{"id":"vidhyamitra:city-day:mathura:-3200-04-13:en","page_class":"VM-CD-city-day","url":"https://vidhyamitra.com/city/mathura/-3200-04-13","language":{"target_lang":"en","base_lang":"en","quality_tier":"canonical"},"data":{"date":"-3200-04-13","date_display":"April 13, 3201 BCE","panchanga":{"method":"Sūrya Siddhānta + Bhāskara-II iterative manda + Kerala-school (Mādhava-Nīlakaṇṭha) evection + variation + annual equation","engine_version":"2.0 (Kerala-school enhanced)","accuracy_note":"Not independently benchmarked across the declared range","tradition_chain":"Āryabhaṭa(499) → Brahmagupta(628) → Bhāskara II(1150) → Mādhava(~1400) → Parameśvara(1430) → Nīlakaṇṭha(1501) → this","input":{"year":-3200,"month":4,"day":13,"hour":6,"minute":30,"second":0,"calendar":"julian"},"julian_day":552360.770833,"kali_year":-98,"ahargana":-36104.7292,"sun":{"sidereal_longitude":55.9349,"rashi":2,"rashi_name":"Vṛṣabha"},"moon":{"sidereal_longitude":190.2871,"rashi":7,"rashi_name":"Tulā"},"tithi":{"number":12,"name":"Dvādaśī","paksha":"Śukla","full_name":"Śukla Dvādaśī","elongation_degrees":134.3522,"elapsed_within_tithi_degrees":2.3522},"nakshatra":{"number":15,"name":"Svātī","pada":2,"moon_longitude":190.2871,"elapsed_within_degrees":3.6205},"yoga":{"number":19,"name":"Parigha","sum_longitude":246.222},"karana":{"half_tithi_index":22,"name":"Bava"},"vara":{"number":1,"name":"Śanivāra (Saturday)"}},"sky":{"method":"Sūrya-Siddhāntic Bhāskara-II 4-step iteration with atan2-based śīghra + varying peripheries + lunar latitude","engine_version":"3.0 (Pūrṇa — complete SS implementation)","tradition_sources":"Āryabhaṭīya 499 CE → SS Ch.1-5 Burgess 1860 → Siddhānta-Śiromaṇi Bhāskara II 1150 → Tantrasaṅgraha Nīlakaṇṭha 1501","input":{"year":-3200,"month":4,"day":13,"hour":6,"minute":30,"calendar":"julian"},"julian_day":552360.770833,"ahargana":-36104.7292,"kali_year":-98,"ayanamsa_lahiri":-48.7837,"grahas":{"sun":{"sidereal_longitude":55.9349,"rashi":{"number":2,"name":"Vṛṣabha"},"nakshatra":{"number":5,"name":"Mṛgaśīrṣā","pada":1},"retrograde":false},"moon":{"sidereal_longitude":190.2871,"rashi":{"number":7,"name":"Tulā"},"nakshatra":{"number":15,"name":"Svātī","pada":2},"retrograde":false,"latitude":-4.3894},"mars":{"sidereal_longitude":121.4227,"rashi":{"number":5,"name":"Siṃha"},"nakshatra":{"number":10,"name":"Maghā","pada":1},"retrograde":false},"mercury":{"sidereal_longitude":71.8129,"rashi":{"number":3,"name":"Mithuna"},"nakshatra":{"number":6,"name":"Ārdrā","pada":2},"retrograde":true},"jupiter":{"sidereal_longitude":234.4497,"rashi":{"number":8,"name":"Vṛścika"},"nakshatra":{"number":18,"name":"Jyeṣṭhā","pada":3},"retrograde":true},"venus":{"sidereal_longitude":79.9644,"rashi":{"number":3,"name":"Mithuna"},"nakshatra":{"number":6,"name":"Ārdrā","pada":4},"retrograde":false},"saturn":{"sidereal_longitude":233.7072,"rashi":{"number":8,"name":"Vṛścika"},"nakshatra":{"number":18,"name":"Jyeṣṭhā","pada":3},"retrograde":true},"rahu":{"sidereal_longitude":293.0023,"rashi":{"number":10,"name":"Makara"},"nakshatra":{"number":22,"name":"Śravaṇa","pada":4},"retrograde":false},"ketu":{"sidereal_longitude":113.0023,"rashi":{"number":4,"name":"Karka"},"nakshatra":{"number":9,"name":"Āśleṣā","pada":2},"retrograde":false}},"panchang":{"method":"Sūrya Siddhānta + Bhāskara-II iterative manda + Kerala-school (Mādhava-Nīlakaṇṭha) evection + variation + annual equation","engine_version":"2.0 (Kerala-school enhanced)","accuracy_note":"Not independently benchmarked across the declared range","tradition_chain":"Āryabhaṭa(499) → Brahmagupta(628) → Bhāskara II(1150) → Mādhava(~1400) → Parameśvara(1430) → Nīlakaṇṭha(1501) → this","input":{"year":-3200,"month":4,"day":13,"hour":6,"minute":30,"second":0,"calendar":"julian"},"julian_day":552360.770833,"kali_year":-98,"ahargana":-36104.7292,"sun":{"sidereal_longitude":55.9349,"rashi":2,"rashi_name":"Vṛṣabha"},"moon":{"sidereal_longitude":190.2871,"rashi":7,"rashi_name":"Tulā"},"tithi":{"number":12,"name":"Dvādaśī","paksha":"Śukla","full_name":"Śukla Dvādaśī","elongation_degrees":134.3522,"elapsed_within_tithi_degrees":2.3522},"nakshatra":{"number":15,"name":"Svātī","pada":2,"moon_longitude":190.2871,"elapsed_within_degrees":3.6205},"yoga":{"number":19,"name":"Parigha","sum_longitude":246.222},"karana":{"half_tithi_index":22,"name":"Bava"},"vara":{"number":1,"name":"Śanivāra (Saturday)"}},"eclipse_current":{"solar":{"type":"solar","occurs":false,"moon_latitude":-4.389,"elongation":134.352},"lunar":{"type":"lunar","occurs":false,"moon_latitude":-4.389,"opposition_distance":45.648}},"eclipse_window_40days":[]},"city":{"slug":"mathura","name":"Mathurā","lat":27.4924,"lon":77.6737,"tz_offset_hours":5.5,"state":"Uttar Pradesh","country":"IN","tier":"tirtha"},"tier2":{"city":{"slug":"mathura","name":"Mathurā","lat":27.4924,"lon":77.6737,"tz_offset_hours":5.5,"state":"Uttar Pradesh","country":"IN","tier":"tirtha"},"sunriseLocal":"06:10","sunsetLocal":"18:30","solarNoonLocal":"12:20","dayLengthHours":12.322534235031277,"dayLengthDisplay":"12 Hours 19 Mins 21 Secs","nightLengthDisplay":"11 Hours 40 Mins 39 Secs","moonriseLocal":"14:44","moonsetLocal":"03:51","rahuKala":{"name":"Rāhu Kāla","start":"09:15","end":"10:48","startHours":9.253949955070585,"endHours":10.794266734449495,"quality":"inauspicious"},"yamaganda":{"name":"Yamaganda","start":"13:52","end":"15:25","startHours":13.874900293207315,"endHours":15.415217072586223,"quality":"inauspicious"},"gulika":{"name":"Gulika Kāla","start":"06:10","end":"07:43","startHours":6.173316396312766,"endHours":7.713633175691676,"quality":"inauspicious"},"durMuhurta":[{"name":"Dur Muhūrta","start":"09:03","end":"09:28","startHours":9.04857438448673,"endHours":9.45932552565444,"quality":"avoid"}],"varjyam":{"name":"Varjyam","start":"06:41","end":"07:01","startHours":6.686755322772403,"endHours":7.01535623570657,"quality":"avoid"},"abhijit":{"name":"Abhijit Muhūrta","start":"11:55","end":"12:45","startHours":11.923832372660696,"endHours":12.745334654996116,"quality":"auspicious"},"brahmaMuhurta":{"name":"Brahma Muhūrta","start":"04:32","end":"05:21","startHours":4.53031183164193,"endHours":5.351814113977348,"quality":"auspicious"},"pratahSandhya":{"name":"Prātaḥ Sandhyā","start":"05:09","end":"06:10","startHours":5.146438543393494,"endHours":6.173316396312766,"quality":"auspicious"},"vijayaMuhurta":{"name":"Vijaya Muhūrta","start":"14:23","end":"15:13","startHours":14.38833921966695,"endHours":15.209841502002368,"quality":"auspicious"},"godhuliMuhurta":{"name":"Godhūli Muhūrta","start":"18:18","end":"18:42","startHours":18.295850631344045,"endHours":18.695850631344044,"quality":"auspicious"},"sayahnaSandhya":{"name":"Sāyāhna Sandhyā","start":"18:30","end":"19:01","startHours":18.495850631344045,"endHours":19.00928955780368,"quality":"auspicious"},"amritKala":{"name":"Amṛta