{"id":"vidhyamitra:city-day:mathura:-3110-01-03:en","page_class":"VM-CD-city-day","url":"https://vidhyamitra.com/city/mathura/-3110-01-03","language":{"target_lang":"en","base_lang":"en","quality_tier":"canonical"},"data":{"date":"-3110-01-03","date_display":"January 3, 3111 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":-3110,"month":1,"day":3,"hour":6,"minute":30,"second":0,"calendar":"julian"},"julian_day":585132.770833,"kali_year":-9,"ahargana":-3332.7292,"sun":{"sidereal_longitude":317.3122,"rashi":11,"rashi_name":"Kumbha"},"moon":{"sidereal_longitude":12.534,"rashi":1,"rashi_name":"Meṣa"},"tithi":{"number":5,"name":"Pañcamī","paksha":"Śukla","full_name":"Śukla Pañcamī","elongation_degrees":55.2218,"elapsed_within_tithi_degrees":7.2218},"nakshatra":{"number":1,"name":"Aśvinī","pada":4,"moon_longitude":12.534,"elapsed_within_degrees":12.534},"yoga":{"number":25,"name":"Brahma","sum_longitude":329.8462},"karana":{"half_tithi_index":9,"name":"Bālava"},"vara":{"number":6,"name":"Guruvāra (Thursday)"}},"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":-3110,"month":1,"day":3,"hour":6,"minute":30,"calendar":"julian"},"julian_day":585132.770833,"ahargana":-3332.7292,"kali_year":-9,"ayanamsa_lahiri":-47.5303,"grahas":{"sun":{"sidereal_longitude":317.3122,"rashi":{"number":11,"name":"Kumbha"},"nakshatra":{"number":24,"name":"Śatabhiṣā","pada":4},"retrograde":false},"moon":{"sidereal_longitude":12.534,"rashi":{"number":1,"name":"Meṣa"},"nakshatra":{"number":1,"name":"Aśvinī","pada":4},"retrograde":false,"latitude":1.2354},"mars":{"sidereal_longitude":27.6383,"rashi":{"number":1,"name":"Meṣa"},"nakshatra":{"number":3,"name":"Kṛttikā","pada":1},"retrograde":false},"mercury":{"sidereal_longitude":331.026,"rashi":{"number":12,"name":"Mīna"},"nakshatra":{"number":25,"name":"Pūrva Bhādrapadā","pada":4},"retrograde":false},"jupiter":{"sidereal_longitude":78.8657,"rashi":{"number":3,"name":"Mithuna"},"nakshatra":{"number":6,"name":"Ārdrā","pada":4},"retrograde":true},"venus":{"sidereal_longitude":357.5061,"rashi":{"number":12,"name":"Mīna"},"nakshatra":{"number":27,"name":"Revatī","pada":4},"retrograde":false},"saturn":{"sidereal_longitude":252.2409,"rashi":{"number":9,"name":"Dhanu"},"nakshatra":{"number":19,"name":"Mūla","pada":4},"retrograde":false},"rahu":{"sidereal_longitude":356.584,"rashi":{"number":12,"name":"Mīna"},"nakshatra":{"number":27,"name":"Revatī","pada":3},"retrograde":false},"ketu":{"sidereal_longitude":176.584,"rashi":{"number":6,"name":"Kanyā"},"nakshatra":{"number":14,"name":"Citrā","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":-3110,"month":1,"day":3,"hour":6,"minute":30,"second":0,"calendar":"julian"},"julian_day":585132.770833,"kali_year":-9,"ahargana":-3332.7292,"sun":{"sidereal_longitude":317.3122,"rashi":11,"rashi_name":"Kumbha"},"moon":{"sidereal_longitude":12.534,"rashi":1,"rashi_name":"Meṣa"},"tithi":{"number":5,"name":"Pañcamī","paksha":"Śukla","full_name":"Śukla Pañcamī","elongation_degrees":55.2218,"elapsed_within_tithi_degrees":7.2218},"nakshatra":{"number":1,"name":"Aśvinī","pada":4,"moon_longitude":12.534,"elapsed_within_degrees":12.534},"yoga":{"number":25,"name":"Brahma","sum_longitude":329.8462},"karana":{"half_tithi_index":9,"name":"Bālava"},"vara":{"number":6,"name":"Guruvāra (Thursday)"}},"eclipse_current":{"solar":{"type":"solar","occurs":false,"moon_latitude":1.235,"elongation":55.222},"lunar":{"type":"lunar","occurs":false,"moon_latitude":1.235,"opposition_distance":124.778}},"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":"07:12","sunsetLocal":"17:36","solarNoonLocal":"12:24","dayLengthHours":10.401451392365308,"dayLengthDisplay":"10 Hours 24 Mins 05 Secs","nightLengthDisplay":"13 Hours 35 Mins 55 Secs","moonriseLocal":"10:30","moonsetLocal":"21:39","rahuKala":{"name":"Rāhu Kāla","start":"13:42","end":"15:00","startHours":13.698425104556634,"endHours":14.998606528602297,"quality":"inauspicious"},"yamaganda":{"name":"Yamaganda","start":"07:12","end":"08:30","startHours":7.197517984328316,"endHours":8.497699408373979,"quality":"inauspicious"},"gulika":{"name":"Gulika Kāla","start":"09:48","end":"11:06","startHours":9.797880832419644,"endHours":11.098062256465306,"quality":"inauspicious"},"durMuhurta":[{"name":"Dur Muhūrta","start":"09:37","end":"09:58","startHours":9.624523309213554,"endHours":9.971238355625731,"quality":"avoid"}],"varjyam":{"name":"Varjyam","start":"07:38","end":"07:54","startHours":7.630911792343538,"endHours":7.908283829473279,"quality":"avoid"},"abhijit":{"name":"Abhijit Muhūrta","start":"12:03","end":"12:45","startHours":12.051528634098792,"endHours":12.744958726923146,"quality":"auspicious"},"brahmaMuhurta":{"name":"Brahma Muhūrta","start":"05:49","end":"06:30","startHours":5.810657798679609,"endHours":6.504087891503962,"quality":"auspicious"},"pratahSandhya":{"name":"Prātaḥ Sandhyā","start":"06:20","end":"07:12","startHours":6.330730368297874,"endHours":7.197517984328316,"quality":"auspicious"},"vijayaMuhurta":{"name":"Vijaya Muhūrta","start":"14:08","end":"14:50","startHours":14.131818912571855,"endHours":14.82524900539621,"quality":"auspicious"},"godhuliMuhurta":{"name":"Godhūli Muhūrta","start":"17:24","end":"17:48","startHours":17.398969376693625,"endHours":17.798969376693623,"quality":"auspicious"},"sayahnaSandhya":{"name":"Sāyāhna Sandhyā","start":"17:36","end":"18:02","startHours":17.598969376693624,"endHours":18.032363184708846,"quality":"auspicious"},"amritKala":{"name":"Amṛta Kāla","start":"17:21","end":"19:06","startHours":17.348969376693624,"endHours":19.098969376693624,"quality":"auspicious"},"nishitaMuhurta":{"name":"Niśīta Muhūrta","start":"00:03","end":"00:45","startHours":24.05152863409879,"endHours":24.744958726923148,"quality":"auspicious"},"dayChoghadiyas":[{"name":"Śubha","start":"07:12","end":"08:30","startHours":7.197517984328316,"endHours":8.497699408373979,"quality":"auspicious"},{"name":"Roga","start":"08:30","end":"09:48","startHours":8.497699408373979,"endHours":9.797880832419644,"quality":"inauspicious"},{"name":"Udveg","start":"09:48","end":"11:06","startHours":9.797880832419644,"endHours":11.098062256465306,"quality":"inauspicious"},{"name":"Chala","start":"11:06","end":"12:24","startHours":11.098062256465306,"endHours":12.39824368051097,"quality":"neutral"},{"name":"Labha","start":"12:24","end":"13:42","startHours":12.39824368051097,"endHours":13.698425104556634,"quality":"auspicious"},{"name":"Amṛta","start":"13:42","end":"15:00","startHours":13.698425104556634,"endHours":14.998606528602297,"quality":"auspicious"},{"name":"Kāla","start":"15:00","end":"16:18","startHours":14.998606528602297,"endHours":16.298787952647963,"quality":"inauspicious"},{"name":"Śubha","start":"16:18","end":"17:36","startHours":16.298787952647963,"endHours":17.598969376693624,"quality":"auspicious"}],"nightChoghadiyas":[{"name":"Amṛta","start":"17:36","end":"19:18","startHours":17.598969376693624,"endHours":19.29878795264796,"quality":"auspicious"},{"name":"Kāla","start":"19:18","end":"21:00","startHours":19.29878795264796,"endHours":20.9986065286023,"quality":"inauspicious"},{"name":"Śubha","start":"21:00","end":"22:42","startHours":20.9986065286023,"endHours":22.698425104556634,"quality":"auspicious"},{"name":"Roga","start":