{"id":"vidhyamitra:city-day:mathura:-3164-12-11:en","page_class":"VM-CD-city-day","url":"https://vidhyamitra.com/city/mathura/-3164-12-11","language":{"target_lang":"en","base_lang":"en","quality_tier":"canonical"},"data":{"date":"-3164-12-11","date_display":"December 11, 3165 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":-3164,"month":12,"day":11,"hour":6,"minute":30,"second":0,"calendar":"julian"},"julian_day":565751.770833,"kali_year":-62,"ahargana":-22713.7292,"sun":{"sidereal_longitude":294.7388,"rashi":10,"rashi_name":"Makara"},"moon":{"sidereal_longitude":234.3486,"rashi":8,"rashi_name":"Vṛścika"},"tithi":{"number":25,"name":"Daśamī","paksha":"Kṛṣṇa","full_name":"Kṛṣṇa Daśamī","elongation_degrees":299.6097,"elapsed_within_tithi_degrees":11.6097},"nakshatra":{"number":18,"name":"Jyeṣṭhā","pada":3,"moon_longitude":234.3486,"elapsed_within_degrees":7.6819},"yoga":{"number":13,"name":"Vyāghāta","sum_longitude":169.0874},"karana":{"half_tithi_index":49,"name":"Viṣṭi"},"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":-3164,"month":12,"day":11,"hour":6,"minute":30,"calendar":"julian"},"julian_day":565751.770833,"ahargana":-22713.7292,"kali_year":-62,"ayanamsa_lahiri":-48.2715,"grahas":{"sun":{"sidereal_longitude":294.7388,"rashi":{"number":10,"name":"Makara"},"nakshatra":{"number":23,"name":"Dhaniṣṭhā","pada":1},"retrograde":false},"moon":{"sidereal_longitude":234.3486,"rashi":{"number":8,"name":"Vṛścika"},"nakshatra":{"number":18,"name":"Jyeṣṭhā","pada":3},"retrograde":false,"latitude":-4.2043},"mars":{"sidereal_longitude":322.8497,"rashi":{"number":11,"name":"Kumbha"},"nakshatra":{"number":25,"name":"Pūrva Bhādrapadā","pada":1},"retrograde":false},"mercury":{"sidereal_longitude":288.5546,"rashi":{"number":10,"name":"Makara"},"nakshatra":{"number":22,"name":"Śravaṇa","pada":3},"retrograde":false},"jupiter":{"sidereal_longitude":272.0845,"rashi":{"number":10,"name":"Makara"},"nakshatra":{"number":21,"name":"Uttara Āṣāḍhā","pada":2},"retrograde":false},"venus":{"sidereal_longitude":309.0766,"rashi":{"number":11,"name":"Kumbha"},"nakshatra":{"number":24,"name":"Śatabhiṣā","pada":1},"retrograde":false},"saturn":{"sidereal_longitude":309.5747,"rashi":{"number":11,"name":"Kumbha"},"nakshatra":{"number":24,"name":"Śatabhiṣā","pada":1},"retrograde":false},"rahu":{"sidereal_longitude":303.4827,"rashi":{"number":11,"name":"Kumbha"},"nakshatra":{"number":23,"name":"Dhaniṣṭhā","pada":4},"retrograde":false},"ketu":{"sidereal_longitude":123.4827,"rashi":{"number":5,"name":"Siṃha"},"nakshatra":{"number":10,"name":"Maghā","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":-3164,"month":12,"day":11,"hour":6,"minute":30,"second":0,"calendar":"julian"},"julian_day":565751.770833,"kali_year":-62,"ahargana":-22713.7292,"sun":{"sidereal_longitude":294.7388,"rashi":10,"rashi_name":"Makara"},"moon":{"sidereal_longitude":234.3486,"rashi":8,"rashi_name":"Vṛścika"},"tithi":{"number":25,"name":"Daśamī","paksha":"Kṛṣṇa","full_name":"Kṛṣṇa Daśamī","elongation_degrees":299.6097,"elapsed_within_tithi_degrees":11.6097},"nakshatra":{"number":18,"name":"Jyeṣṭhā","pada":3,"moon_longitude":234.3486,"elapsed_within_degrees":7.6819},"yoga":{"number":13,"name":"Vyāghāta","sum_longitude":169.0874},"karana":{"half_tithi_index":49,"name":"Viṣṭi"},"vara":{"number":1,"name":"Śanivāra (Saturday)"}},"eclipse_current":{"solar":{"type":"solar","occurs":false,"moon_latitude":-4.204,"elongation":60.39},"lunar":{"type":"lunar","occurs":false,"moon_latitude":-4.204,"opposition_distance":119.61}},"eclipse_window_40days":[{"offset_days":20,"type":"lunar","occurs":true,"moon_latitude":-0.952,"opposition_distance":0.355}]},"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":"06:56","sunsetLocal":"17:30","solarNoonLocal":"12:13","dayLengthHours":10.569205510669008,"dayLengthDisplay":"10 Hours 34 Mins 09 Secs","nightLengthDisplay":"13 Hours 25 Mins 51 Secs","moonriseLocal":"02:14","moonsetLocal":"14:09","rahuKala":{"name":"Rāhu Kāla","start":"09:35","end":"10:54","startHours":9.579650577590535,"endHours":10.90080126642416,"quality":"inauspicious"},"yamaganda":{"name":"Yamaganda","start":"13:33","end":"14:52","startHours":13.543102644091412,"endHours":14.864253332925038,"quality":"inauspicious"},"gulika":{"name":"Gulika Kāla","start":"06:56","end":"08:16","startHours":6.937349199923282,"endHours":8.258499888756909,"quality":"inauspicious"},"durMuhurta":[{"name":"Dur Muhūrta","start":"09:24","end":"09:45","startHours":9.403497152412717,"endHours":9.75580400276835,"quality":"avoid"}],"varjyam":{"name":"Varjyam","start":"07:23","end":"07:40","startHours":7.377732762867824,"endHours":7.659578243152331,"quality":"avoid"},"abhijit":{"name":"Abhijit Muhūrta","start":"11:52","end":"12:34","startHours":11.869645104902153,"endHours":12.57425880561342,"quality":"auspicious"},"brahmaMuhurta":{"name":"Brahma Muhūrta","start":"05:32","end":"06:14","startHours":5.528121798500747,"endHours":6.232735499212015,"quality":"auspicious"},"pratahSandhya":{"name":"Prātaḥ Sandhyā","start":"06:03","end":"06:56","startHours":6.056582074034198,"endHours":6.937349199923282,"quality":"auspicious"},"vijayaMuhurta":{"name":"Vijaya Muhūrta","start":"13:59","end":"14:41","startHours":13.983486207035952,"endHours":14.688099907747219,"quality":"auspicious"},"godhuliMuhurta":{"name":"Godhūli Muhūrta","start":"17:18","end":"17:42","startHours":17.30655471059229,"endHours":17.70655471059229,"quality":"auspicious"},"sayahnaSandhya":{"name":"Sāyāhna Sandhyā","start":"17:30","end":"17:57","startHours":17.50655471059229,"endHours":17.946938273536833,"quality":"auspicious"},"amritKala":{"name":"Amṛta Kāla","start":"17:15","end":"19:00","startHours":17.25655471059229,"endHours":19.00655471059229,"quality":"auspicious"},"nishitaMuhurta":{"name":"Niśīta Muhūrta","start":"23:52","end":"00:34","startHours":23.86964510490215,"endHours":24.57425880561342,"quality":"auspicious"},"dayChoghadiyas":[{"name":"Kāla","start":"06:56","end":"08:16","startHours":6.937349199923282,"endHours":8.258499888756909,"quality":"inauspicious"},{"name":"Śubha","start":"08:16","end":"09:35","startHours":8.258499888756909,"endHours":9.579650577590535,"quality":"auspicious"},{"name":"Roga","start":"09:35","end":"10:54","startHours":9.579650577590535,"endHours":10.90080126642416,"quality":"inauspicious"},{"name":"Udveg","start":"10:54","end":"12:13","startHours":10.90080126642416,"endHours":12.221951955257786,"quality":"inauspicious"},{"name":"Chala","start":"12:13","end":"13:33","startHours":12.221951955257786,"endHours":13.543102644091412,"quality":"neutral"},{"name":"Labha","start":"13:33","end":"14:52","startHours":13.543102644091412,"endHours":14.864253332925038,"quality":"auspicious"},{"name":"Amṛta","start":"14:52","end":"16:11","startHours":14.864253332925038,"endHours":16.185404021758664,"quality":"auspicious"},{"name":"Kāla","start":"16:11","end":"17:30","startHours":16.185404021758664,"endHours":17.50655471059229,"quality":"inauspicious"}],"nightChoghadiyas":[{"name":"Labha","start":"17:30","end":"19:11","startHours":17.50655471059229,"endHours":19.185404021758664,"quality":"auspicious"},{"name":"Amṛta","start":"19:11","end":"20:52","startHours":19.185404021758664,"endHours":20.86425333292504,"quality":"auspicious"},{"name":"Kāla","start":"20:52","end":"22:33","startHours":20.86425333292504,"endHours":22.543102644091412,"quality":"inauspicious"},{"name":"Śubha","start":"22:33","end":"00:13","startHours":22.543102644091412,"endHours":24.221951955257786,"quality":"auspicious"},{"name":"Roga","start":"00:13","end":"01:54","startHours":24.221951955257786,"endHours":25.90080126642416,"quality":"inauspicious"},{"name":"Udveg","start":"01:54","end":"03:35","startHours":25.90080126642416,"endHours":27.579650577590535,"quality":"inauspicious"},{"name":"Chala","start":"03:35","end":"05:16","startHours":27.579650577590535,"endHours":29.25849988875691,"quality":"neutral"},{"name":"Labha","start":"05:16","end":"06:56","startHours":29.25849988875691,"endHours":30.937349199923283,"quality":"auspicious"}],"horas":[{"name":"Hora 1","start":"06:56","end":"07:56","startHours":6.937349199923282,"endHours":7.937349199923282,"planetary_lord":"Saturn"},{"name":"Hora 2","start":"07:56","end":"08:56","startHours":7.937349199923282,"endHours":8.937349199923283,"planetary_lord":"Moon"},{"name":"Hora 3","start":"08:56","end":"09:56","startHours":8.937349199923283,"endHours":9.937349199923283,"planetary_lord":"Mercury"},{"name":"Hora 4","start":"09:56","end":"10:56","startHours":9.937349199923283,"endHours":10.937349199923283,"planetary_lord":"Venus"},{"name":"Hora 5","start":"10:56","end":"11:56","startHours":10.937349199923283,"endHours":11.937349199923283,"planetary_lord":"Sun"},{"name":"Hora 6","start":"11:56","end":"12:56","startHours":11.937349199923283,"endHours":12.937349199923283,"planetary_lord":"Mars"},{"name":"Hora 7","start":"12:56","end":"13:56","startHours":12.937349199923283,"endHours":13.937349199923283,"planetary_lord":"Jupiter"},{"name":"Hora 8","start":"13:56","end":"14:56","startHours":13.937349199923283,"endHours":14.937349199923283,"planetary_lord":"Saturn"},{"name":"Hora 9","start":"14:56","end":"15:56","startHours":14.937349199923283,"endHours":15.937349199923283,"planetary_lord":"Moon"},{"name":"Hora 10","start":"15:56","end":"16:56","startHours":15.937349199923283,"endHours":16.937349199923283,"planetary_lord":"Mercury"},{"name":"Hora 11","start":"16:56","end":"17:56","startHours":16.937349199923283,"endHours":17.937349199923283,"planetary_lord":"Venus"},{"name":"Hora 12","start":"17:56","end":"18:56","startHours":17.937349199923283,"endHours":18.937349199923283,"planetary_lord":"Sun"},{"name":"Hora 13","start":"18:56","end":"19:56","startHours":18.937349199923283,"endHours":19.937349199923283,"planetary_lord":"Mars"},{"name":"Hora 14","start":"19:56","end":"20:56","startHours":19.937349199923283,"endHours":20.937349199923283,"planetary_lord":"Jupiter"},{"name":"Hora 15","start":"20:56","end":"21:56","startHours":20.937349199923283,"endHours":21.937349199923283,"planetary_lord":"Saturn"},{"name":"Hora 16","start":"21:56","end":"22:56","startHours":21.937349199923283,"endHours":22.937349199923283,"planetary_lord":"Moon"},{"name":"Hora 17","start":"22:56","end":"23:56","startHours":22.937349199923283,"endHours":23.937349199923283,"planetary_lord":"Mercury"},{"name":"Hora 18","start":"23:56","end":"00:56","startHours":23.937349199923283,"endHours":24.937349199923283,"planetary_lord":"Venus"},{"name":"Hora 