{"id":"vidhyamitra:city-day:mathura:-3181-10-30:en","page_class":"VM-CD-city-day","url":"https://vidhyamitra.com/city/mathura/-3181-10-30","language":{"target_lang":"en","base_lang":"en","quality_tier":"canonical"},"data":{"date":"-3181-10-30","date_display":"October 30, 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":10,"day":30,"hour":6,"minute":30,"second":0,"calendar":"julian"},"julian_day":559499.770833,"kali_year":-79,"ahargana":-28965.7292,"sun":{"sidereal_longitude":251.055,"rashi":9,"rashi_name":"Dhanu"},"moon":{"sidereal_longitude":298.1018,"rashi":10,"rashi_name":"Makara"},"tithi":{"number":4,"name":"Caturthī","paksha":"Śukla","full_name":"Śukla Caturthī","elongation_degrees":47.0468,"elapsed_within_tithi_degrees":11.0468},"nakshatra":{"number":23,"name":"Dhaniṣṭhā","pada":2,"moon_longitude":298.1018,"elapsed_within_degrees":4.7684},"yoga":{"number":15,"name":"Vajra","sum_longitude":189.1567},"karana":{"half_tithi_index":7,"name":"Viṣṭi"},"vara":{"number":0,"name":"Śukravāra (Friday)"}},"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":10,"day":30,"hour":6,"minute":30,"calendar":"julian"},"julian_day":559499.770833,"ahargana":-28965.7292,"kali_year":-79,"ayanamsa_lahiri":-48.5106,"grahas":{"sun":{"sidereal_longitude":251.055,"rashi":{"number":9,"name":"Dhanu"},"nakshatra":{"number":19,"name":"Mūla","pada":4},"retrograde":false},"moon":{"sidereal_longitude":298.1018,"rashi":{"number":10,"name":"Makara"},"nakshatra":{"number":23,"name":"Dhaniṣṭhā","pada":2},"retrograde":false,"latitude":1.7826},"mars":{"sidereal_longitude":279.9711,"rashi":{"number":10,"name":"Makara"},"nakshatra":{"number":21,"name":"Uttara Āṣāḍhā","pada":4},"retrograde":false},"mercury":{"sidereal_longitude":252.4657,"rashi":{"number":9,"name":"Dhanu"},"nakshatra":{"number":19,"name":"Mūla","pada":4},"retrograde":false},"jupiter":{"sidereal_longitude":125.2916,"rashi":{"number":5,"name":"Siṃha"},"nakshatra":{"number":10,"name":"Maghā","pada":2},"retrograde":true},"venus":{"sidereal_longitude":298.2032,"rashi":{"number":10,"name":"Makara"},"nakshatra":{"number":23,"name":"Dhaniṣṭhā","pada":2},"retrograde":false},"saturn":{"sidereal_longitude":123.917,"rashi":{"number":5,"name":"Siṃha"},"nakshatra":{"number":10,"name":"Maghā","pada":2},"retrograde":true},"rahu":{"sidereal_longitude":274.7437,"rashi":{"number":10,"name":"Makara"},"nakshatra":{"number":21,"name":"Uttara Āṣāḍhā","pada":3},"retrograde":false},"ketu":{"sidereal_longitude":94.7437,"rashi":{"number":4,"name":"Karka"},"nakshatra":{"number":8,"name":"Puṣya","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":-3181,"month":10,"day":30,"hour":6,"minute":30,"second":0,"calendar":"julian"},"julian_day":559499.770833,"kali_year":-79,"ahargana":-28965.7292,"sun":{"sidereal_longitude":251.055,"rashi":9,"rashi_name":"Dhanu"},"moon":{"sidereal_longitude":298.1018,"rashi":10,"rashi_name":"Makara"},"tithi":{"number":4,"name":"Caturthī","paksha":"Śukla","full_name":"Śukla Caturthī","elongation_degrees":47.0468,"elapsed_within_tithi_degrees":11.0468},"nakshatra":{"number":23,"name":"Dhaniṣṭhā","pada":2,"moon_longitude":298.1018,"elapsed_within_degrees":4.7684},"yoga":{"number":15,"name":"Vajra","sum_longitude":189.1567},"karana":{"half_tithi_index":7,"name":"Viṣṭi"},"vara":{"number":0,"name":"Śukravāra (Friday)"}},"eclipse_current":{"solar":{"type":"solar","occurs":false,"moon_latitude":1.783,"elongation":47.047},"lunar":{"type":"lunar","occurs":false,"moon_latitude":1.783,"opposition_distance":132.953}},"eclipse_window_40days":[{"offset_days":11,"type":"lunar","occurs":true,"moon_latitude":0.741,"opposition_distance":2.308}]},"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":"06:17","sunsetLocal":"17:48","solarNoonLocal":"12:03","dayLengthHours":11.512946200370182,"dayLengthDisplay":"11 