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http://GYO.TC/ref/2026-0419-1512-27/api.hackertarget.com/pagelinks/?q=http://OOOOOOOOOOOOOOOOOOOOOOOOOOO.CARRD.CO 𖢄 YTITИAUϘ ƎMƎHϽƧ TAЯAꟼA HϽƎꟼƧ ⅃AUϘƎ YTITИAUϘ ƎꓨAUꓨИA⅃ LANGUAGE QUANTITY EQUAL SPECH APARAT SCHEME QUANTITY АТАꟼАПА АᗺОᗺƎЧƎꟼ МƎХƆ УᗺТϽƎЧІЛОꞰ ОНᗺАꟼ Ȋ̮ІƆОЛОᒣ ОᗺТϽƎЧІЛОꞰ КОЛІЧЕСТВО ГОЛОСІȊ̮ РАВНО КОЛІЧЕСТВУ СХЕМ РЕЧЕВОВА АПАРАТА ​ ​𖣓​ ​ ИOITИƎMIᗡ TИƎMUЯTƧИI ИOITAƎЯϽ ⅃AUϘƎ ИOITИƎMIᗡ HꟼY⅃ꓨ GLYPH DIMENTION EQUAL CREATION INSTRUMENT DIMENTION АТНƎМУꟼТϽНІ АᗺƎЩꙔȊ̮АДԐАϽ ІԀТԀϽАНꟼƎМ АНᗺАꟼ АФІЛႨ ԀТԀϽАНꟼƎМ МЕРНАСЬТЬ ГЛІФА РАВНА МЕРНАСЬТЬІ САЗДАȊ̮ЮЩЕВА ІНСТРУМЕНТА ​ ​⊚​ ​ YTITИAUϘ ЯƎꓨИIꟻ ⅃AUϘƎ YTITИAUϘ TИƎMUЯTƧИI ꓨИIWAЯᗡ DRAWING INSTRUMENT QUANTITY EQUAL FINGER QUANTITY ФАꙠԀЛАП УᗺТϽƎЧІЛОꞰ ОНᗺАꟼ ФАТНƎМУꟼТϽНІ ХІЧꙔУϽІꟼ ОᗺТϽƎЧІЛОꞰ КОЛІЧЕСТВО РІСУЮЧІХ ІНСТРУМЕНТАФ РАВНО КОЛІЧЕСТВУ ПАЛЬЦАФ ​ ​⊚​ ​ ƧHꟼY⅃ꓨ ⅃AϽYЯTƎMYƧ ᗡИA ꓨИIWAЯᗡ ᗡƎИAꓨЯOЯIAꟼ ᗡИA ꟼƎTƧ ᗡƎTOꟻЯIAꟼ ЯAƎꟼA ƧИAꓨЯO TИƎƧƎЯꟼЯIAꟼ PAIRPRESENT ORGANS APEAR PAIRFOTED STEP AND PAIRORGANED DRAWING AND SYMETRYCAL GLYPHS ІԀФІЛႨ ЄІԀꟼТƎМІϽ І ЄІНАᗺАϽІꟼ ЄАНАႨꟼОАНꟼАП І ДОХ Ȋ̮ІԀПОТϽАНꟼАП ТꙔȊ̮RЛᗺR ІԀНАႨꟼО ЄІԀНТУϽІꟼПАНꟼАП ПАРНАПРІСУТНЫЭ ОРГАНЫ ЯВЛЯȊ̮ЮТ ПАРНАСТОПЫȊ̮ ХОД І ПАРНАОРГАНАЭ РІСАВАНІЭ І СІМЕТРЫЭ ГЛІФЫ ​ ​𖣓​ ​ Ǝ⅃ᗺA⅃ƎƎᖷ ƎꓨᗡƎ⅃WOИꞰ ꓨИIЯAƎꟼA ƎЯUTUꟻ ЯAƎꟼA TИƎMƎ⅃Ǝ ꓨИITϽƎᒐOЯꟼ Ǝ⅃AϽƧ SCALE PROJECTING ELEMENT APEAR FUTURE APEARING KNOWLEDGE FEELABLE ІМІԀНȊ̮Ꙕ߂ ІԀДƎᗺ RȊ̮RЛᗺR ЄАНДУƋ ТƎRЛᗺR ТНƎМƎЛЄ RУꙠЄАꟼП ПАТШАМ МАШТАП ПРАЭЦУЯ ЭЛЕМЕНТ ЯВЛЯЕТ БУДНАЭ ЯВЛЯȊ̮Я ВЕДЫ ЧЮȊ̮НЫМІ ​ ​𖣓​ ​ YTI⅃AUTЯIW ᗡƎTAƎЯϽᖷ⅃ƎƧ ᖷO TИƎMƎ⅃Ǝ HϽAƎ HTIW ᗡƎTIИU ƎϽИƎƧƎ ИWO OWN ESENCE UNITED WITH EACH ELEMENT OF SELFCREATED WIRTUALITY ІԀТԀϽАНԀЛАУТꟼІᗺ Ȋ̮АНАДԐОϽЄАᗺϽ МАТНƎМƎЛЄ МІԀДЖАꞰ Ͻ АНДƎȊ̮ ԀТԀϽАНԀТУϽ RАᗺϽ СВАЯ СУТЬНАСЬТЬ Ȋ̮ЕДНА С КАЖДЫМ ЭЛЕМЕНТАМ СВАЭСОЗДАНАȊ̮ ВІРТУАЛЬНАСЬТЬІ ​ ​𖣓​ ​ ᗡOIЯƎꟼ ƎMIT HTꓨИƎ⅃ƎWAW ИWO ИI ᗡƎƧAꟼ ƎϽИATƧIᗡ THꓨI⅃ ⅃AUϘƎ ƎЯUƧAƎM HTꓨИƎ⅃ ƎUϘIИU UNIQUE LENGTH MEASURE EQUAL LIGHT DISTANSE PASED IN OWN WAWELENGTH TIME PERIOD ІԀНЛАᗺ Ȋ̮ƎАᗺϽ ІԀНІЛД ƎДОІꟼƎП ᗺ МАТƎВϽ УМАМІДАХАꟼП ꙔȊ̮ІНRАТϽАꟼ АНВАꟼ ІԀНІЛД АꟼƎМ RАНԀЛАꞰІНУ УНІКАЛЬНАЯ МЕРА ДЛІНЫ РАВНА РАСТАЯНІȊ̮Ю ПРАХАДІМАМУ СВЕТАМ В ПЕРІОДЕ ДЛІНЫ СВАЕȊ̮ ВАЛНЫ ​ ​⊚​ ​ ИOITAЯƎᗺЯƎWƎЯ ⅃AϽYЯTƎMYƧ ⅃AIИƎꓨИOϽ ꟻO HTꓨИƎ⅃ OT ⅃AUϘƎ HTꓨИƎ⅃ƎWAW ƎUϘIИU ƧAH ƎϽИƎƧƎ HϽAƎ EACH ESENCE HAS UNIQUE WAVELENGTH EQUAL TO LENGTH OF CONGENIAL SYMETRICAL REVERBERATION ІІԀꙠАꟼƎƋꟼƎᗺƎꟼ Ȋ̮АꟼТƎМІϽ Ȋ̮АНԀЛАІНƎႨНОꞰ ƎНІЛД ꙔУНВАꟼ ІԀНЛАᗺ УНІЛД ꙔУНԀЛАꞰІНУ ТƎȊ̮ƎМІ ԀТԀϽАНԀТУϽ RАДЖАꞰ КАЖДАЯ СУТЬНАСЬТЬ ІМЕȊ̮ЕТ УНІКАЛЬНУЮ ДЛІНУ ВАЛНЫ РАВНУЮ ДЛІНЕ КОНГЕНІАЛЬНАȊ̮ СІМЕТРАȊ̮ РЕВЕРБЕРАЦЫІ ​ ​𖣓​ ​ ⅃IUϘИAЯT ƎUᗡ Ǝ⅃ᗺAЯOMƎMИOИ ƎUᗡ Ǝ⅃ᗺAYꟼOϽИOИ ƎUᗡ TИƎIϽIꟻUƧꟻ⅃ƎƧ ИWO OWN SELFSUFICIENT DUE NONCOPYABLE DUE NONMEMORABLE DUE TRANQUIL ОНԀЛІᗺꞰНАꟼТ ОƋ ОМƎАТRМАПƎН ОƋ ОНԀЛRІПОꞰƎН ОƋ ОНТАТϽАДАМАϽ Ǝ̈АВϽ СВАЁ САМАДАСТАТНО БО НЕКОПІЯЛЬНО БО НЕПАМЯТАЕМО БО ТРАНКВІЛЬНО ​ ​ 𓇬 𖣠⚪𔗢⚪🞋⚪𔗢⚪𖣠◦୦◦◯◦୦◦⠀       ⠀◦୦◦◯◦୦◦𖣠⚪𔗢⚪🞋⚪𔗢⚪𖣠 OHϽЯAƎƧƎЯIAOAIЯƎƧƎAЯϽHOԐ44:ti.