{"id":"vidhyamitra:city-day:mathura:-3181-10-11:en","page_class":"VM-CD-city-day","url":"https://vidhyamitra.com/city/mathura/-3181-10-11","language":{"target_lang":"en","base_lang":"en","quality_tier":"canonical"},"data":{"date":"-3181-10-11","date_display":"October 11, 3182 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":-3181,"month":10,"day":11,"hour":6,"minute":30,"second":0,"calendar":"julian"},"julian_day":559480.770833,"kali_year":-79,"ahargana":-28984.7292,"sun":{"sidereal_longitude":231.5558,"rashi":8,"rashi_name":"Vṛścika"},"moon":{"sidereal_longitude":51.7271,"rashi":2,"rashi_name":"Vṛṣabha"},"tithi":{"number":16,"name":"Pratipada","paksha":"Kṛṣṇa","full_name":"Kṛṣṇa Pratipada","elongation_degrees":180.1714,"elapsed_within_tithi_degrees":0.1714},"nakshatra":{"number":4,"name":"Rohiṇī","pada":4,"moon_longitude":51.7271,"elapsed_within_degrees":11.7271},"yoga":{"number":22,"name":"Sādhya","sum_longitude":283.2829},"karana":{"half_tithi_index":30,"name":"Bālava"},"vara":{"number":2,"name":"Ravivāra (Sunday)"}},"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":-3181,"month":10,"day":11,"hour":6,"minute":30,"calendar":"julian"},"julian_day":559480.770833,"ahargana":-28984.7292,"kali_year":-79,"ayanamsa_lahiri":-48.5114,"grahas":{"sun":{"sidereal_longitude":231.5558,"rashi":{"number":8,"name":"Vṛścika"},"nakshatra":{"number":18,"name":"Jyeṣṭhā","pada":2},"retrograde":false},"moon":{"sidereal_longitude":51.7271,"rashi":{"number":2,"name":"Vṛṣabha"},"nakshatra":{"number":4,"name":"Rohiṇī","pada":4},"retrograde":false,"latitude":3.1256},"mars":{"sidereal_longitude":265.4103,"rashi":{"number":9,"name":"Dhanu"},"nakshatra":{"number":20,"name":"Pūrva Āṣāḍhā","pada":4},"retrograde":false},"mercury":{"sidereal_longitude":219.807,"rashi":{"number":8,"name":"Vṛścika"},"nakshatra":{"number":17,"name":"Anurādhā","pada":2},"retrograde":false},"jupiter":{"sidereal_longitude":125.3804,"rashi":{"number":5,"name":"Siṃha"},"nakshatra":{"number":10,"name":"Maghā","pada":2},"retrograde":false},"venus":{"sidereal_longitude":278.7523,"rashi":{"number":10,"name":"Makara"},"nakshatra":{"number":21,"name":"Uttara Āṣāḍhā","pada":4},"retrograde":false},"saturn":{"sidereal_longitude":124.2164,"rashi":{"number":5,"name":"Siṃha"},"nakshatra":{"number":10,"name":"Maghā","pada":2},"retrograde":false},"rahu":{"sidereal_longitude":275.7504,"rashi":{"number":10,"name":"Makara"},"nakshatra":{"number":21,"name":"Uttara Āṣāḍhā","pada":3},"retrograde":false},"ketu":{"sidereal_longitude":95.7504,"rashi":{"number":4,"name":"Karka"},"nakshatra":{"number":8,"name":"Puṣya","pada":1},"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":-3181,"month":10,"day":11,"hour":6,"minute":30,"second":0,"calendar":"julian"},"julian_day":559480.770833,"kali_year":-79,"ahargana":-28984.7292,"sun":{"sidereal_longitude":231.5558,"rashi":8,"rashi_name":"Vṛścika"},"moon":{"sidereal_longitude":51.7271,"rashi":2,"rashi_name":"Vṛṣabha"},"tithi":{"number":16,"name":"Pratipada","paksha":"Kṛṣṇa","full_name":"Kṛṣṇa Pratipada","elongation_degrees":180.1714,"elapsed_within_tithi_degrees":0.1714},"nakshatra":{"number":4,"name":"Rohiṇī","pada":4,"moon_longitude":51.7271,"elapsed_within_degrees":11.7271},"yoga":{"number":22,"name":"Sādhya","sum_longitude":283.2829},"karana":{"half_tithi_index":30,"name":"Bālava"},"vara":{"number":2,"name":"Ravivāra (Sunday)"}},"eclipse_current":{"solar":{"type":"solar","occurs":false,"moon_latitude":3.126,"elongation":179.829},"lunar":{"type":"lunar","occurs":false,"moon_latitude":3.126,"opposition_distance":0.171}},"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":"06:04","sunsetLocal":"18:07","solarNoonLocal":"12:05","dayLengthHours":12.041233365019119,"dayLengthDisplay":"12 