), the doctrinal cluster of Trikona & Ekadhipatya Shodhana (Ashtakavarga Reductions) (BALA-06) is cross-indexed across 2,624 verified passages and 1,629 numbered shlokas in 18 Sanskrit treatises.
BALA-06)Codified in Brihat Parashara Hora Shastra Chapters 68–70 & Ashtakavarga Grantha and Brihat Jataka Chapter 9 & Phaladeepika Chapter 23, Trikona & Ekadhipatya Shodhana (Ashtakavarga Reductions) operates under the mathematical invariant Stage 1: Trikona Shodhana (4 Elemental Triads) ; Stage 2: Ekadhipatya (5 Dual Lords): To distill net permanent potency (Shodya Pinda) from raw Bhinnashtakavarga tables, the astronomer applies two sequential matrix reductions: Trikona Shodhana (subtracting the lowest bindu value within each of the four elemental trines from all three signs of that trine) followed by Ekadhipatya Shodhana (reducing pairs of signs ruled by Mars, Mercury, Jupiter, Venus, and Saturn based on planetary occupancy).
SHASTRIC MECHANICSMathematical Formulation & Structural Rules of Trikona & Ekadhipatya Shodhana (Ashtakavarga Reductions)
After completing both reductions, each sign's residual bindus are multiplied by Parashara's Rashi Gunakara (Sign Multipliers: Vrishabha/Simha = 10, Mithuna/Vrishchika = 8, Mesha/Tula = 7, Kanya/Makara = 5, Karka = 4, Dhanu = 9, Kumbha = 11, Meena = 12) to yield the Rashi Pinda. Simultaneously, signs occupied by planets are multiplied by Graha Gunakara (Sun = 5, Moon = 5, Mars = 8, Mercury = 5, Jupiter = 10, Venus = 7, Saturn = 5) to yield the Graha Pinda; their sum is the Shodya Pinda.
The structural matrix below details the exact computational parameters, degree thresholds, and classical interpretive clauses for Trikona & Ekadhipatya Shodhana (Ashtakavarga Reductions) (BALA-06) as preserved in Brihat Parashara Hora Shastra Chapters 68–70 & Ashtakavarga Grantha.
| Reduction / Pinda Stage | Governing Mathematical Rule | Occupied versus Unoccupied Clause | Resulting Analytical Metric |
|---|---|---|---|
| Trikona Shodhana | For each triad (c1, c2, c3), subtract min(c1, c2, c3) from all three |
If any sign in the triad has 0 bindus, no reduction is performed (Varahamihira) |
Eliminates baseline elemental noise and isolates net trinal surplus in classical Jyotish horoscopy. |
| Ekadhipatya (Both Empty) | Equal values to set both to 0; Unequal to set higher to equal lower |
Applies to Mesha/Vrishchika, Vrishabha/Tula, Mithuna/Kanya, Dhanu/Meena, Makara/Kumbha |
Balances dual-ruled signs when neither sign contains a physical Graha in classical Jyotish horoscopy. |
| Ekadhipatya (One Occupied) | If occupied < unoccupied to subtract occupied from unoccupied; if occupied > unoccupied to keep both |
If both signs contain planets, no Ekadhipatya reduction is performed |
Preserves bindus anchored by actual planetary presence in classical Jyotish horoscopy. |
| Shodya Pinda Synthesis | Rashi_Pinda + Graha_Pinda |
Multiplied by |
Determines exact transit Nakshatra and Rashi triggers for career and longevity in classical Jyotish horoscopy. |
MULTI-TREATISE SHASTRA CONCORDANCECorpus Distribution of Trikona & Ekadhipatya Shodhana (Ashtakavarga Reductions) Across 18 Sanskrit Shastras
The concordance table below maps how Trikona & Ekadhipatya Shodhana (Ashtakavarga Reductions) (BALA-06) and its taxonomic family (topics) are distributed across the eighteen classical Sanskrit treatises of jyotish_corpus_core_v3, linking Brihat Parashara Hora Shastra Chapters 68–70 & Ashtakavarga Grantha with Brihat Jataka Chapter 9 & Phaladeepika Chapter 23.
| Sanskrit Treatise | Verified Passages | Chapter Coverage | Analytical Scope |
|---|---|---|---|
| Ashtakavarga Grantha | 398 passages |
17 ch / 271 v |
Documents mathematical definitions, house parameters, and interpretive synthesis for Trikona & Ekadhipatya Shodhana (Ashtakavarga Reductions) (BALA-06) across 17 chapters. |
| Brihat Parashara Hora Shastra | 375 passages |
66 ch / 297 v |
Documents mathematical definitions, house parameters, and interpretive synthesis for Trikona & Ekadhipatya Shodhana (Ashtakavarga Reductions) (BALA-06) across 66 chapters. |
| Prashna Marga | 236 passages |
15 ch / 179 v |
Documents mathematical definitions, house parameters, and interpretive synthesis for Trikona & Ekadhipatya Shodhana (Ashtakavarga Reductions) (BALA-06) across 15 chapters. |
| Saravali | 230 passages |
29 ch / 141 v |
Documents mathematical definitions, house parameters, and interpretive synthesis for Trikona & Ekadhipatya Shodhana (Ashtakavarga Reductions) (BALA-06) across 29 chapters. |
| Brihat Jataka | 226 passages |
20 ch / 129 v |
Documents mathematical definitions, house parameters, and interpretive synthesis for Trikona & Ekadhipatya Shodhana (Ashtakavarga Reductions) (BALA-06) across 20 chapters. |
| Brihat Samhita | 214 passages |
58 ch / 180 v |
Documents mathematical definitions, house parameters, and interpretive synthesis for Trikona & Ekadhipatya Shodhana (Ashtakavarga Reductions) (BALA-06) across 58 chapters. |
VERBATIM CORPUS FOLIO & CHART SYNTHESISArchival Public-Domain Folio Excerpt for Trikona & Ekadhipatya Shodhana (Ashtakavarga Reductions)
This archival verse passage for Trikona & Ekadhipatya Shodhana (Ashtakavarga Reductions) (BALA-06) is extracted from the public-domain edition of Brihat Parashara Hora Shastra (Chapter 3, Verse 65) indexed in jyotish_corpus_core_v3.
CORPUSPROVENANCE: Brihat Parashara Hora Shastra | SourceID: archive_brihat-parashara-hora-sastra | Chapter 3, Verse 65 "ngitude at a given moment to get the exact position of the all inauspicious Dhoom Reduce Dhoom from 12 R is to arrive at Vyatipat Vyatipat is also inauspicious Add six R is to V yatipat to know the position of Parivesh He is extremely inauspicious Deduct Parivesh from 12 R is"
Multiplying a planet's Shodya Pinda by 7 and dividing by 27 gives the exact Nakshatra remainder (counted from Ashwini) where Saturn's or Rahu's transit triggers crucial biographical turning points.
SUTRA BLACK LABEL · INDIVIDUAL EPHEMERIS SYNTHESISCompute Trikona & Ekadhipatya Shodhana (Ashtakavarga Reductions) for Individual Birth Coordinates
This encyclopedia entry documents the classical algorithms of Trikona & Ekadhipatya Shodhana (Ashtakavarga Reductions) (BALA-06). To execute birth-second DE441
BALA-06 Precision EngineDE441Ephemeris (0.001°)16 Shodashavarga ChartsVerbatim Shloka Provenance