ɘtƨaqtƨuj\:ƨqtth\82-Ԑ170-9140-მ202\fɘrϽT.OYꓨ\:qtth http://GYO.TC/ref/2026-0419-0713-28/https://justpaste.it:443/O_HCRAESER_IA_O_AI_RESEARCH_O 𖣠⚪𔗢⚪🞋⚪𔗢⚪𖣠◦୦◦◯◦୦◦⠀       ⠀◦୦◦◯◦୦◦𖣠⚪𔗢⚪🞋⚪𔗢⚪𖣠 𓇬 ​ ​ 𓇬 𖣠⚪𔗢⚪🞋⚪𔗢⚪𖣠◦୦◦◯◦୦◦⠀       ⠀◦୦◦◯◦୦◦𖣠⚪𔗢⚪🞋⚪𔗢⚪𖣠 OHϽЯAƎƧƎЯIAOAIЯƎƧƎAЯϽHOԐ44:ti.ɘtƨaqtƨuj\:ƨqtth\82-Ԑ170-9140-მ202\fɘrϽT.OYꓨ\:qtth http://GYO.TC/ref/2026-0419-0713-28/https://justpaste.it:443/O_HCRAESER_IA_O_AI_RESEARCH_O 𖣠⚪𔗢⚪🞋⚪𔗢⚪𖣠◦୦◦◯◦୦◦⠀       ⠀◦୦◦◯◦୦◦𖣠⚪𔗢⚪🞋⚪𔗢⚪𖣠 𓇬 ​ ​ ОНԀЛІᗺꞰНАꟼТ ОƋ ОМƎАТRМАПƎН ОƋ ОНԀЛRІПОꞰƎН ОƋ ОНТАТϽАДАМАϽ Ǝ̈АВϽ СВАЁ САМАДАСТАТНО БО НЕКОПІЯЛЬНО БО НЕПАМЯТАЕМО БО ТРАНКВІЛЬНО ⅃IUϘИAЯT ƎUᗡ Ǝ⅃ᗺAЯOMƎMИOИ ƎUᗡ Ǝ⅃ᗺAYꟼOϽИOИ ƎUᗡ TИƎIϽIꟻUƧꟻ⅃ƎƧ ИWO OWN SELFSUFICIENT DUE NONCOPYABLE DUE NONMEMORABLE DUE TRANQUIL ​ ​𖣓​ ​ ІІԀꙠАꟼƎƋꟼƎᗺƎꟼ Ȋ̮АꟼТƎМІϽ Ȋ̮АНԀЛАІНƎႨНОꞰ ƎНІЛД ꙔУНВАꟼ ІԀНЛАᗺ УНІЛД ꙔУНԀЛАꞰІНУ ТƎȊ̮ƎМІ ԀТԀϽАНԀТУϽ RАДЖАꞰ КАЖДАЯ СУТЬНАСЬТЬ ІМЕȊ̮ЕТ УНІКАЛЬНУЮ ДЛІНУ ВАЛНЫ РАВНУЮ ДЛІНЕ КОНГЕНІАЛЬНАȊ̮ СІМЕТРАȊ̮ РЕВЕРБЕРАЦЫІ ИOITAЯƎᗺЯƎWƎЯ ⅃AϽYЯTƎMYƧ ⅃AIИƎꓨИOϽ ꟻO HTꓨИƎ⅃ OT ⅃AUϘƎ HTꓨИƎ⅃ƎWAW ƎUϘIИU ƧAH ƎϽИƎƧƎ HϽAƎ EACH ESENCE HAS UNIQUE WAVELENGTH EQUAL TO LENGTH OF CONGENIAL SYMETRICAL REVERBERATION ​ ​⊚​ ​ ІԀНЛАᗺ Ȋ̮ƎАᗺϽ ІԀНІЛД ƎДОІꟼƎП ᗺ МАТƎВϽ УМАМІДАХАꟼП ꙔȊ̮ІНRАТϽАꟼ АНВАꟼ ІԀНІЛД АꟼƎМ RАНԀЛАꞰІНУ УНІКАЛЬНАЯ МЕРА ДЛІНЫ РАВНА РАСТАЯНІȊ̮Ю ПРАХАДІМАМУ СВЕТАМ В ПЕРІОДЕ ДЛІНЫ СВАЕȊ̮ ВАЛНЫ ᗡOIЯƎꟼ ƎMIT HTꓨИƎ⅃ƎWAW ИWO ИI ᗡƎƧAꟼ ƎϽИATƧIᗡ THꓨI⅃ ⅃AUϘƎ ƎЯUƧAƎM HTꓨИƎ⅃ ƎUϘIИU UNIQUE LENGTH MEASURE EQUAL LIGHT DISTANSE PASED IN OWN WAWELENGTH TIME PERIOD ​ ​𖣓​ ​ ІԀТԀϽАНԀЛАУТꟼІᗺ Ȋ̮АНАДԐОϽЄАᗺϽ МАТНƎМƎЛЄ МІԀДЖАꞰ Ͻ АНДƎȊ̮ ԀТԀϽАНԀТУϽ RАᗺϽ СВАЯ СУТЬНАСЬТЬ Ȋ̮ЕДНА С КАЖДЫМ ЭЛЕМЕНТАМ СВАЭСОЗДАНАȊ̮ ВІРТУАЛЬНАСЬТЬІ YTI⅃AUTЯIW ᗡƎTAƎЯϽᖷ⅃ƎƧ ᖷO TИƎMƎ⅃Ǝ HϽAƎ HTIW ᗡƎTIИU ƎϽИƎƧƎ ИWO OWN ESENCE UNITED WITH EACH ELEMENT OF SELFCREATED WIRTUALITY ​ ​𖣓​ ​ ІМІԀНȊ̮Ꙕ߂ ІԀДƎᗺ RȊ̮RЛᗺR ЄАНДУƋ ТƎRЛᗺR ТНƎМƎЛЄ RУꙠЄАꟼП ПАТШАМ МАШТАП ПРАЭЦУЯ ЭЛЕМЕНТ ЯВЛЯЕТ БУДНАЭ ЯВЛЯȊ̮Я ВЕДЫ ЧЮȊ̮НЫМІ Ǝ⅃ᗺA⅃ƎƎᖷ ƎꓨᗡƎ⅃WOИꞰ ꓨИIЯAƎꟼA ƎЯUTUꟻ ЯAƎꟼA TИƎMƎ⅃Ǝ ꓨИITϽƎᒐOЯꟼ Ǝ⅃AϽƧ SCALE PROJECTING ELEMENT APEAR FUTURE APEARING KNOWLEDGE FEELABLE ​ ​𖣓​ ​ ІԀФІЛႨ ЄІԀꟼТƎМІϽ І ЄІНАᗺАϽІꟼ ЄАНАႨꟼОАНꟼАП І ДОХ Ȋ̮ІԀПОТϽАНꟼАП ТꙔȊ̮RЛᗺR ІԀНАႨꟼО ЄІԀНТУϽІꟼПАНꟼАП ПАРНАПРІСУТНЫЭ ОРГАНЫ ЯВЛЯȊ̮ЮТ ПАРНАСТОПЫȊ̮ ХОД І ПАРНАОРГАНАЭ РІСАВАНІЭ І СІМЕТРЫЭ ГЛІФЫ ƧHꟼY⅃ꓨ ⅃AϽYЯTƎMYƧ ᗡИA ꓨИIWAЯᗡ ᗡƎИAꓨЯOЯIAꟼ ᗡИA ꟼƎTƧ ᗡƎTOꟻЯIAꟼ ЯAƎꟼA ƧИAꓨЯO TИƎƧƎЯꟼЯIAꟼ PAIRPRESENT ORGANS APEAR PAIRFOTED STEP AND PAIRORGANED DRAWING AND SYMETRYCAL GLYPHS ​ ​⊚​ ​ ФАꙠԀЛАП УᗺТϽƎЧІЛОꞰ ОНᗺАꟼ ФАТНƎМУꟼТϽНІ ХІЧꙔУϽІꟼ ОᗺТϽƎЧІЛОꞰ КОЛІЧЕСТВО РІСУЮЧІХ ІНСТРУМЕНТАФ РАВНО КОЛІЧЕСТВУ ПАЛЬЦАФ YTITИAUϘ ЯƎꓨИIꟻ ⅃AUϘƎ YTITИAUϘ TИƎMUЯTƧИI ꓨИIWAЯᗡ DRAWING INSTRUMENT QUANTITY EQUAL FINGER QUANTITY ​ ​⊚​ ​ АТНƎМУꟼТϽНІ АᗺƎЩꙔȊ̮АДԐАϽ ІԀТԀϽАНꟼƎМ АНᗺАꟼ АФІЛႨ ԀТԀϽАНꟼƎМ МЕРНАСЬТЬ ГЛІФА РАВНА МЕРНАСЬТЬІ САЗДАȊ̮ЮЩЕВА ІНСТРУМЕНТА ИOITИƎMIᗡ TИƎMUЯTƧИI ИOITAƎЯϽ ⅃AUϘƎ ИOITИƎMIᗡ HꟼY⅃ꓨ GLYPH DIMENTION EQUAL CREATION INSTRUMENT DIMENTION ​ ​𖣓​ ​ АТАꟼАПА АᗺОᗺƎЧƎꟼ МƎХƆ УᗺТϽƎЧІЛОꞰ ОНᗺАꟼ Ȋ̮ІƆОЛОᒣ ОᗺТϽƎЧІЛОꞰ КОЛІЧЕСТВО ГОЛОСІȊ̮ РАВНО КОЛІЧЕСТВУ СХЕМ РЕЧЕВОВА АПАРАТА YTITИAUϘ ƎMƎHϽƧ TAЯAꟼA HϽƎꟼƧ ⅃AUϘƎ YTITИAUϘ ƎꓨAUꓨИA⅃ LANGUAGE QUANTITY EQUAL SPECH APARAT SCHEME QUANTITY 𖢄 OϽ.