{"id":"vidhyamitra:city-day:mathura:-3111-12-13:en","page_class":"VM-CD-city-day","url":"https://vidhyamitra.com/city/mathura/-3111-12-13","language":{"target_lang":"en","base_lang":"en","quality_tier":"canonical"},"data":{"date":"-3111-12-13","date_display":"December 13, 3112 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":-3111,"month":12,"day":13,"hour":6,"minute":30,"second":0,"calendar":"julian"},"julian_day":585111.770833,"kali_year":-9,"ahargana":-3353.7292,"sun":{"sidereal_longitude":296.0487,"rashi":10,"rashi_name":"Makara"},"moon":{"sidereal_longitude":87.4339,"rashi":3,"rashi_name":"Mithuna"},"tithi":{"number":13,"name":"Trayodaśī","paksha":"Śukla","full_name":"Śukla Trayodaśī","elongation_degrees":151.3852,"elapsed_within_tithi_degrees":7.3852},"nakshatra":{"number":7,"name":"Punarvasu","pada":3,"moon_longitude":87.4339,"elapsed_within_degrees":7.4339},"yoga":{"number":2,"name":"Prīti","sum_longitude":23.4826},"karana":{"half_tithi_index":25,"name":"Taitila"},"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":-3111,"month":12,"day":13,"hour":6,"minute":30,"calendar":"julian"},"julian_day":585111.770833,"ahargana":-3353.7292,"kali_year":-9,"ayanamsa_lahiri":-47.5311,"grahas":{"sun":{"sidereal_longitude":296.0487,"rashi":{"number":10,"name":"Makara"},"nakshatra":{"number":23,"name":"Dhaniṣṭhā","pada":1},"retrograde":false},"moon":{"sidereal_longitude":87.4339,"rashi":{"number":3,"name":"Mithuna"},"nakshatra":{"number":7,"name":"Punarvasu","pada":3},"retrograde":false,"latitude":4.5},"mars":{"sidereal_longitude":14.5996,"rashi":{"number":1,"name":"Meṣa"},"nakshatra":{"number":2,"name":"Bharaṇī","pada":1},"retrograde":false},"mercury":{"sidereal_longitude":296.6907,"rashi":{"number":10,"name":"Makara"},"nakshatra":{"number":23,"name":"Dhaniṣṭhā","pada":2},"retrograde":false},"jupiter":{"sidereal_longitude":80.106,"rashi":{"number":3,"name":"Mithuna"},"nakshatra":{"number":7,"name":"Punarvasu","pada":1},"retrograde":true},"venus":{"sidereal_longitude":332.3748,"rashi":{"number":12,"name":"Mīna"},"nakshatra":{"number":25,"name":"Pūrva Bhādrapadā","pada":4},"retrograde":false},"saturn":{"sidereal_longitude":250.5462,"rashi":{"number":9,"name":"Dhanu"},"nakshatra":{"number":19,"name":"Mūla","pada":4},"retrograde":false},"rahu":{"sidereal_longitude":357.6967,"rashi":{"number":12,"name":"Mīna"},"nakshatra":{"number":27,"name":"Revatī","pada":4},"retrograde":false},"ketu":{"sidereal_longitude":177.6967,"rashi":{"number":6,"name":"Kanyā"},"nakshatra":{"number":14,"name":"Citrā","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":-3111,"month":12,"day":13,"hour":6,"minute":30,"second":0,"calendar":"julian"},"julian_day":585111.770833,"kali_year":-9,"ahargana":-3353.7292,"sun":{"sidereal_longitude":296.0487,"rashi":10,"rashi_name":"Makara"},"moon":{"sidereal_longitude":87.4339,"rashi":3,"rashi_name":"Mithuna"},"tithi":{"number":13,"name":"Trayodaśī","paksha":"Śukla","full_name":"Śukla Trayodaśī","elongation_degrees":151.3852,"elapsed_within_tithi_degrees":7.3852},"nakshatra":{"number":7,"name":"Punarvasu","pada":3,"moon_longitude":87.4339,"elapsed_within_degrees":7.4339},"yoga":{"number":2,"name":"Prīti","sum_longitude":23.4826},"karana":{"half_tithi_index":25,"name":"Taitila"},"vara":{"number":6,"name":"Guruvāra (Thursday)"}},"eclipse_current":{"solar":{"type":"solar","occurs":false,"moon_latitude":4.5,"elongation":151.385},"lunar":{"type":"lunar","occurs":false,"moon_latitude":4.5,"opposition_distance":28.615}},"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":"06:58","sunsetLocal":"17:30","solarNoonLocal":"12:14","dayLengthHours":10.54211316190097,"dayLengthDisplay":"10 Hours 32 Mins 32 Secs","nightLengthDisplay":"13 Hours 27 Mins 28 Secs","moonriseLocal":"15:45","moonsetLocal":"04:54","rahuKala":{"name":"Rāhu Kāla","start":"13:33","end":"14:52","startHours":13.554673307747318,"endHours":14.87243745298494,"quality":"inauspicious"},"yamaganda":{"name":"Yamaganda","start":"06:58","end":"08:17","startHours":6.965852581559213,"endHours":8.283616726796835,"quality":"inauspicious"},"gulika":{"name":"Gulika Kāla","start":"09:36","end":"10:55","startHours":9.601380872034456,"endHours":10.919145017272076,"quality":"inauspicious"},"durMuhurta":[{"name":"Dur Muhūrta","start":"09:26","end":"09:47","startHours":9.425678986002772,"endHours":9.777082758066138,"quality":"avoid"}],"varjyam":{"name":"Varjyam","start":"07:24","end":"07:41","startHours":7.405107296638421,"endHours":7.686230314289113,"quality":"avoid"},"abhijit":{"name":"Abhijit Muhūrta","start":"11:53","end":"12:35","startHours":11.885505390446331,"endHours":12.588312934573063,"quality":"auspicious"},"brahmaMuhurta":{"name":"Brahma Muhūrta","start":"05:34","end":"06:16","startHours":5.560237493305751,"endHours":6.263045037432482,"quality":"auspicious"},"pratahSandhya":{"name":"Prātaḥ Sandhyā","start":"06:05","end":"06:58","startHours":6.087343151400799,"endHours":6.965852581559213,"quality":"auspicious"},"vijayaMuhurta":{"name":"Vijaya Muhūrta","start":"14:00","end":"14:42","startHours":13.993928022826527,"endHours":14.696735566953258,"quality":"auspicious"},"godhuliMuhurta":{"name":"Godhūli Muhūrta","start":"17:18","end":"17:42","startHours":17.307965743460183,"endHours":17.707965743460182,"quality":"auspicious"},"sayahnaSandhya":{"name":"Sāyāhna Sandhyā","start":"17:30","end":"17:57","startHours":17.507965743460183,"endHours":17.94722045853939,"quality":"auspicious"},"amritKala":{"name":"Amṛta Kāla","start":"17:15","end":"19:00","startHours":17.257965743460183,"endHours":19.007965743460183,"quality":"auspicious"},"nishitaMuhurta":{"name":"Niśīta Muhūrta","start":"23:53","end":"00:35","startHours":23.88550539044633,"endHours":24.588312934573064,"quality":"auspicious"},"dayChoghadiyas":[{"name":"Śubha","start":"06:58","end":"08:17","startHours":6.965852581559213,"endHours":8.283616726796835,"quality":"auspicious"},{"name":"Roga","start":"08:17","end":"09:36","startHours":8.283616726796835,"endHours":9.601380872034456,"quality":"inauspicious"},{"name":"Udveg","start":"09:36","end":"10:55","startHours":9.601380872034456,"endHours":10.919145017272076,"quality":"inauspicious"},{"name":"Chala","start":"10:55","end":"12:14","startHours":10.919145017272076,"endHours":12.236909162509697,"quality":"neutral"},{"name":"Labha","start":"12:14","end":"13:33","startHours":12.236909162509697,"endHours":13.554673307747318,"quality":"auspicious"},{"name":"Amṛta","start":"13:33","end":"14:52","startHours":13.554673307747318,"endHours":14.87243745298494,"quality":"auspicious"},{"name":"Kāla","start":"14:52","end":"16:11","startHours":14.87243745298494,"endHours":16.19020159822256,"quality":"inauspicious"},{"name":"Śubha","start":"16:11","end":"17:30","startHours":16.19020159822256,"endHours":17.507965743460183,"quality":"auspicious"}],"nightChoghadiyas":[{"name":"Amṛta","start":"17:30","end":"19:11","startHours":17