19","start":"00:56","end":"01:56","startHours":24.937349199923283,"endHours":25.937349199923283,"planetary_lord":"Sun"},{"name":"Hora 20","start":"01:56","end":"02:56","startHours":25.937349199923283,"endHours":26.937349199923283,"planetary_lord":"Mars"},{"name":"Hora 21","start":"02:56","end":"03:56","startHours":26.937349199923283,"endHours":27.937349199923283,"planetary_lord":"Jupiter"},{"name":"Hora 22","start":"03:56","end":"04:56","startHours":27.937349199923283,"endHours":28.937349199923283,"planetary_lord":"Saturn"},{"name":"Hora 23","start":"04:56","end":"05:56","startHours":28.937349199923283,"endHours":29.937349199923283,"planetary_lord":"Moon"},{"name":"Hora 24","start":"05:56","end":"06:56","startHours":29.937349199923283,"endHours":30.937349199923283,"planetary_lord":"Mercury"}],"taraBala":{"favorable_nakshatras":["Aśvinī","Bharaṇī","Kṛttikā","Rohiṇī","Mṛgaśirā","Maghā","Pūrva Phalgunī","Uttara Phalgunī","Hasta","Citrā","Mūla","Pūrva Āṣāḍhā","Uttara Āṣāḍhā","Śravaṇa","Dhaniṣṭhā"],"unfavorable_nakshatras":["Ārdrā","Punarvasu","Puṣya","Aśleṣā","Svātī","Viśākhā","Anurādhā","Jyeṣṭhā","Śatabhiṣaj","Pūrva Bhādrapadā","Uttara Bhādrapadā","Revatī"],"nature":"Janma-tara if same nakshatra; favorable for 15 nakshatras"},"chandraBala":{"favorable_rashis":["Meṣa","Vṛṣabha","Siṃha","Kanyā","Vṛścika","Makara"],"unfavorable_rashis":["Mithuna","Karka","Tulā","Dhanu","Kumbha","Mīna"]},"dishaShool":"East (Pūrva)","chandraVasa":"North-East","rahuVasa":"East","anandadiYoga":{"name":"Padma","quality":"Auspicious"},"tropicalRitu":"Hemanta (Pre-winter) (tropical)","vedicRitu":"Hemanta (Pre-winter)","tropicalAyana":"Dakṣiṇāyana","vedicAyana":"Uttarāyaṇa","meta":{"method":"BOB-History Sūrya-Siddhānta + Vidhyamitra Tier-2 spherical localization","declination":-21.386290028908235,"eotMinutes":5.988082684532823,"ayanamsa":-48.2715}},"calendars":{"vikram_samvat":-3107,"saka_samvat":-3242,"bengali_samvat":-3757,"malayalam_era":-3988,"nanakshahi_year":-4633,"lunar_month":"Māgha","lunar_month_paksha_full":"Māgha Kṛṣṇa Pakṣa","lunar_month_system":"purnimanta","lunar_month_purnimanta":"Māgha","lunar_month_amanta":"Māgha","lunar_month_is_adhika":false,"lunar_month_purnimanta_is_adhika":false,"lunar_month_amanta_is_adhika":false,"solar_month":"Makara (Tai)","ritu":"Śiśira (Winter)","display_summary":"Māgha Kṛṣṇa Daśamī · Vikram -3107 undefined · Śaka -3242 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 December 11, 3165 BCE · Mathurā · Vidhyamitra","description":"December 11, 3165 BCE for Mathurā: Kṛṣṇa Daśamī, sūryodaya 06:56, sūryāsta 17:30.","schema_org_type":"Article","canonical":"https://vidhyamitra.com/city/mathura/-3164-12-11","hreflang_alternates":{"en":"https://vidhyamitra.com/city/mathura/-3164-12-11","sa":"https://sa.vidhyamitra.com/city/mathura/-3164-12-11","hi":"https://hi.vidhyamitra.com/city/mathura/-3164-12-11","x-default":"https://vidhyamitra.com/city/mathura/-3164-12-11"}},"provenance":[{"pillar":"BOB-History","pillar_version":"2.12.0","method":"Sūrya-Siddhānta first-principles + Bhāskara II + Kerala-school (Mādhava-Nīlakaṇṭha) corrections","retrieved_at":"2026-08-10T21:52:34.690Z","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":"2026-08-10T21:52:34.690Z","verification":{"type":"community-validated","markers":["modern-reference checked timing on Narasiṁha Jayantī 2026"],"confidence":"verified"}}],"meta":{"generated_at":"2026-08-10T21:52:34.690Z","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"}}}