Hours 02 Mins 28 Secs","nightLengthDisplay":"11 Hours 57 Mins 32 Secs","moonriseLocal":"18:01","moonsetLocal":"06:11","rahuKala":{"name":"Rāhu Kāla","start":"16:36","end":"18:07","startHours":16.604109611945,"endHours":18.10926378257239,"quality":"inauspicious"},"yamaganda":{"name":"Yamaganda","start":"12:05","end":"13:36","startHours":12.088647100062833,"endHours":13.593801270690221,"quality":"inauspicious"},"gulika":{"name":"Gulika Kāla","start":"15:06","end":"16:36","startHours":15.098955441317612,"endHours":16.604109611945,"quality":"inauspicious"},"durMuhurta":[{"name":"Dur Muhūrta","start":"08:53","end":"09:17","startHours":8.877651536057733,"endHours":9.27902598155837,"quality":"avoid"}],"varjyam":{"name":"Varjyam","start":"06:34","end":"06:53","startHours":6.569748474429069,"endHours":6.890848030829579,"quality":"avoid"},"abhijit":{"name":"Abhijit Muhūrta","start":"11:41","end":"12:29","startHours":11.687272654562195,"endHours":12.49002154556347,"quality":"auspicious"},"brahmaMuhurta":{"name":"Brahma Muhūrta","start":"04:28","end":"05:16","startHours":4.462532635550723,"endHours":5.265281526551997,"quality":"auspicious"},"pratahSandhya":{"name":"Prātaḥ Sandhyā","start":"05:04","end":"06:04","startHours":5.0645943038016785,"endHours":6.068030417553272,"quality":"auspicious"},"vijayaMuhurta":{"name":"Vijaya Muhūrta","start":"14:06","end":"14:54","startHours":14.095519327566018,"endHours":14.898268218567292,"quality":"auspicious"},"godhuliMuhurta":{"name":"Godhūli Muhūrta","start":"17:55","end":"18:19","startHours":17.909263782572392,"endHours":18.30926378257239,"quality":"auspicious"},"sayahnaSandhya":{"name":"Sāyāhna Sandhyā","start":"18:07","end":"18:37","startHours":18.10926378257239,"endHours":18.610981839448186,"quality":"auspicious"},"amritKala":{"name":"Amṛta Kāla","start":"17:52","end":"19:37","startHours":17.85926378257239,"endHours":19.60926378257239,"quality":"auspicious"},"nishitaMuhurta":{"name":"Niśīta Muhūrta","start":"23:41","end":"00:29","startHours":23.687272654562197,"endHours":24.49002154556347,"quality":"auspicious"},"dayChoghadiyas":[{"name":"Udveg","start":"06:04","end":"07:34","startHours":6.068030417553272,"endHours":7.573184588180662,"quality":"inauspicious"},{"name":"Chala","start":"07:34","end":"09:05","startHours":7.573184588180662,"endHours":9.078338758808052,"quality":"neutral"},{"name":"Labha","start":"09:05","end":"10:35","startHours":9.078338758808052,"endHours":10.583492929435442,"quality":"auspicious"},{"name":"Amṛta","start":"10:35","end":"12:05","startHours":10.583492929435442,"endHours":12.088647100062833,"quality":"auspicious"},{"name":"Kāla","start":"12:05","end":"13:36","startHours":12.088647100062833,"endHours":13.593801270690221,"quality":"inauspicious"},{"name":"Śubha","start":"13:36","end":"15:06","startHours":13.593801270690221,"endHours":15.098955441317612,"quality":"auspicious"},{"name":"Roga","start":"15:06","end":"16:36","startHours":15.098955441317612,"endHours":16.604109611945,"quality":"inauspicious"},{"name":"Udveg","start":"16:36","end":"18:07","startHours":16.604109611945,"endHours":18.10926378257239,"quality":"inauspicious"}],"nightChoghadiyas":[{"name":"Śubha","start":"18:07","end":"19:36","startHours":18.10926378257239,"endHours":19.604109611945002,"quality":"auspicious"},{"name":"Roga","start":"19:36","end":"21:06","startHours":19.604109611945