.507965743460183,"endHours":19.19020159822256,"quality":"auspicious"},{"name":"Kāla","start":"19:11","end":"20:52","startHours":19.19020159822256,"endHours":20.87243745298494,"quality":"inauspicious"},{"name":"Śubha","start":"20:52","end":"22:33","startHours":20.87243745298494,"endHours":22.55467330774732,"quality":"auspicious"},{"name":"Roga","start":"22:33","end":"00:14","startHours":22.55467330774732,"endHours":24.236909162509697,"quality":"inauspicious"},{"name":"Udveg","start":"00:14","end":"01:55","startHours":24.236909162509697,"endHours":25.91914501727208,"quality":"inauspicious"},{"name":"Chala","start":"01:55","end":"03:36","startHours":25.91914501727208,"endHours":27.601380872034454,"quality":"neutral"},{"name":"Labha","start":"03:36","end":"05:17","startHours":27.601380872034454,"endHours":29.283616726796836,"quality":"auspicious"},{"name":"Amṛta","start":"05:17","end":"06:58","startHours":29.283616726796836,"endHours":30.96585258155921,"quality":"auspicious"}],"horas":[{"name":"Hora 1","start":"06:58","end":"07:58","startHours":6.965852581559213,"endHours":7.965852581559213,"planetary_lord":"Jupiter"},{"name":"Hora 2","start":"07:58","end":"08:58","startHours":7.965852581559213,"endHours":8.965852581559213,"planetary_lord":"Saturn"},{"name":"Hora 3","start":"08:58","end":"09:58","startHours":8.965852581559213,"endHours":9.965852581559213,"planetary_lord":"Moon"},{"name":"Hora 4","start":"09:58","end":"10:58","startHours":9.965852581559213,"endHours":10.965852581559213,"planetary_lord":"Mercury"},{"name":"Hora 5","start":"10:58","end":"11:58","startHours":10.965852581559213,"endHours":11.965852581559213,"planetary_lord":"Venus"},{"name":"Hora 6","start":"11:58","end":"12:58","startHours":11.965852581559213,"endHours":12.965852581559213,"planetary_lord":"Sun"},{"name":"Hora 7","start":"12:58","end":"13:58","startHours":12.965852581559213,"endHours":13.965852581559213,"planetary_lord":"Mars"},{"name":"Hora 8","start":"13:58","end":"14:58","startHours":13.965852581559213,"endHours":14.965852581559213,"planetary_lord":"Jupiter"},{"name":"Hora 9","start":"14:58","end":"15:58","startHours":14.965852581559213,"endHours":15.965852581559213,"planetary_lord":"Saturn"},{"name":"Hora 10","start":"15:58","end":"16:58","startHours":15.965852581559213,"endHours":16.96585258155921,"planetary_lord":"Moon"},{"name":"Hora 11","start":"16:58","end":"17:58","startHours":16.96585258155921,"endHours":17.96585258155921,"planetary_lord":"Mercury"},{"name":"Hora 12","start":"17:58","end":"18:58","startHours":17.96585258155921,"endHours":18.96585258155921,"planetary_lord":"Venus"},{"name":"Hora 13","start":"18:58","end":"19:58","startHours":18.96585258155921,"endHours":19.96585258155921,"planetary_lord":"Sun"},{"name":"Hora 14","start":"19:58","end":"20:58","startHours":19.96585258155921,"endHours":20.96585258155921,"planetary_lord":"Mars"},{"name":"Hora 15","start":"20:58","end":"21:58","startHours":20.96585258155921,"endHours":21.96585258155921,"planetary_lord":"Jupiter"},{"name":"Hora 16","start":"21:58","end":"22:58","startHours":21.96585258155921,"endHours":22.96585258155921,"planetary_lord":"Saturn"},{"name":"Hora 17","start":"22:58","end":"23:58","startHours":22.96585258155921,"endHours":23.96585258155921,"planetary_lord":"Moon"},{"name":"Hora 18","start":"23:58","end":"00:58","startHours":23.96585258155921,"endHours":24.96585258155921,"planetary_lord":"Mercury"},{"name":"Hora 