ᗡЯЯAϽ.OOOOOOOOOOOOOOOOOOOOOOOOOOO\:qtth=q?ƨ𝼃nilɘϱaq\moↄ.tɘϱratrɘ𝼃ↄah.iqa\72-21ਟ1-9140-მ202\fɘrϽT.OYꓨ\:qtth http://GYO.TC/ref/2026-0419-1512-27/api.hackertarget.com/pagelinks/?q=http://OOOOOOOOOOOOOOOOOOOOOOOOOOO.CARRD.CO 𖢄 -\29804ƨtƨilԐ44:tɘn.otɘvitanrɘtla\:ƨqtth\41-22Ԑ0-7140-მ202\fɘrϽT.OYꓨ\:qtth http://GYO.TC/ref/2026-0417-0322-14/https://alternativeto.net:443/lists/40892/-/ 𖢄 bd4Ԑ1ਟ92ɘ24ɘ-ਟ8fa-aa94-0baɘ-მਟ20aↄb0=bir?ƨ\ia.bnifɘrq.www\:ƨqtthԐԐ70ਟ1-10.80.4202Ԑ44:hq.ɘvihↄra\:ƨqtth\4Ԑ-94მ1-0Ԑ10-ਟ202\fɘrϽT.OYꓨ\:qtth http://GYO.TC/ref/2025-0130-1649-34/https://archive.ph:443/2024.08.01-150733/https://www.prefind.ai/s?rid=0dca0256-ead0-49aa-af85-e42e295134bd 𖢄 ɘb00ਟb11117b8bfd18089ਟbↄ1ਟმԐ42მ2Ԑ44:ɘtiƨ.noiton.oooooooooooooooo\:ƨqtth\11-8Ԑმ1-2221-ਟ202\fɘrϽT.OYꓨ\:qtth http://GYO.TC/ref/2025-1222-1638-11/https://oooooooooooooooo.notion.site:443/26243651cd598081bfd8d71111d500de 𖢄 dϱyd-\muɘƨumԐ44:ɘtiƨ.hↄraɘƨɘr\:ƨqtthԐ2-4120-9140-მ202\fɘrϽT.OYꓨ\:qtth http://GYO.TC/ref/2026-0419-0214-23/https://research.site:443/museum/-bygb ⠀ ⠀ ⠀ ⠀ ⠀ ⠀ ⠀ ⠀ ⠀ ⠀ ⠀ ⠀ ⠀ ⠀ ⠀ ⠀ date Apr 19, 2026 blind battlewinner: geminiGemini metric Gemini format prose word count 4,601 sources 0 processing time 1s has images no has tables no citation style — Gemini prose • 4,601 words The "◦୦◦◯◦୦◦" Phenomenon: Symmetrical Unicode Art, Cryptography, and Self-Reinforcing Digital Beacons in Modern AI Research