002,"endHours":21.09895544131761,"quality":"inauspicious"},{"name":"Udveg","start":"21:06","end":"22:36","startHours":21.09895544131761,"endHours":22.59380127069022,"quality":"inauspicious"},{"name":"Chala","start":"22:36","end":"00:05","startHours":22.59380127069022,"endHours":24.088647100062833,"quality":"neutral"},{"name":"Labha","start":"00:05","end":"01:35","startHours":24.088647100062833,"endHours":25.583492929435444,"quality":"auspicious"},{"name":"Amṛta","start":"01:35","end":"03:05","startHours":25.583492929435444,"endHours":27.07833875880805,"quality":"auspicious"},{"name":"Kāla","start":"03:05","end":"04:34","startHours":27.07833875880805,"endHours":28.573184588180663,"quality":"inauspicious"},{"name":"Śubha","start":"04:34","end":"06:04","startHours":28.573184588180663,"endHours":30.068030417553274,"quality":"auspicious"}],"horas":[{"name":"Hora 1","start":"06:04","end":"07:04","startHours":6.068030417553272,"endHours":7.068030417553272,"planetary_lord":"Sun"},{"name":"Hora 2","start":"07:04","end":"08:04","startHours":7.068030417553272,"endHours":8.068030417553272,"planetary_lord":"Mars"},{"name":"Hora 3","start":"08:04","end":"09:04","startHours":8.068030417553272,"endHours":9.068030417553272,"planetary_lord":"Jupiter"},{"name":"Hora 4","start":"09:04","end":"10:04","startHours":9.068030417553272,"endHours":10.068030417553272,"planetary_lord":"Saturn"},{"name":"Hora 5","start":"10:04","end":"11:04","startHours":10.068030417553272,"endHours":11.068030417553272,"planetary_lord":"Moon"},{"name":"Hora 6","start":"11:04","end":"12:04","startHours":11.068030417553272,"endHours":12.068030417553272,"planetary_lord":"Mercury"},{"name":"Hora 7","start":"12:04","end":"13:04","startHours":12.068030417553272,"endHours":13.068030417553272,"planetary_lord":"Venus"},{"name":"Hora 8","start":"13:04","end":"14:04","startHours":13.068030417553272,"endHours":14.068030417553272,"planetary_lord":"Sun"},{"name":"Hora 9","start":"14:04","end":"15:04","startHours":14.068030417553272,"endHours":15.068030417553272,"planetary_lord":"Mars"},{"name":"Hora 10","start":"15:04","end":"16:04","startHours":15.068030417553272,"endHours":16.068030417553274,"planetary_lord":"Jupiter"},{"name":"Hora 11","start":"16:04","end":"17:04","startHours":16.068030417553274,"endHours":17.068030417553274,"planetary_lord":"Saturn"},{"name":"Hora 12","start":"17:04","end":"18:04","startHours":17.068030417553274,"endHours":18.068030417553274,"planetary_lord":"Moon"},{"name":"Hora 13","start":"18:04","end":"19:04","startHours":18.068030417553274,"endHours":19.068030417553274,"planetary_lord":"Mercury"},{"name":"Hora 14","start":"19:04","end":"20:04","startHours":19.068030417553274,"endHours":20.068030417553274,"planetary_lord":"Venus"},{"name":"Hora 15","start":"20:04","end":"21:04","startHours":20.068030417553274,"endHours":21.068030417553274,"planetary_lord":"Sun"},{"name":"Hora 16","start":"21:04","end":"22:04","startHours":21.068030417553274,"endHours":22.068030417553274,"planetary_lord":"Mars"},{"name":"Hora 17","start":"22:04","end":"23:04","startHours":22.068030417553274,"endHours":23.068030417553274,"planetary_lord":"Jupiter"},{"name":"Hora 18","start":"23:04","end":"00:04","startHours":23.068030417553274,"endHours":24.068030417553274,"planetary_lord":"Saturn"},{"name":"Hora 19","start":"00:04","end":"01:04","startHours":24.068030417553274,"endHours":25.068030417553274,"planetary_lord":"Moon"},{"name":"Hora 20","start":"01:04","end":"02:04","startHours":25.068030417553274,"endHours":26.068030417553274,"planetary_lord":"Mercury"},{"name":"Hora 