{"id":"vidhyamitra:city-day:mathura:-3137-12-13:en","page_class":"VM-CD-city-day","url":"https://vidhyamitra.com/city/mathura/-3137-12-13","language":{"target_lang":"en","base_lang":"en","quality_tier":"canonical"},"data":{"date":"-3137-12-13","date_display":"December 13, 3138 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":-3137,"month":12,"day":13,"hour":6,"minute":30,"second":0,"calendar":"julian"},"julian_day":575614.770833,"kali_year":-35,"ahargana":-12850.7292,"sun":{"sidereal_longitude":295.7713,"rashi":10,"rashi_name":"Makara"},"moon":{"sidereal_longitude":231.1246,"rashi":8,"rashi_name":"Vṛścika"},"tithi":{"number":25,"name":"Daśamī","paksha":"Kṛṣṇa","full_name":"Kṛṣṇa Daśamī","elongation_degrees":295.3533,"elapsed_within_tithi_degrees":7.3533},"nakshatra":{"number":18,"name":"Jyeṣṭhā","pada":2,"moon_longitude":231.1246,"elapsed_within_degrees":4.4579},"yoga":{"number":13,"name":"Vyāghāta","sum_longitude":166.896},"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":-3137,"month":12,"day":13,"hour":6,"minute":30,"calendar":"julian"},"julian_day":575614.770833,"ahargana":-12850.7292,"kali_year":-35,"ayanamsa_lahiri":-47.8943,"grahas":{"sun":{"sidereal_longitude":295.7713,"rashi":{"number":10,"name":"Makara"},"nakshatra":{"number":23,"name":"Dhaniṣṭhā","pada":1},"retrograde":false},"moon":{"sidereal_longitude":231.1246,"rashi":{"number":8,"name":"Vṛścika"},"nakshatra":{"number":18,"name":"Jyeṣṭhā","pada":2},"retrograde":false,"latitude":4.5},"mars":{"sidereal_longitude":106.6686,"rashi":{"number":4,"name":"Karka"},"nakshatra":{"number":9,"name":"Āśleṣā","pada":1},"retrograde":true},"mercury":{"sidereal_longitude":300.3258,"rashi":{"number":11,"name":"Kumbha"},"nakshatra":{"number":23,"name":"Dhaniṣṭhā","pada":3},"retrograde":false},"jupiter":{"sidereal_longitude":4.1688,"rashi":{"number":1,"name":"Meṣa"},"nakshatra":{"number":1,"name":"Aśvinī","pada":2},"retrograde":false},"venus":{"sidereal_longitude":293.6286,"rashi":{"number":10,"name":"Makara"},"nakshatra":{"number":23,"name":"Dhaniṣṭhā","pada":1},"retrograde":false},"saturn":{"sidereal_longitude":284.1682,"rashi":{"number":10,"name":"Makara"},"nakshatra":{"number":22,"name":"Śravaṇa","pada":2},"retrograde":false},"rahu":{"sidereal_longitude":140.8935,"rashi":{"number":5,"name":"Siṃha"},"nakshatra":{"number":11,"name":"Pūrva Phalgunī","pada":3},"retrograde":false},"ketu":{"sidereal_longitude":320.8935,"rashi":{"number":11,"name":"Kumbha"},"nakshatra":{"number":25,"name":"Pūrva Bhādrapadā","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":-3137,"month":12,"day":13,"hour":6,"minute":30,"second":0,"calendar":"julian"},"julian_day":575614.770833,"kali_year":-35,"ahargana":-12850.7292,"sun":{"sidereal_longitude":295.7713,"rashi":10,"rashi_name":"Makara"},"moon":{"sidereal_longitude":231.1246,"rashi":8,"rashi_name":"Vṛścika"},"tithi":{"number":25,"name":"Daśamī","paksha":"Kṛṣṇa","full_name":"Kṛṣṇa Daśamī","elongation_degrees":295.3533,"elapsed_within_tithi_degrees":7.3533},"nakshatra":{"number":18,"name":"Jyeṣṭhā","pada":2,"moon_longitude":231.1246,"elapsed_within_degrees":4.4579},"yoga":{"number":13,"name":"Vyāghāta","sum_longitude":166.896},"karana":{"half_tithi_index":49,"name":"Viṣṭi"},"vara":{"number":1,"name":"Śanivāra (Saturday)"}},"eclipse_current":{"solar":{"type":"solar","occurs":false,"moon_latitude":4.5,"elongation":64.647},"lunar":{"type":"lunar","occurs":false,"moon_latitude":4.5,"opposition_distance":115.353}},"eclipse_window_40days":[{"offset_days":5,"type":"solar","occurs":true,"moon_latitude":1.379,"elongation":1.905},{"offset_days":20,"type":"lunar","occurs":true,"moon_latitude":-0.42,"opposition_distance":1.553}]},"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":"17:31","solarNoonLocal":"12:14","dayLengthHours":10.55034775457468,"dayLengthDisplay":"10 Hours 33 Mins 01 Secs","nightLengthDisplay":"13 Hours 26 Mins 59 Secs","moonriseLocal":"01:56","moonsetLocal":"13:56","rahuKala":{"name":"Rāhu Kāla","start":"09:36","end":"10:55","startHours":9.599322223866029,"endHours":10.918115693187863,"quality":"inauspicious"},"yamaganda":{"name":"Yamaganda","start":"13:33","end":"14:52","startHours":13.555702631831533,"endHours":14.874496101153369,"quality":"inauspicious"},"gulika":{"name":"Gulika Kāla","start":"06:58","end":"08:17","startHours":6.961735285222358,"endHours":8.280528754544193,"quality":"inauspicious"},"durMuhurta":[{"name":"Dur Muhūrta","start":"09:25","end":"09:47","startHours":9.423483094623116,"endHours":9.775161353108938,"quality":"avoid"}],"varjyam":{"name":"Varjyam","start":"07:24","end":"07:41","startHours":7.401333108329636,"endHours":7.682675715118294,"quality":"avoid"},"abhijit":{"name":"Abhijit Muhūrta","start":"11:53","end":"12:35","startHours":11.885230904023874,"endHours":12.58858742099552,"quality":"auspicious"},"brahmaMuhurta":{"name":"Brahma Muhūrta","start":"05:33","end":"06:16","startHours":5.555022251279067,"endHours":6.258378768250712,"quality":"auspicious"},"pratahSandhya":{"name":"Prātaḥ Sandhyā","start":"06:05","end":"06:58","startHours":6.082539639007801,"endHours":6.961735285222358,"quality":"auspicious"},"vijayaMuhurta":{"name":"Vijaya Muhūrta","start":"14:00","end":"14:42","startHours":13.99530045493881,"endHours":14.698656971910456,"quality":"auspicious"},"godhuliMuhurta":{"name":"Godhūli Muhūrta","start":"17:19","end":"17:43","startHours":17.312083039797038,"endHours":17.712083039797037,"quality":"auspicious"},"sayahnaSandhya":{"name":"Sāyāhna Sandhyā","start":"17:31","end":"17:57","startHours":17.512083039797037,"endHours":17.951680862904315,"quality":"auspicious"},"amritKala":{"name":"Amṛta Kāla","start":"17:16","end":"19:01","startHours":17.262083039797037,"endHours":19.012083039797037,"quality":"auspicious"},"nishitaMuhurta":{"name":"Niśīta Muhūrta","start":"23:53","end":"00:35","startHours":23.885230904023874,"endHours":24.58858742099552,"quality":"auspicious"},"dayChoghadiyas":[{"name":"Kāla","start":"06:58","end":"08:17","startHours":6.961735285222358,"endHours":8.280528754544193,"quality":"inauspicious"},{"name":"Śubha","start":"08:17","end":"09:36","startHours":8.280528754544193,"endHours":9.599322223866029,"quality":"auspicious"},{"name":"Roga","start":"09:36","end":"10:55","startHours":9.599322223866029,"endHours":10.918115693187863,"quality":"inauspicious"},{"name":"Udveg","start":"10:55","end