"22:42","end":"00:24","startHours":22.698425104556634,"endHours":24.39824368051097,"quality":"inauspicious"},{"name":"Udveg","start":"00:24","end":"02:06","startHours":24.39824368051097,"endHours":26.098062256465305,"quality":"inauspicious"},{"name":"Chala","start":"02:06","end":"03:48","startHours":26.098062256465305,"endHours":27.797880832419644,"quality":"neutral"},{"name":"Labha","start":"03:48","end":"05:30","startHours":27.797880832419644,"endHours":29.49769940837398,"quality":"auspicious"},{"name":"Amṛta","start":"05:30","end":"07:12","startHours":29.49769940837398,"endHours":31.197517984328314,"quality":"auspicious"}],"horas":[{"name":"Hora 1","start":"07:12","end":"08:12","startHours":7.197517984328316,"endHours":8.197517984328316,"planetary_lord":"Jupiter"},{"name":"Hora 2","start":"08:12","end":"09:12","startHours":8.197517984328316,"endHours":9.197517984328316,"planetary_lord":"Saturn"},{"name":"Hora 3","start":"09:12","end":"10:12","startHours":9.197517984328316,"endHours":10.197517984328316,"planetary_lord":"Moon"},{"name":"Hora 4","start":"10:12","end":"11:12","startHours":10.197517984328316,"endHours":11.197517984328316,"planetary_lord":"Mercury"},{"name":"Hora 5","start":"11:12","end":"12:12","startHours":11.197517984328316,"endHours":12.197517984328316,"planetary_lord":"Venus"},{"name":"Hora 6","start":"12:12","end":"13:12","startHours":12.197517984328316,"endHours":13.197517984328316,"planetary_lord":"Sun"},{"name":"Hora 7","start":"13:12","end":"14:12","startHours":13.197517984328316,"endHours":14.197517984328316,"planetary_lord":"Mars"},{"name":"Hora 8","start":"14:12","end":"15:12","startHours":14.197517984328316,"endHours":15.197517984328316,"planetary_lord":"Jupiter"},{"name":"Hora 9","start":"15:12","end":"16:12","startHours":15.197517984328316,"endHours":16.197517984328314,"planetary_lord":"Saturn"},{"name":"Hora 10","start":"16:12","end":"17:12","startHours":16.197517984328314,"endHours":17.197517984328314,"planetary_lord":"Moon"},{"name":"Hora 11","start":"17:12","end":"18:12","startHours":17.197517984328314,"endHours":18.197517984328314,"planetary_lord":"Mercury"},{"name":"Hora 12","start":"18:12","end":"19:12","startHours":18.197517984328314,"endHours":19.197517984328314,"planetary_lord":"Venus"},{"name":"Hora 13","start":"19:12","end":"20:12","startHours":19.197517984328314,"endHours":20.197517984328314,"planetary_lord":"Sun"},{"name":"Hora 14","start":"20:12","end":"21:12","startHours":20.197517984328314,"endHours":21.197517984328314,"planetary_lord":"Mars"},{"name":"Hora 15","start":"21:12","end":"22:12","startHours":21.197517984328314,"endHours":22.197517984328314,"planetary_lord":"Jupiter"},{"name":"Hora 16","start":"22:12","end":"23:12","startHours":22.197517984328314,"endHours":23.197517984328314,"planetary_lord":"Saturn"},{"name":"Hora 17","start":"23:12","end":"00:12","startHours":23.197517984328314,"endHours":24.197517984328314,"planetary_lord":"Moon"},{"name":"Hora 18","start":"00:12","end":"01:12","startHours":24.197517984328314,"endHours":25.197517984328314,"planetary_lord":"Mercury"},{"name":"Hora 19","start":"01:12","end":"02:12","startHours":25.197517984328314,"endHours":26.197517984328314,"planetary_lord":"Venus"},{"name":"Hora 20","start":"02:12","end":"03:12","startHours":26.197517984328314,"endHours":27.197517984328314,"planetary_lord":"Sun"},{"name":"Hora 21","start":"03:12","end":"04:12","startHours":27.197517984328314,"endHours":28.197517984328314,"planetary_lord":"Mars"},{"name":"Hora 22","start":"04:12","end":"05:12","startHours":28.197517984328314,"endHours":29.197517984328314,"planetary_lord":"Jupiter"},{"name":"Hora 