{"id":"vidhyamitra:city-day:mathura:-3181-09-12:en","page_class":"VM-CD-city-day","url":"https://vidhyamitra.com/city/mathura/-3181-09-12","language":{"target_lang":"en","base_lang":"en","quality_tier":"canonical"},"data":{"date":"-3181-09-12","date_display":"September 12, 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":9,"day":12,"hour":6,"minute":30,"second":0,"calendar":"julian"},"julian_day":559451.770833,"kali_year":-79,"ahargana":-29013.7292,"sun":{"sidereal_longitude":202.0513,"rashi":7,"rashi_name":"Tulā"},"moon":{"sidereal_longitude":30.8793,"rashi":2,"rashi_name":"Vṛṣabha"},"tithi":{"number":16,"name":"Pratipada","paksha":"Kṛṣṇa","full_name":"Kṛṣṇa Pratipada","elongation_degrees":188.828,"elapsed_within_tithi_degrees":8.828},"nakshatra":{"number":3,"name":"Kṛttikā","pada":2,"moon_longitude":30.8793,"elapsed_within_degrees":4.2126},"yoga":{"number":18,"name":"Varīyān","sum_longitude":232.9307},"karana":{"half_tithi_index":31,"name":"Kaulava"},"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":-3181,"month":9,"day":12,"hour":6,"minute":30,"calendar":"julian"},"julian_day":559451.770833,"ahargana":-29013.7292,"kali_year":-79,"ayanamsa_lahiri":-48.5125,"grahas":{"sun":{"sidereal_longitude":202.0513,"rashi":{"number":7,"name":"Tulā"},"nakshatra":{"number":16,"name":"Viśākhā","pada":1},"retrograde":false},"moon":{"sidereal_longitude":30.8793,"rashi":{"number":2,"name":"Vṛṣabha"},"nakshatra":{"number":3,"name":"Kṛttikā","pada":2},"retrograde":false,"latitude":4.1232},"mars":{"sidereal_longitude":243.5421,"rashi":{"number":9,"name":"Dhanu"},"nakshatra":{"number":19,"name":"Mūla","pada":2},"retrograde":false},"mercury":{"sidereal_longitude":187.3101,"rashi":{"number":7,"name":"Tulā"},"nakshatra":{"number":15,"name":"Svātī","pada":1},"retrograde":false},"jupiter":{"sidereal_longitude":123.4452,"rashi":{"number":5,"name":"Siṃha"},"nakshatra":{"number":10,"name":"Maghā","pada":2},"retrograde":false},"venus":{"sidereal_longitude":246.0607,"rashi":{"number":9,"name":"Dhanu"},"nakshatra":{"number":19,"name":"Mūla","pada":2},"retrograde":false},"saturn":{"sidereal_longitude":123.3956,"rashi":{"number":5,"name":"Siṃha"},"nakshatra":{"number":10,"name":"Maghā","pada":2},"retrograde":false},"rahu":{"sidereal_longitude":277.287,"rashi":{"number":10,"name":"Makara"},"nakshatra":{"number":21,"name":"Uttara Āṣāḍhā","pada":4},"retrograde":false},"ketu":{"sidereal_longitude":97.287,"rashi":{"number":4,"name":"Karka"},"nakshatra":{"number":8,"name":"Puṣya","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":-3181,"month":9,"day":12,"hour":6,"minute":30,"second":0,"calendar":"julian"},"julian_day":559451.770833,"kali_year":-79,"ahargana":-29013.7292,"sun":{"sidereal_longitude":202.0513,"rashi":7,"rashi_name":"Tulā"},"moon":{"sidereal_longitude":30.8793,"rashi":2,"rashi_name":"Vṛṣabha"},"tithi":{"number":16,"name":"Pratipada","paksha":"Kṛṣṇa","full_name":"Kṛṣṇa Pratipada","elongation_degrees":188.828,"elapsed_within_tithi_degrees":8.828},"nakshatra":{"number":3,"name":"Kṛttikā","pada":2,"moon_longitude":30.8793,"elapsed_within_degrees":4.2126},"yoga":{"number":18,"name":"Varīyān","sum_longitude":232.9307},"karana":{"half_tithi_index":31,"name":"Kaulava"},"vara":{"number":1,"name":"Śanivāra (Saturday)"}},"eclipse_current":{"solar":{"type":"solar","occurs":false,"moon_latitude":4.123,"elongation":171.172},"lunar":{"type":"lunar","occurs":false,"moon_latitude":4.123,"opposition_distance":8.828}},"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":"05:50","sunsetLocal":"18:40","solarNoonLocal":"12:15","dayLengthHours":12.844841169144019,"dayLengthDisplay":"12 Hours 50 Mins 41 Secs","nightLengthDisplay":"11 Hours 09 Mins 19 Secs","moonriseLocal":"19:02","moonsetLocal":"06:38","rahuKala":{"name":"Rāhu Kāla","start":"09:02","end":"10:39","startHours":9.037484448580905,"endHours":10.643089594723907,"quality":"inauspicious"},"yamaganda":{"name":"Yamaganda","start":"13:51","end":"15:28","startHours":13.854299887009912,"endHours":15.459905033152914,"quality":"inauspicious"},"gulika":{"name":"Gulika Kāla","start":"05:50","end":"07:26","startHours":5.8262741562949,"endHours":7.431879302437903,"quality":"inauspicious"},"durMuhurta":[{"name":"Dur Muhūrta","start":"08:49","end":"09:15","startHours":8.823403762428505,"endHours":9.251565134733305,"quality":"avoid"}],"varjyam":{"name":"Varjyam","start":"06:22","end":"06:42","startHours":6.361475871675901,"endHours":6.704004969519741,"quality":"avoid"},"abhijit":{"name":"Abhijit Muhūrta","start":"11:49","end":"12:41","startHours":11.820533368562108,"endHours":12.676856113171711,"quality":"auspicious"},"brahmaMuhurta":{"name":"Brahma Muhūrta","start":"04:07","end":"04:58","startHours":4.113628667075698,"endHours":4.969951411685299,"quality":"auspicious"},"pratahSandhya":{"name":"Prātaḥ Sandhyā","start":"04:45","end":"05:50","startHours":4.7558707255328985,"endHours":5.8262741562949,"quality":"auspicious"},"vijayaMuhurta":{"name":"Vijaya Muhūrta","start":"14:23","end":"15:15","startHours":14.389501602390913,"endHours":15.245824347000514,"quality":"auspicious"},"godhuliMuhurta":{"name":"Godhūli Muhūrta","start":"18:28","end":"18:52","startHours":18.47111532543892,"endHours":18.871115325438918,"quality":"auspicious"},"sayahnaSandhya":{"name":"Sāyāhna Sandhyā","start":"18:40","end":"19:12","startHours":18.67111532543892,"endHours":19.20631704081992,"quality":"auspicious"},"amritKala":{"name":"Amṛta Kāla","start":"18:25","end":"20:10","startHours":18.42111532543892,"endHours":20.17111532543892,"quality":"auspicious"},"nishitaMuhurta":{"name":"Niśīta Muhūrta","start":"23:49","end":"00:41","startHours":23.82053336856211,"endHours":24.67685611317171,"quality":"auspicious"},"dayChoghadiyas":[{"name":"Kāla","start":"05:50","end":"07:26","startHours":5.8262741562949,"endHours":7.431879302437903,"quality":"inauspicious"},{"name":"Śubha","start":"07:26","end":"09:02","startHours":7.431879302437903,"endHours":9.037484448580905,"quality":"auspicious"},{"name":"Roga","start":"09:02","end":"10:39","startHours":9.037484448580905,"endHours":10.643089594723907,"quality":"inauspicious"},{"name":"Udveg","start":"10:39","end":"12:15","startHours":10.643089594723907,"endHours":12.24869474086691,"quality":"inauspicious"},{"name":"Chala","start":"12:15","end":"13:51","startHours":12.24869474086691,"endHours":13.854299887009912,"quality":"neutral"},{"name":"Labha","start":"13:51","end":"15:28","startHours":13.854299887009912,"endHours":15.459905033152914,"quality":"auspicious"},{"name":"Amṛta","start":"15:28","end":"17:04","startHours":15.459905033152914,"endHours":17.065510179295917,"quality":"auspicious"},{"name":"Kāla","start":"17:04","end":"18:40","startHours":17.065510179295917,"endHours":18.67111532543892,"quality