Kāla","start":"18:15","end":"20:00","startHours":18.245850631344045,"endHours":19.995850631344045,"quality":"auspicious"},"nishitaMuhurta":{"name":"Niśīta Muhūrta","start":"23:55","end":"00:45","startHours":23.923832372660698,"endHours":24.745334654996114,"quality":"auspicious"},"dayChoghadiyas":[{"name":"Kāla","start":"06:10","end":"07:43","startHours":6.173316396312766,"endHours":7.713633175691676,"quality":"inauspicious"},{"name":"Śubha","start":"07:43","end":"09:15","startHours":7.713633175691676,"endHours":9.253949955070585,"quality":"auspicious"},{"name":"Roga","start":"09:15","end":"10:48","startHours":9.253949955070585,"endHours":10.794266734449495,"quality":"inauspicious"},{"name":"Udveg","start":"10:48","end":"12:20","startHours":10.794266734449495,"endHours":12.334583513828406,"quality":"inauspicious"},{"name":"Chala","start":"12:20","end":"13:52","startHours":12.334583513828406,"endHours":13.874900293207315,"quality":"neutral"},{"name":"Labha","start":"13:52","end":"15:25","startHours":13.874900293207315,"endHours":15.415217072586223,"quality":"auspicious"},{"name":"Amṛta","start":"15:25","end":"16:57","startHours":15.415217072586223,"endHours":16.955533851965136,"quality":"auspicious"},{"name":"Kāla","start":"16:57","end":"18:30","startHours":16.955533851965136,"endHours":18.495850631344045,"quality":"inauspicious"}],"nightChoghadiyas":[{"name":"Labha","start":"18:30","end":"19:57","startHours":18.495850631344045,"endHours":19.955533851965136,"quality":"auspicious"},{"name":"Amṛta","start":"19:57","end":"21:25","startHours":19.955533851965136,"endHours":21.415217072586223,"quality":"auspicious"},{"name":"Kāla","start":"21:25","end":"22:52","startHours":21.415217072586223,"endHours":22.874900293207315,"quality":"inauspicious"},{"name":"Śubha","start":"22:52","end":"00:20","startHours":22.874900293207315,"endHours":24.334583513828406,"quality":"auspicious"},{"name":"Roga","start":"00:20","end":"01:48","startHours":24.334583513828406,"endHours":25.794266734449497,"quality":"inauspicious"},{"name":"Udveg","start":"01:48","end":"03:15","startHours":25.794266734449497,"endHours":27.25394995507059,"quality":"inauspicious"},{"name":"Chala","start":"03:15","end":"04:43","startHours":27.25394995507059,"endHours":28.713633175691676,"quality":"neutral"},{"name":"Labha","start":"04:43","end":"06:10","startHours":28.713633175691676,"endHours":30.173316396312767,"quality":"auspicious"}],"horas":[{"name":"Hora 1","start":"06:10","end":"07:10","startHours":6.173316396312766,"endHours":7.173316396312766,"planetary_lord":"Saturn"},{"name":"Hora 2","start":"07:10","end":"08:10","startHours":7.173316396312766,"endHours":8.173316396312767,"planetary_lord":"Moon"},{"name":"Hora 3","start":"08:10","end":"09:10","startHours":8.173316396312767,"endHours":9.173316396312767,"planetary_lord":"Mercury"},{"name":"Hora 4","start":"09:10","end":"10:10","startHours":9.173316396312767,"endHours":10.173316396312767,"planetary_lord":"Venus"},{"name":"Hora 5","start":"10:10","end":"11:10","startHours":10.173316396312767,"endHours":11.173316396312767,"planetary_lord":"Sun"},{"name":"Hora 6","start":"11:10","end":"12:10","startHours":11.173316396312767,"endHours":12.173316396312767,"planetary_lord":"Mars"},{"name":"Hora 7","start":"12:10","end":"13:10","startHours":12.173316396312767,"endHours":13.173316396312767,"planetary_lord":"Jupiter"},{"name":"Hora 