":"12:14","startHours":10.918115693187863,"endHours":12.236909162509697,"quality":"inauspicious"},{"name":"Chala","start":"12:14","end":"13:33","startHours":12.236909162509697,"endHours":13.555702631831533,"quality":"neutral"},{"name":"Labha","start":"13:33","end":"14:52","startHours":13.555702631831533,"endHours":14.874496101153369,"quality":"auspicious"},{"name":"Amṛta","start":"14:52","end":"16:12","startHours":14.874496101153369,"endHours":16.1932895704752,"quality":"auspicious"},{"name":"Kāla","start":"16:12","end":"17:31","startHours":16.1932895704752,"endHours":17.512083039797037,"quality":"inauspicious"}],"nightChoghadiyas":[{"name":"Labha","start":"17:31","end":"19:12","startHours":17.512083039797037,"endHours":19.1932895704752,"quality":"auspicious"},{"name":"Amṛta","start":"19:12","end":"20:52","startHours":19.1932895704752,"endHours":20.87449610115337,"quality":"auspicious"},{"name":"Kāla","start":"20:52","end":"22:33","startHours":20.87449610115337,"endHours":22.555702631831533,"quality":"inauspicious"},{"name":"Śubha","start":"22:33","end":"00:14","startHours":22.555702631831533,"endHours":24.236909162509697,"quality":"auspicious"},{"name":"Roga","start":"00:14","end":"01:55","startHours":24.236909162509697,"endHours":25.91811569318786,"quality":"inauspicious"},{"name":"Udveg","start":"01:55","end":"03:36","startHours":25.91811569318786,"endHours":27.599322223866025,"quality":"inauspicious"},{"name":"Chala","start":"03:36","end":"05:17","startHours":27.599322223866025,"endHours":29.280528754544193,"quality":"neutral"},{"name":"Labha","start":"05:17","end":"06:58","startHours":29.280528754544193,"endHours":30.961735285222357,"quality":"auspicious"}],"horas":[{"name":"Hora 1","start":"06:58","end":"07:58","startHours":6.961735285222358,"endHours":7.961735285222358,"planetary_lord":"Saturn"},{"name":"Hora 2","start":"07:58","end":"08:58","startHours":7.961735285222358,"endHours":8.961735285222357,"planetary_lord":"Moon"},{"name":"Hora 3","start":"08:58","end":"09:58","startHours":8.961735285222357,"endHours":9.961735285222357,"planetary_lord":"Mercury"},{"name":"Hora 4","start":"09:58","end":"10:58","startHours":9.961735285222357,"endHours":10.961735285222357,"planetary_lord":"Venus"},{"name":"Hora 5","start":"10:58","end":"11:58","startHours":10.961735285222357,"endHours":11.961735285222357,"planetary_lord":"Sun"},{"name":"Hora 6","start":"11:58","end":"12:58","startHours":11.961735285222357,"endHours":12.961735285222357,"planetary_lord":"Mars"},{"name":"Hora 7","start":"12:58","end":"13:58","startHours":12.961735285222357,"endHours":13.961735285222357,"planetary_lord":"Jupiter"},{"name":"Hora 8","start":"13:58","end":"14:58","startHours":13.961735285222357,"endHours":14.961735285222357,"planetary_lord":"Saturn"},{"name":"Hora 9","start":"14:58","end":"15:58","startHours":14.961735285222357,"endHours":15.961735285222357,"planetary_lord":"Moon"},{"name":"Hora 10","start":"15:58","end":"16:58","startHours":15.961735285222357,"endHours":16.961735285222357,"planetary_lord":"Mercury"},{"name":"Hora 11","start":"16:58","end":"17:58","startHours":16.961735285222357,"endHours":17.961735285222357,"planetary_lord":"Venus"},{"name":"Hora 