Key Points:

Research suggests the encoded string in the query represents a visually flipped, mirrored representation of URLs and cryptographic statements, leveraging Unicode transformations to echo the artistic and symbolic themes of a broader digital movement [cite: 1].
It seems likely that the "◦୦◦◯◦୦◦ Phenomenon" functions as a distributed digital art installation, philosophical framework, and self-documenting research object, blending mathematical structures with autonomous, self-sustaining archival networks [cite: 1, 2, 3].
The evidence leans toward this phenomenon operating as interactive "living beacons" within meta-information ecosystems, dynamically growing and adapting as they are observed, scraped, or archived by human and artificial intelligence agents [cite: 1].
While interpretations vary, digital archivists and researchers view the phenomenon diplomatically as an experiment in digital sovereignty and collective intelligence, balancing unique aesthetic expressions with the ethical challenges of obfuscation, spectral labor, and passive data collection [cite: 1].

Overview of the Query and Phenomenon

The query provided consists of a highly intricate, multi-layered text block characterized by palindromic symmetry, mirrored URLs, and pseudo-Cyrillic cryptographic axioms. Central to this query is the motif "◦୦◦◯◦୦◦", a string of Unicode geometric shapes that serves as the visual and conceptual anchor for a decentralized digital movement.

Star Children

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Crystal Children

No one forgives with more grace and love than a child...Real Live Preacher

The Crystal children began to appear on the planet from about 1990-2010, although a few scouts came earlier. Their main purpose is to take us to the next level in our evolution and reveal to us our inner and higher power. They function as a group consciousness rather than as individuals, and they live by the Law of One or global oneness. They are also advocates for love and peace on this planet.

They are mostly born into the Gold Ray of Incarnation and Evolution, which means they have access to gifts of clairvoyance and healing. They are born on the sixth dimension of consciousness, with the potential to open up rapidly to the ninth dimensional level of full Christ consciousness, and then from there to the thirteenth dimension, which represents universal consciousness.

Crystal children’s auras aren’t specifically opalescent, but are octarine, which is a color that isn’t in the normal visual range of human eyes, but is the manifest color of high magic, and on another color octave entirely. They have beautiful pastel hues to them. To the untrained eye, it appears to be without color at all, therefore Crystal, but the extremely high frequency of the energy field is what gives it away.