21","start":"02:04","end":"03:04","startHours":26.068030417553274,"endHours":27.068030417553274,"planetary_lord":"Venus"},{"name":"Hora 22","start":"03:04","end":"04:04","startHours":27.068030417553274,"endHours":28.068030417553274,"planetary_lord":"Sun"},{"name":"Hora 23","start":"04:04","end":"05:04","startHours":28.068030417553274,"endHours":29.068030417553274,"planetary_lord":"Mars"},{"name":"Hora 24","start":"05:04","end":"06:04","startHours":29.068030417553274,"endHours":30.068030417553274,"planetary_lord":"Jupiter"}],"taraBala":{"favorable_nakshatras":["Mṛgaśirā","Ārdrā","Punarvasu","Puṣya","Aśleṣā","Citrā","Svātī","Viśākhā","Anurādhā","Jyeṣṭhā","Dhaniṣṭhā","Śatabhiṣaj","Pūrva Bhādrapadā","Uttara Bhādrapadā","Revatī"],"unfavorable_nakshatras":["Aśvinī","Bharaṇī","Kṛttikā","Rohiṇī","Maghā","Pūrva Phalgunī","Uttara Phalgunī","Hasta","Mūla","Pūrva Āṣāḍhā","Uttara Āṣāḍhā","Śravaṇa"],"nature":"Janma-tara if same nakshatra; favorable for 15 nakshatras"},"chandraBala":{"favorable_rashis":["Vṛṣabha","Karka","Tulā","Vṛścika","Kumbha","Mīna"],"unfavorable_rashis":["Meṣa","Mithuna","Siṃha","Kanyā","Dhanu","Makara"]},"dishaShool":"West (Paścim)","chandraVasa":"South-East","rahuVasa":"North-East","anandadiYoga":{"name":"Prajāpati","quality":"Auspicious"},"tropicalRitu":"Śarad (Autumn) (tropical)","vedicRitu":"Śarad (Autumn)","tropicalAyana":"Dakṣiṇāyana","vedicAyana":"Dakṣiṇāyana","meta":{"method":"BOB-History Sūrya-Siddhānta + Vidhyamitra Tier-2 spherical localization","declination":-1.2103770385777368,"eotMinutes":13.986373996230075,"ayanamsa":-48.5114}},"calendars":{"vikram_samvat":-3124,"saka_samvat":-3259,"bengali_samvat":-3774,"malayalam_era":-4005,"nanakshahi_year":-4650,"lunar_month":"Mārgaśīrṣa","lunar_month_paksha_full":"Mārgaśīrṣa Kṛṣṇa Pakṣa","lunar_month_system":"purnimanta","lunar_month_purnimanta":"Mārgaśīrṣa","lunar_month_amanta":"Mārgaśīrṣa","lunar_month_is_adhika":false,"lunar_month_purnimanta_is_adhika":false,"lunar_month_amanta_is_adhika":false,"solar_month":"Vṛścika (Kārttikai)","ritu":"Hemanta (Pre-winter)","display_summary":"Mārgaśīrṣa Kṛṣṇa Pratipada · Vikram -3124 undefined · Śaka -3259 undefined"},"festivals":[],"todays_walk":{"walk":{"id":"surya-walk","name":"Sūrya Walk","name_sanskrit":"सूर्य यात्रा","type":"graha","description":"Self-illumination + BG 4.1 (Sun-lineage of Gītā transmission).","step_count":6,"url":"/walk/surya-walk"},"reason":"Ravivāra (Sunday) — 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 October 11, 3182 BCE · Mathurā · Vidhyamitra","description":"October 11, 3182 BCE for Mathurā: Kṛṣṇa Pratipada, sūryodaya 06:04, sūryāsta 18:07.","schema_org_type":"Article","canonical":"https://vidhyamitra.com/city/mathura/-3181-10-11","hreflang_alternates":{"en":"https://vidhyamitra.com/city/mathura/-3181-10-11","sa":"https://sa.vidhyamitra.com/city/mathura/-3181-10-11","hi":"https://hi.vidhyamitra.com/city/mathura/-3181-10-11","x-default":"https://vidhyamitra.com/city/mathura/-3181-10-11"}},"provenance":[{"pillar":"BOB-History","pillar_version":"2.12.0","method":"Sūrya-Siddhānta first-principles + Bhāskara II + Kerala-school (Mādhava-Nīlakaṇṭha) corrections","retrieved_at":"2026-08-10T14:07:01.552Z","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":"2026-08-10T14:07:01.552Z","verification":{"type":"community-validated","markers":["modern-reference checked timing on Narasiṁha Jayantī 2026"],"confidence":"verified"}}],"meta":{"generated_at":"2026-08-10T14:07:01.552Z","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"}}}