23","start":"05:12","end":"06:12","startHours":29.197517984328314,"endHours":30.197517984328314,"planetary_lord":"Saturn"},{"name":"Hora 24","start":"06:12","end":"07:12","startHours":30.197517984328314,"endHours":31.197517984328314,"planetary_lord":"Moon"}],"taraBala":{"favorable_nakshatras":["Bharaṇī","Kṛttikā","Rohiṇī","Mṛgaśirā","Ārdrā","Pūrva Phalgunī","Uttara Phalgunī","Hasta","Citrā","Svātī","Pūrva Āṣāḍhā","Uttara Āṣāḍhā","Śravaṇa","Dhaniṣṭhā","Śatabhiṣaj"],"unfavorable_nakshatras":["Aśvinī","Punarvasu","Puṣya","Aśleṣā","Maghā","Viśākhā","Anurādhā","Jyeṣṭhā","Mūla","Pūrva Bhādrapadā","Uttara Bhādrapadā","Revatī"],"nature":"Janma-tara if same nakshatra; favorable for 15 nakshatras"},"chandraBala":{"favorable_rashis":["Meṣa","Mithuna","Kanyā","Tulā","Makara","Kumbha"],"unfavorable_rashis":["Vṛṣabha","Karka","Siṃha","Vṛścika","Dhanu","Mīna"]},"dishaShool":"South (Dakṣiṇa)","chandraVasa":"East","rahuVasa":"North-West","anandadiYoga":{"name":"Mṛtyu","quality":"Inauspicious"},"tropicalRitu":"Hemanta (Pre-winter) (tropical)","vedicRitu":"Śiśira (Winter)","tropicalAyana":"Dakṣiṇāyana","vedicAyana":"Uttarāyaṇa","meta":{"method":"BOB-History Sūrya-Siddhānta + Vidhyamitra Tier-2 spherical localization","declination":-23.43632005401255,"eotMinutes":-4.589420830658165,"ayanamsa":-47.5303}},"calendars":{"vikram_samvat":-3053,"saka_samvat":-3188,"bengali_samvat":-3703,"malayalam_era":-3934,"nanakshahi_year":-4579,"lunar_month":"Phālguna","lunar_month_paksha_full":"Phālguna Śukla Pakṣa","lunar_month_system":"purnimanta","lunar_month_purnimanta":"Phālguna","lunar_month_amanta":"Phālguna","lunar_month_is_adhika":false,"lunar_month_purnimanta_is_adhika":false,"lunar_month_amanta_is_adhika":false,"solar_month":"Kumbha (Māsi)","ritu":"Śiśira (Winter)","display_summary":"Phālguna Śukla Pañcamī · Vikram -3053 undefined · Śaka -3188 undefined"},"festivals":[],"todays_walk":{"walk":{"id":"guru-walk","name":"Bṛhaspati Walk","name_sanskrit":"गुरु यात्रा","type":"graha","description":"Wisdom transmission + BG 4.34.","step_count":8,"url":"/walk/guru-walk"},"reason":"Guruvāra (Thursday) — 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 January 3, 3111 BCE · Mathurā · Vidhyamitra","description":"January 3, 3111 BCE for Mathurā: Śukla Pañcamī, sūryodaya 07:12, sūryāsta 17:36.","schema_org_type":"Article","canonical":"https://vidhyamitra.com/city/mathura/-3110-01-03","hreflang_alternates":{"en":"https://vidhyamitra.com/city/mathura/-3110-01-03","sa":"https://sa.vidhyamitra.com/city/mathura/-3110-01-03","hi":"https://hi.vidhyamitra.com/city/mathura/-3110-01-03","x-default":"https://vidhyamitra.com/city/mathura/-3110-01-03"}},"provenance":[{"pillar":"BOB-History","pillar_version":"2.12.0","method":"Sūrya-Siddhānta first-principles + Bhāskara II + Kerala-school (Mādhava-Nīlakaṇṭha) corrections","retrieved_at":"2026-09-08T17:40:59.164Z","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":"2026-09-08T17:40:59.164Z","verification":{"type":"community-validated","markers":["modern-reference checked timing on Narasiṁha Jayantī 2026"],"confidence":"verified"}}],"meta":{"generated_at":"2026-09-08T17:40:59.164Z","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":["Hosted scripture","Named-tradition interpretation","Original Vidhyamitra contemplation","Bhūmi-born material medium","Vidhyamitra portal","Responsible reader in their own kṣetra"],"claim_boundary":"The legacy purna_chain field carries a source-to-reader sequence, not a revealed physical descent, universal cosmology, or proof that software is conscious.","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"}}}