Hours 30 Mins 47 Secs","nightLengthDisplay":"12 Hours 29 Mins 13 Secs","moonriseLocal":"09:56","moonsetLocal":"20:26","rahuKala":{"name":"Rāhu Kāla","start":"10:37","end":"12:03","startHours":10.608471493799296,"endHours":12.047589768845569,"quality":"inauspicious"},"yamaganda":{"name":"Yamaganda","start":"14:56","end":"16:22","startHours":14.925826318938114,"endHours":16.364944593984387,"quality":"inauspicious"},"gulika":{"name":"Gulika Kāla","start":"07:44","end":"09:10","startHours":7.7302349437067495,"endHours":9.169353218753022,"quality":"inauspicious"},"durMuhurta":[{"name":"Dur Muhūrta","start":"08:59","end":"09:22","startHours":8.977470782080186,"endHours":9.361235655425858,"quality":"avoid"}],"varjyam":{"name":"Varjyam","start":"06:46","end":"07:05","startHours":6.7708227603425675,"endHours":7.077834659019105,"quality":"avoid"},"abhijit":{"name":"Abhijit Muhūrta","start":"11:40","end":"12:26","startHours":11.663824895499895,"endHours":12.43135464219124,"quality":"auspicious"},"brahmaMuhurta":{"name":"Brahma Muhūrta","start":"04:45","end":"05:31","startHours":4.756057175277786,"endHours":5.523586921969131,"quality":"auspicious"},"pratahSandhya":{"name":"Prātaḥ Sandhyā","start":"05:20","end":"06:17","startHours":5.331704485296295,"endHours":6.291116668660477,"quality":"auspicious"},"vijayaMuhurta":{"name":"Vijaya Muhūrta","start":"13:58","end":"14:44","startHours":13.966414135573931,"endHours":14.733943882265276,"quality":"auspicious"},"godhuliMuhurta":{"name":"Godhūli Muhūrta","start":"17:36","end":"18:00","startHours":17.60406286903066,"endHours":18.00406286903066,"quality":"auspicious"},"sayahnaSandhya":{"name":"Sāyāhna Sandhyā","start":"17:48","end":"18:17","startHours":17.80406286903066,"endHours":18.28376896071275,"quality":"auspicious"},"amritKala":{"name":"Amṛta Kāla","start":"17:33","end":"19:18","startHours":17.55406286903066,"endHours":19.30406286903066,"quality":"auspicious"},"nishitaMuhurta":{"name":"Niśīta Muhūrta","start":"23:40","end":"00:26","startHours":23.663824895499896,"endHours":24.43135464219124,"quality":"auspicious"},"dayChoghadiyas":[{"name":"Chala","start":"06:17","end":"07:44","startHours":6.291116668660477,"endHours":7.7302349437067495,"quality":"neutral"},{"name":"Labha","start":"07:44","end":"09:10","startHours":7.7302349437067495,"endHours":9.169353218753022,"quality":"auspicious"},{"name":"Amṛta","start":"09:10","end":"10:37","startHours":9.169353218753022,"endHours":10.608471493799296,"quality":"auspicious"},{"name":"Kāla","start":"10:37","end":"12:03","startHours":10.608471493799296,"endHours":12.047589768845569,"quality":"inauspicious"},{"name":"Śubha","start":"12:03","end":"13:29","startHours":12.047589768845569,"endHours":13.486708043891841,"quality":"auspicious"},{"name":"Roga","start":"13:29","end":"14:56","startHours":13.486708043891841,"endHours":14.925826318938114,"quality":"inauspicious"},{"name":"Udveg","start":"14:56","end":"16:22","startHours":14.925826318938114,"endHours":16.364944593984387,"quality":"inauspicious"},{"name":"Chala","start":"16:22","end":"17:48","startHours":16.364944593984387,"endHours":17.80406286903066,"quality":"neutral"}],"nightChoghadiyas":[{"name":"Roga","start":"17:48","end":"19:22","startHours":17.80406286903066,"endHours":19.364944593984387,"quality":"inauspicious"},{"name":"Udveg","start":"19:22","end":"20:56","startHours":19.364944593984387,"endHours":20.925826318938114,"quality":"inauspicious"},{"name":"Chala","start":"20:56","end":"22:29","startHours":20.925826318938114,"endHours":22.48670804389184,"quality":"neutral"},{"name":"Labha","start":"22:29","end":"00:03","startHours":22.48670804389184,"endHours":24.04758976884557,"quality":"auspicious"},{"name":"Amṛta","start":"00:03","end":"01:37","startHours":24.04758976884557,"endHours":25.608471493799296,"quality":"auspicious"},{"name":"Kāla","start":"01:37","end":"03:10","startHours":25.608471493799296,"endHours":27.169353218753024,"quality":"inauspicious"},{"name":"Śubha","start":"03:10","end":"04:44","startHours":27.169353218753024,"endHours":28.730234943706748,"quality":"auspicious"},{"name":"Roga","start":"04:44","end":"06:17","startHours":28.730234943706748,"endHours":30.29111666866048,"quality":"inauspicious"}],"horas":[{"name":"Hora 1","start":"06:17","end":"07:17","startHours":6.291116668660477,"endHours":7.291116668660477,"planetary_lord":"Venus"},{"name":"Hora 2","start":"07:17","end":"08:17","startHours":7.291116668660477,"endHours":8.291116668660477,"planetary_lord":"Sun"},{"name":"Hora 3","start":"08:17","end":"09:17","startHours":8.291116668660477,"endHours":9.291116668660477,"planetary_lord":"Mars"},{"name":"Hora 4","start":"09:17","end":"10:17","startHours":9.291116668660477,"endHours":10.291116668660477,"planetary_lord":"Jupiter"},{"name":"Hora 5","start":"10:17","end":"11:17","startHours":10.291116668660477,"endHours":11.291116668660477,"planetary_lord":"Saturn"},{"name":"Hora 6","start":"11:17","end":"12:17","startHours":11.291116668660477,"endHours":12.291116668660477,"planetary_lord":"Moon"},{"name":"Hora 7","start":"12:17","end":"13:17","startHours":12.291116668660477,"endHours":13.291116668660477,"planetary_lord":"Mercury"},{"name":"Hora 8","start":"13:17","end":"14:17","startHours":13.291116668660477,"endHours":14.291116668660477,"planetary_lord":"Venus"},{"name":"Hora 9","start":"14:17","end":"15:17","startHours":14.291116668660477,"endHours":15.291116668660477,"planetary_lord":"Sun"},{"name":"Hora 10","start":"15:17","end":"16:17","startHours":15.291116668660477,"endHours":16.29111666866048,"planetary_lord":"Mars"},{"name":"Hora 11","start":"16:17","end":"17:17","startHours":16.29111666866048,"endHours":17.29111666866048,"planetary_lord":"Jupiter"},{"name":"Hora 12","start":"17:17","end":"18:17","startHours":17.29111666866048,"endHours":18.29111666866048,"planetary_lord":"Saturn"},{"name":"Hora 13","start":"18:17","end":"19:17","startHours":18.29111666866048,"endHours":19.29111666866048,"planetary_lord":"Moon"},{"name":"Hora 14","start":"19:17","end":"20:17","startHours":19.29111666866048,"endHours":20.29111666866048,"planetary_lord":"Mercury"},{"name":"Hora 15","start":"20:17","end":"21:17","startHours":20.29111666866048,"endHours":21.29111666866048,"planetary_lord":"Venus"},{"name":"Hora 16","start":"21:17","end":"22:17","startHours":21.29111666866048,"endHours":22.29111666866048,"planetary_lord":"Sun"},{"name":"Hora 17","start":"22:17","end":"23:17","startHours":22.29111666866048,"endHours":23.29111666866048,"planetary_lord":"Mars"},{"name":"Hora 18","start":"23:17","end":"00:17","startHours":23.29111666866048,"endHours":24.29111666866048,"planetary_lord":"Jupiter"},{"name":"Hora 19","start":"00:17","end":"01:17","startHours":24.29111666866048,"endHours":25.29111666866048,"planetary_lord":"Saturn"},{"name":"Hora 20","start":"01:17","end":"02:17","startHours":25.29111666866048,"endHours":26.29111666866048,"planetary_lord":"Moon"},{"name":"Hora 21","start":"02:17","end":"03:17","startHours":26.29111666866048,"endHours":27.29111666866048,"planetary_lord":"Mercury"},{"name":"Hora 22","start":"03:17","end":"04:17","startHours":27.29111666866048,"endHours":28.29111666866048,"planetary_lord":"Venus"},{"name":"Hora 