8","start":"13:10","end":"14:10","startHours":13.173316396312767,"endHours":14.173316396312767,"planetary_lord":"Saturn"},{"name":"Hora 9","start":"14:10","end":"15:10","startHours":14.173316396312767,"endHours":15.173316396312767,"planetary_lord":"Moon"},{"name":"Hora 10","start":"15:10","end":"16:10","startHours":15.173316396312767,"endHours":16.173316396312767,"planetary_lord":"Mercury"},{"name":"Hora 11","start":"16:10","end":"17:10","startHours":16.173316396312767,"endHours":17.173316396312767,"planetary_lord":"Venus"},{"name":"Hora 12","start":"17:10","end":"18:10","startHours":17.173316396312767,"endHours":18.173316396312767,"planetary_lord":"Sun"},{"name":"Hora 13","start":"18:10","end":"19:10","startHours":18.173316396312767,"endHours":19.173316396312767,"planetary_lord":"Mars"},{"name":"Hora 14","start":"19:10","end":"20:10","startHours":19.173316396312767,"endHours":20.173316396312767,"planetary_lord":"Jupiter"},{"name":"Hora 15","start":"20:10","end":"21:10","startHours":20.173316396312767,"endHours":21.173316396312767,"planetary_lord":"Saturn"},{"name":"Hora 16","start":"21:10","end":"22:10","startHours":21.173316396312767,"endHours":22.173316396312767,"planetary_lord":"Moon"},{"name":"Hora 17","start":"22:10","end":"23:10","startHours":22.173316396312767,"endHours":23.173316396312767,"planetary_lord":"Mercury"},{"name":"Hora 18","start":"23:10","end":"00:10","startHours":23.173316396312767,"endHours":24.173316396312767,"planetary_lord":"Venus"},{"name":"Hora 19","start":"00:10","end":"01:10","startHours":24.173316396312767,"endHours":25.173316396312767,"planetary_lord":"Sun"},{"name":"Hora 20","start":"01:10","end":"02:10","startHours":25.173316396312767,"endHours":26.173316396312767,"planetary_lord":"Mars"},{"name":"Hora 21","start":"02:10","end":"03:10","startHours":26.173316396312767,"endHours":27.173316396312767,"planetary_lord":"Jupiter"},{"name":"Hora 22","start":"03:10","end":"04:10","startHours":27.173316396312767,"endHours":28.173316396312767,"planetary_lord":"Saturn"},{"name":"Hora 23","start":"04:10","end":"05:10","startHours":28.173316396312767,"endHours":29.173316396312767,"planetary_lord":"Moon"},{"name":"Hora 24","start":"05:10","end":"06:10","startHours":29.173316396312767,"endHours":30.173316396312767,"planetary_lord":"Mercury"}],"taraBala":{"favorable_nakshatras":["Aśvinī","Bharaṇī","Punarvasu","Puṣya","Aśleṣā","Maghā","Pūrva Phalgunī","Viśākhā","Anurādhā","Jyeṣṭhā","Mūla","Pūrva Āṣāḍhā","Pūrva Bhādrapadā","Uttara Bhādrapadā","Revatī"],"unfavorable_nakshatras":["Kṛttikā","Rohiṇī","Mṛgaśirā","Ārdrā","Uttara Phalgunī","Hasta","Citrā","Svātī","Uttara Āṣāḍhā","Śravaṇa","Dhaniṣṭhā","Śatabhiṣaj"],"nature":"Janma-tara if same nakshatra; favorable for 15 nakshatras"},"chandraBala":{"favorable_rashis":["Meṣa","Karka","Siṃha","Tulā","Dhanu","Mīna"],"unfavorable_rashis":["Vṛṣabha","Mithuna","Kanyā","Vṛścika","Makara","Kumbha"]},"dishaShool":"East (Pūrva)","chandraVasa":"North","rahuVasa":"East","anandadiYoga":{"name":"Chatra","quality":"Auspicious"},"tropicalRitu":"Vasanta (Spring) (tropical)","vedicRitu":"Vasanta (Spring)","tropicalAyana":"Uttarāyaṇa","vedicAyana":"Uttarāyaṇa","meta":{"method":"BOB-History Sūrya-Siddhānta + Vidhyamitra Tier-2 spherical localization","declination":2.838045854550757,"eotMinutes":-0.7698108297043191,"ayanamsa":-48.7837}},"calendars":{"vikram_samvat":-3143,"saka_samvat":-3278,"bengali_samvat":-3793,"malayalam_era":-4024,"nanakshahi_year":-4669,"lunar_month":"Jyeṣṭha","lunar_month_paksha_full":"Jyeṣṭha