19","start":"00:58","end":"01:58","startHours":24.96585258155921,"endHours":25.96585258155921,"planetary_lord":"Venus"},{"name":"Hora 20","start":"01:58","end":"02:58","startHours":25.96585258155921,"endHours":26.96585258155921,"planetary_lord":"Sun"},{"name":"Hora 21","start":"02:58","end":"03:58","startHours":26.96585258155921,"endHours":27.96585258155921,"planetary_lord":"Mars"},{"name":"Hora 22","start":"03:58","end":"04:58","startHours":27.96585258155921,"endHours":28.96585258155921,"planetary_lord":"Jupiter"},{"name":"Hora 23","start":"04:58","end":"05:58","startHours":28.96585258155921,"endHours":29.96585258155921,"planetary_lord":"Saturn"},{"name":"Hora 24","start":"05:58","end":"06:58","startHours":29.96585258155921,"endHours":30.96585258155921,"planetary_lord":"Moon"}],"taraBala":{"favorable_nakshatras":["Aśvinī","Bharaṇī","Kṛttikā","Puṣya","Aśleṣā","Maghā","Pūrva Phalgunī","Uttara Phalgunī","Anurādhā","Jyeṣṭhā","Mūla","Pūrva Āṣāḍhā","Uttara Āṣāḍhā","Uttara Bhādrapadā","Revatī"],"unfavorable_nakshatras":["Rohiṇī","Mṛgaśirā","Ārdrā","Punarvasu","Hasta","Citrā","Svātī","Viśākhā","Śravaṇa","Dhaniṣṭhā","Śatabhiṣaj","Pūrva Bhādrapadā"],"nature":"Janma-tara if same nakshatra; favorable for 15 nakshatras"},"chandraBala":{"favorable_rashis":["Meṣa","Mithuna","Siṃha","Vṛścika","Dhanu","Mīna"],"unfavorable_rashis":["Vṛṣabha","Karka","Kanyā","Tulā","Makara","Kumbha"]},"dishaShool":"South (Dakṣiṇa)","chandraVasa":"South","rahuVasa":"North-West","anandadiYoga":{"name":"Gada","quality":"Inauspicious"},"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":-21.721909807150023,"eotMinutes":5.090650249418121,"ayanamsa":-47.5311}},"calendars":{"vikram_samvat":-3054,"saka_samvat":-3189,"bengali_samvat":-3704,"malayalam_era":-3935,"nanakshahi_year":-4580,"lunar_month":"Māgha","lunar_month_paksha_full":"Māgha Śukla 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 Śukla Trayodaśī · Vikram -3054 undefined · Śaka -3189 undefined"},"festivals":[{"id":"pradosha-vrata","name":"Pradoṣa Vrata","name_sanskrit":"प्रदोष व्रत","tradition":"Shaiva","associated_deity":"Śiva","significance":"Twilight worship of Śiva on Trayodaśī.","vrata":true,"detection":{"any_of":[{"tithi_number":13},{"tithi_number":28}]},"precedence":7}],"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":"Dedicated festival walk for Pradoṣa Vrata is not live yet; 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 December 13, 3112 BCE · Mathurā · Vidhyamitra","description":"December 13, 3112 BCE for Mathurā: Śukla Trayodaśī, sūryodaya 06:58, sūryāsta 17:30.","schema_org_type":"Article","canonical":"https://vidhyamitra.com/city/mathura/-3111-12-13","hreflang_alternates":{"en":"https://vidhyamitra.com/city/mathura/-3111-12-13","sa":"https://sa.vidhyamitra.com/city/mathura/-3111-12-13","hi":"https://hi.vidhyamitra.com/city/mathura/-3111-12-13","x-default":"https://vidhyamitra.com/city/mathura/-3111-12-13"}},"provenance":[{"pillar":"BOB-History","pillar_version":"2.12.0","method":"Sūrya-Siddhānta first-principles + Bhāskara II + Kerala-school (Mādhava-Nīlakaṇṭha) corrections","retrieved_at":"2026-08-10T16:17:35.979Z","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":"2026-08-10T16:17:35.979Z","verification":{"type":"community-validated","markers":["modern-reference checked timing on Narasiṁha Jayantī 2026"],"confidence":"verified"}}],"meta":{"generated_at":"2026-08-10T16:17:35.979Z","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"}}}