":"inauspicious"}],"nightChoghadiyas":[{"name":"Labha","start":"18:40","end":"20:04","startHours":18.67111532543892,"endHours":20.065510179295917,"quality":"auspicious"},{"name":"Amṛta","start":"20:04","end":"21:28","startHours":20.065510179295917,"endHours":21.459905033152914,"quality":"auspicious"},{"name":"Kāla","start":"21:28","end":"22:51","startHours":21.459905033152914,"endHours":22.854299887009912,"quality":"inauspicious"},{"name":"Śubha","start":"22:51","end":"00:15","startHours":22.854299887009912,"endHours":24.24869474086691,"quality":"auspicious"},{"name":"Roga","start":"00:15","end":"01:39","startHours":24.24869474086691,"endHours":25.643089594723907,"quality":"inauspicious"},{"name":"Udveg","start":"01:39","end":"03:02","startHours":25.643089594723907,"endHours":27.037484448580905,"quality":"inauspicious"},{"name":"Chala","start":"03:02","end":"04:26","startHours":27.037484448580905,"endHours":28.431879302437903,"quality":"neutral"},{"name":"Labha","start":"04:26","end":"05:50","startHours":28.431879302437903,"endHours":29.8262741562949,"quality":"auspicious"}],"horas":[{"name":"Hora 1","start":"05:50","end":"06:50","startHours":5.8262741562949,"endHours":6.8262741562949,"planetary_lord":"Saturn"},{"name":"Hora 2","start":"06:50","end":"07:50","startHours":6.8262741562949,"endHours":7.8262741562949,"planetary_lord":"Moon"},{"name":"Hora 3","start":"07:50","end":"08:50","startHours":7.8262741562949,"endHours":8.8262741562949,"planetary_lord":"Mercury"},{"name":"Hora 4","start":"08:50","end":"09:50","startHours":8.8262741562949,"endHours":9.8262741562949,"planetary_lord":"Venus"},{"name":"Hora 5","start":"09:50","end":"10:50","startHours":9.8262741562949,"endHours":10.8262741562949,"planetary_lord":"Sun"},{"name":"Hora 6","start":"10:50","end":"11:50","startHours":10.8262741562949,"endHours":11.8262741562949,"planetary_lord":"Mars"},{"name":"Hora 7","start":"11:50","end":"12:50","startHours":11.8262741562949,"endHours":12.8262741562949,"planetary_lord":"Jupiter"},{"name":"Hora 8","start":"12:50","end":"13:50","startHours":12.8262741562949,"endHours":13.8262741562949,"planetary_lord":"Saturn"},{"name":"Hora 9","start":"13:50","end":"14:50","startHours":13.8262741562949,"endHours":14.8262741562949,"planetary_lord":"Moon"},{"name":"Hora 10","start":"14:50","end":"15:50","startHours":14.8262741562949,"endHours":15.8262741562949,"planetary_lord":"Mercury"},{"name":"Hora 11","start":"15:50","end":"16:50","startHours":15.8262741562949,"endHours":16.8262741562949,"planetary_lord":"Venus"},{"name":"Hora 12","start":"16:50","end":"17:50","startHours":16.8262741562949,"endHours":17.8262741562949,"planetary_lord":"Sun"},{"name":"Hora 13","start":"17:50","end":"18:50","startHours":17.8262741562949,"endHours":18.8262741562949,"planetary_lord":"Mars"},{"name":"Hora 14","start":"18:50","end":"19:50","startHours":18.8262741562949,"endHours":19.8262741562949,"planetary_lord":"Jupiter"},{"name":"Hora 15","start":"19:50","end":"20:50","startHours":19.8262741562949,"endHours":20.8262741562949,"planetary_lord":"Saturn"},{"name":"Hora 16","start":"20:50","end":"21:50","startHours":20.8262741562949,"endHours":21.8262741562949,"planetary_lord":"Moon"},{"name":"Hora 17","start":"21:50","end":"22:50","startHours":21.8262741562949,"endHours":22.8262741562949,"planetary_lord":"Mercury"},{"name":"Hora 18","start":"22:50","end":"23:50","startHours":22.8262741562949,"endHours":23.8262741562949,"planetary_lord":"Venus"},{"name":"Hora 19","start":"23:50","end":"00:50","startHours":23.8262741562949,"endHours":24.8262741562949,"planetary_lord":"Sun"},{"name":"Hora 20","start":"00:50","end":"01:50","startHours":24.8262741562949,"endHours":25.8262741562949,"planetary_lord":"Mars"},{"name":"Hora 21","start":"01:50","end":"02:50","startHours":25.8262741562949,"endHours":26.8262741562949,"planetary_lord":"Jupiter"},{"name":"Hora 22","start":"02:50","end":"03:50","startHours":26.8262741562949,"endHours":27.8262741562949,"planetary_lord":"Saturn"},{"name":"Hora 23","start":"03:50","end":"04:50","startHours":27.8262741562949,"endHours":28.8262741562949,"planetary_lord":"Moon"},{"name":"Hora 24","start":"04:50","end":"05:50","startHours":28.8262741562949,"endHours":29.8262741562949,"planetary_lord":"Mercury"}],"taraBala":{"favorable_nakshatras":["Rohiṇī","Mṛgaśirā","Ārdrā","Punarvasu","Puṣya","Hasta","Citrā","Svātī","Viśākhā","Anurādhā","Śravaṇa","Dhaniṣṭhā","Śatabhiṣaj","Pūrva Bhādrapadā","Uttara Bhādrapadā"],"unfavorable_nakshatras":["Aśvinī","Bharaṇī","Kṛttikā","Aśleṣā","Maghā","Pūrva Phalgunī","Uttara Phalgunī","Jyeṣṭhā","Mūla","Pūrva Āṣāḍhā","Uttara Āṣāḍhā","Revatī"],"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":"East (Pūrva)","chandraVasa":"South-East","rahuVasa":"East","anandadiYoga":{"name":"Sushira","quality":"Auspicious"},"tropicalRitu":"Varṣā (Monsoon) (tropical)","vedicRitu":"Śarad (Autumn)","tropicalAyana":"Dakṣiṇāyana","vedicAyana":"Dakṣiṇāyana","meta":{"method":"BOB-History Sūrya-Siddhānta + Vidhyamitra Tier-2 spherical localization","declination":10.208239521216258,"eotMinutes":4.383515547985428,"ayanamsa":-48.5125}},"calendars":{"vikram_samvat":-3124,"saka_samvat":-3259,"bengali_samvat":-3774,"malayalam_era":-4005,"nanakshahi_year":-4650,"lunar_month":"Kārtika","lunar_month_paksha_full":"Kārtika Kṛṣṇa Pakṣa","lunar_month_system":"purnimanta","lunar_month_purnimanta":"Kārtika","lunar_month_amanta":"Kārtika","lunar_month_is_adhika":false,"lunar_month_purnimanta_is_adhika":false,"lunar_month_amanta_is_adhika":false,"solar_month":"Tulā (Aippasi)","ritu":"Śarad (Autumn)","display_summary":"Kārtika Kṛṣṇa Pratipada · Vikram -3124 undefined · Śaka -3259 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 September 12, 3182 BCE · Mathurā · Vidhyamitra","description":"September 12, 3182 BCE for Mathurā: Kṛṣṇa Pratipada, sūryodaya 05:50, sūryāsta 18:40.","schema_org_type":"Article","canonical":"https://vidhyamitra.com/city/mathura/-3181-09-12","hreflang_alternates":{"en":"https://vidhyamitra.com/city/mathura/-3181-09-12","sa":"https://sa.vidhyamitra.com/city/mathura/-3181-09-12","hi":"https://hi.vidhyamitra.com/city/mathura/-3181-09-12","x-default":"https://vidhyamitra.com/city/mathura/-3181-09-12"}},"provenance":[{"pillar":"BOB-History","pillar_version":"2.12.0","method":"Sūrya-Siddhānta first-principles + Bhāskara II + Kerala-school (Mādhava-Nīlakaṇṭha) corrections","retrieved_at":"2026-08-12T22:04:11.193Z","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":"2026-08-12T22:04:11.193Z","verification":{"type":"community-validated","markers":["modern-reference checked timing on Narasiṁha Jayantī 2026"],"confidence":"verified"}}],"meta":{"generated_at":"2026-08-12T22:04:11.193Z","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"}}}