23","start":"04:17","end":"05:17","startHours":28.29111666866048,"endHours":29.29111666866048,"planetary_lord":"Sun"},{"name":"Hora 24","start":"05:17","end":"06:17","startHours":29.29111666866048,"endHours":30.29111666866048,"planetary_lord":"Mars"}],"taraBala":{"favorable_nakshatras":["Aśvinī","Ārdrā","Punarvasu","Puṣya","Aśleṣā","Maghā","Svātī","Viśākhā","Anurādhā","Jyeṣṭhā","Mūla","Śatabhiṣaj","Pūrva Bhādrapadā","Uttara Bhādrapadā","Revatī"],"unfavorable_nakshatras":["Bharaṇī","Kṛttikā","Rohiṇī","Mṛgaśirā","Pūrva Phalgunī","Uttara Phalgunī","Hasta","Citrā","Pūrva Āṣāḍhā","Uttara Āṣāḍhā","Śravaṇa","Dhaniṣṭhā"],"nature":"Janma-tara if same nakshatra; favorable for 15 nakshatras"},"chandraBala":{"favorable_rashis":["Mithuna","Karka","Tulā","Vṛścika","Makara","Mīna"],"unfavorable_rashis":["Meṣa","Vṛṣabha","Siṃha","Kanyā","Dhanu","Kumbha"]},"dishaShool":"West (Paścim)","chandraVasa":"South-East","rahuVasa":"South-East","anandadiYoga":{"name":"Lumba","quality":"Auspicious"},"tropicalRitu":"Śarad (Autumn) (tropical)","vedicRitu":"Hemanta (Pre-winter)","tropicalAyana":"Dakṣiṇāyana","vedicAyana":"Dakṣiṇāyana","meta":{"method":"BOB-History Sūrya-Siddhānta + Vidhyamitra Tier-2 spherical localization","declination":-8.77127249147259,"eotMinutes":16.449813869265995,"ayanamsa":-48.5106}},"calendars":{"vikram_samvat":-3124,"saka_samvat":-3259,"bengali_samvat":-3774,"malayalam_era":-4005,"nanakshahi_year":-4650,"lunar_month":"Pauṣa","lunar_month_paksha_full":"Pauṣa Śukla Pakṣa","lunar_month_system":"purnimanta","lunar_month_purnimanta":"Pauṣa","lunar_month_amanta":"Pauṣa","lunar_month_is_adhika":false,"lunar_month_purnimanta_is_adhika":false,"lunar_month_amanta_is_adhika":false,"solar_month":"Dhanus (Mārgaḻi)","ritu":"Hemanta (Pre-winter)","display_summary":"Pauṣa Śukla Caturthī · Vikram -3124 undefined · Śaka -3259 undefined"},"festivals":[{"id":"vinayaka-chaturthi","name":"Vināyaka Caturthī (monthly)","name_sanskrit":"विनायक चतुर्थी","tradition":"Pan-Hindu","associated_deity":"Gaṇeśa","significance":"Monthly Śukla-pakṣa Caturthī; auspicious for new ventures.","vrata":true,"detection":{"tithi_number":4,"tithi_paksha":"Śukla"},"precedence":6}],"todays_walk":{"walk":{"id":"shukra-walk","name":"Śukra Walk","name_sanskrit":"शुक्र यात्रा","type":"graha","description":"Beauty + creativity in dharma + BG 10.36.","step_count":5,"url":"/walk/shukra-walk"},"reason":"Dedicated festival walk for Vināyaka Caturthī (monthly) is not live yet; Śukravāra (Friday) — 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 October 30, 3182 BCE · Mathurā · Vidhyamitra","description":"October 30, 3182 BCE for Mathurā: Śukla Caturthī, sūryodaya 06:17, sūryāsta 17:48.","schema_org_type":"Article","canonical":"https://vidhyamitra.com/city/mathura/-3181-10-30","hreflang_alternates":{"en":"https://vidhyamitra.com/city/mathura/-3181-10-30","sa":"https://sa.vidhyamitra.com/city/mathura/-3181-10-30","hi":"https://hi.vidhyamitra.com/city/mathura/-3181-10-30","x-default":"https://vidhyamitra.com/city/mathura/-3181-10-30"}},"provenance":[{"pillar":"BOB-History","pillar_version":"2.12.0","method":"Sūrya-Siddhānta first-principles + Bhāskara II + Kerala-school (Mādhava-Nīlakaṇṭha) corrections","retrieved_at":"2026-09-06T13:20:29.138Z","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":"2026-09-06T13:20:29.138Z","verification":{"type":"community-validated","markers":["modern-reference checked timing on Narasiṁha Jayantī 2026"],"confidence":"verified"}}],"meta":{"generated_at":"2026-09-06T13:20:29.138Z","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"}}}