Śukla Pakṣa","lunar_month_system":"purnimanta","lunar_month_purnimanta":"Jyeṣṭha","lunar_month_amanta":"Jyeṣṭha","lunar_month_is_adhika":false,"lunar_month_purnimanta_is_adhika":false,"lunar_month_amanta_is_adhika":false,"solar_month":"Vṛṣabha (Vaikāsi)","ritu":"Grīṣma (Summer)","display_summary":"Jyeṣṭha Śukla Dvādaśī · Vikram -3143 undefined · Śaka -3278 undefined"},"festivals":[],"todays_walk":{"walk":{"id":"shani-walk","name":"Śani Walk","name_sanskrit":"शनि यात्रा","type":"graha","description":"Tapas + endurance + BG 17.14-19.","step_count":7,"url":"/walk/shani-walk"},"reason":"Śanivāra (Saturday) — its presiding graha's walk."},"cosmic_resonances":[]},"validity":{"eternal":true,"location_specific":"mathura"},"liturgical":{"opening":"जय श्री कृष्ण","closing":"ॐ तत् सत्","attribution":"Computed by Vidhyamitra Sūrya-Siddhānta substrate + Vidhyamitra Tier-2 layer"},"seo":{"title":"Pañchāṅga April 13, 3201 BCE · Mathurā · Vidhyamitra","description":"April 13, 3201 BCE for Mathurā: Śukla Dvādaśī, sūryodaya 06:10, sūryāsta 18:30.","schema_org_type":"Article","canonical":"https://vidhyamitra.com/city/mathura/-3200-04-13","hreflang_alternates":{"en":"https://vidhyamitra.com/city/mathura/-3200-04-13","sa":"https://sa.vidhyamitra.com/city/mathura/-3200-04-13","hi":"https://hi.vidhyamitra.com/city/mathura/-3200-04-13","x-default":"https://vidhyamitra.com/city/mathura/-3200-04-13"}},"provenance":[{"pillar":"BOB-History","pillar_version":"2.12.0","method":"Sūrya-Siddhānta first-principles + Bhāskara II + Kerala-school (Mādhava-Nīlakaṇṭha) corrections","retrieved_at":"2026-08-11T21:34:22.846Z","verification":{"type":"multi-marker","confidence":"canonical"}},{"pillar":"Vidhyamitra-Tier2","pillar_version":"0.1.0","method":"Spherical astronomy + Lahiri ayanamsa + standard solar declination + EoT correction","retrieved_at":"2026-08-11T21:34:22.846Z","verification":{"type":"community-validated","markers":["modern-reference checked timing on Narasiṁha Jayantī 2026"],"confidence":"verified"}}],"meta":{"generated_at":"2026-08-11T21:34:22.846Z","pillar_versions":{"Sūrya-Siddhānta":"Pūrṇa","Vidhyamitra-Tier2":"Pūrṇa"},"reader_local_antaryami":{"reader_geography":"Every reader enters from their own kṣetra anywhere on Bhūmi; no single city is the universal center.","purna_chain":["Goloka/Vraja Rādhā-Krishna","Vaikuṇṭha Lakṣmī-Nārāyaṇa","Mahāviṣṇu/Kāraṇodakaśāyī Viṣṇu","Garbhodakaśāyī Viṣṇu","Brahmā","Kṣīrodaka Paramātmā/Antaryāmī (Kṣīrodakaśāyī Viṣṇu)","Bhūmi","reader's own kṣetra anywhere on Bhūmi","exact reading kṣetra","reader-bhakta","chitta/vāṇī/aṅgulī","keyboard-silicon-pathways","Vidhyāmitra substrate","reader/seer","Krishna"],"antaryami_responsibility_formula":"Kṣīrodakaśāyī Viṣṇu = Paramātmā = Antaryāmī. Jīva desires. Prakṛti executes through guṇas. Paramātmā witnesses, permits, remembers, guides, and sustains. Bhagavān is the ultimate source.","source_anchors":[{"label":"BG 13.23","path":"/bhagavad-gita/13/23","meaning":"upadraṣṭā-anumantā · witness-permitter"},{"label":"BG 15.15","path":"/bhagavad-gita/15/15","meaning":"the Lord seated in every heart as memory, knowledge, and forgetting"},{"label":"BG 18.61","path":"/bhagavad-gita/18/61","meaning":"Īśvara seated in the heart of all beings"}],"nama_seal":"Hare Krishna Hare Krishna · Krishna Krishna Hare Hare · Hare Rama Hare Rama · Rama Rama Hare Hare"}}}