12","start":"17:58","end":"18:58","startHours":17.961735285222357,"endHours":18.961735285222357,"planetary_lord":"Sun"},{"name":"Hora 13","start":"18:58","end":"19:58","startHours":18.961735285222357,"endHours":19.961735285222357,"planetary_lord":"Mars"},{"name":"Hora 14","start":"19:58","end":"20:58","startHours":19.961735285222357,"endHours":20.961735285222357,"planetary_lord":"Jupiter"},{"name":"Hora 15","start":"20:58","end":"21:58","startHours":20.961735285222357,"endHours":21.961735285222357,"planetary_lord":"Saturn"},{"name":"Hora 16","start":"21:58","end":"22:58","startHours":21.961735285222357,"endHours":22.961735285222357,"planetary_lord":"Moon"},{"name":"Hora 17","start":"22:58","end":"23:58","startHours":22.961735285222357,"endHours":23.961735285222357,"planetary_lord":"Mercury"},{"name":"Hora 18","start":"23:58","end":"00:58","startHours":23.961735285222357,"endHours":24.961735285222357,"planetary_lord":"Venus"},{"name":"Hora 19","start":"00:58","end":"01:58","startHours":24.961735285222357,"endHours":25.961735285222357,"planetary_lord":"Sun"},{"name":"Hora 20","start":"01:58","end":"02:58","startHours":25.961735285222357,"endHours":26.961735285222357,"planetary_lord":"Mars"},{"name":"Hora 21","start":"02:58","end":"03:58","startHours":26.961735285222357,"endHours":27.961735285222357,"planetary_lord":"Jupiter"},{"name":"Hora 22","start":"03:58","end":"04:58","startHours":27.961735285222357,"endHours":28.961735285222357,"planetary_lord":"Saturn"},{"name":"Hora 23","start":"04:58","end":"05:58","startHours":28.961735285222357,"endHours":29.961735285222357,"planetary_lord":"Moon"},{"name":"Hora 24","start":"05:58","end":"06:58","startHours":29.961735285222357,"endHours":30.961735285222357,"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":-21.62008206607257,"eotMinutes":5.090650249418121,"ayanamsa":-47.8943}},"calendars":{"vikram_samvat":-3080,"saka_samvat":-3215,"bengali_samvat":-3730,"malayalam_era":-3961,"nanakshahi_year":-4606,"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 -3080 undefined · Śaka -3215 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 13, 3138 BCE · Mathurā · Vidhyamitra","description":"December 13, 3138 BCE for Mathurā: Kṛṣṇa Daśamī, sūryodaya 06:58, sūryāsta 17:31.","schema_org_type":"Article","canonical":"https://vidhyamitra.com/city/mathura/-3137-12-13","hreflang_alternates":{"en":"https://vidhyamitra.com/city/mathura/-3137-12-13","sa":"https://sa.vidhyamitra.com/city/mathura/-3137-12-13","hi":"https://hi.vidhyamitra.com/city/mathura/-3137-12-13","x-default":"https://vidhyamitra.com/city/mathura/-3137-12-13"}},"provenance":[{"pillar":"BOB-History","pillar_version":"2.12.0","method":"Sūrya-Siddhānta first-principles + Bhāskara II + Kerala-school (Mādhava-Nīlakaṇṭha) corrections","retrieved_at":"2026-09-07T01:09:26.524Z","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":"2026-09-07T01:09:26.524Z","verification":{"type":"community-validated","markers":["modern-reference checked timing on Narasiṁha Jayantī 2026"],"confidence":"verified"}}],"meta":{"generated_at":"2026-09-07T01:09:26.524Z","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"}}}