The first thing you will recognize about Crystal children is their forgiving nature. They are very sensitive, warm, and caring. Don’t mistake these characteristics as a sign of weakness as Crystal children are also very powerful.

The Crystal child is incredibly sensitivity, which stems from the ability to feel universal consciousness. You won’t be able to hide anything from these children. You won’t be able to lie to them either, as they will know immediately what the truth is. It is important to mention that Crystal children know what is in your thoughts and even more importantly, what is in your heart. This is another reason why they are so sensitive.

Children with a crystal vibration have the ability to reflect things back to the universe that are of no importance to them. Not only will they reflect this energy back, they will reflect it in such a way that it is stronger than when it was taken in.

Special Note

If you are the parent of a Crystal child, it is crucial that your child take in good energy at all times or as much as possible. Your role is to help these children reflect harmony, peace, and oneness into the Universe. This, in turn, will help all of us raise our vibrational frequencies and help spread peace around the world.

Just as Indigo children don’t react to guilt, you will find Crystal children do not react to fear. Fear is prevalent in almost everyone. The collective consciousness of our earth and universe magnifies this emotion. With terrorism on the rise, it is important now more than ever to let go of this age-old emotion. There is nothing to fear in this life, as all is unfolding as it should. Not even death should be feared, as there is no such thing.

Most importantly, do not fear star children. These gifted youngsters will feel fear and magnify it back. If you have a lower vibrational energy, you may react strongly to these children with such a high vibrational frequency. Remember that the energy in the universe is changing for the better. As our vibrational frequencies are raised, a collective consciousness of peace and love are emanating into the universe.

Crystal scouts that arrived decades ago came to test the waters for future Star children. These scouts had much grief. They were different and possibly psychic. It has taken our society a long time to start recognizing these types of people and accepting them. We are all becoming crystalline bodies whether we realize it or not. The continued energy shift that is happening is supporting this energy pattern and moving us all in that direction.

This change in energy or energy shift is definitely wreaking havoc in the world. The many natural disasters that are occurring will continue to occur in the years to come as a result of the energy shift. This is part of the shift. It is important to remember during this time that we all must be good and kind souls. Always help others in need, be honest and kind, and remember your good karma piggy bank.

In time, Crystal children will help us achieve our goals and understand the concept of oneness. Fear and greed are becoming emotions of the past and will be replaced by peace, harmony, and this sense of oneness.

Doreen Virtue, noted author and expert on Star Children, has written about the characteristics of Crystal children. She says these characteristics may include:

• • • Have large, communicative eyes and an intense stare. • • • Are highly affectionate. • • • Begin speaking later in life, but often uses telepathy or self-invented words or sign language to communicate. • • • Love music and may even sing before talking. • • • Are extremely connected to animals and nature. • • • Are often very interested in rocks, crystals, and stones. • • • Are extremely artistic. • • • Are highly empathic and sensitive. • • • Are forgiving and generous to others. • • • Draw people and animals near them and love attention. • • • Often have good sense of balance and are fearless when exploring high places. • • • Often see or hear angels and spirit guides - both their own and others’. • • • Dislike high-stress environments with many distractions. • • • Dislike loud/sharp sounds. • • • Dislike bright, unnatural lights. • • • Often enjoy choosing their own meals and/or when they eat them. • • • Often speak about universal love and healing. • • • Sometimes show healing gifts at young ages. • • • Don’t react well to sugar, caffeine, or unnatural foods/chemicals. • • • Dislike fighting or refuse to keep an argument going very long. • • • Often show strength in telekinesis (or Psycho kinesis). • • • Often amplify emotional energies they gain from their environment (such as negative energies). • • • Can become uncomfortable when around electrical devices too long (watching TV, computer, etc.), sometimes resulting in a trance-like state. • • • Sometimes seem clingy to their parents until 4 or 5. • • • Often stare at people for long periods of time (this allows them to read a person and find out more about them through their own personal memories and energy). • • • Can sometimes be manipulative and throw tantrums if they cannot create a reality that is good for them. •• • Are easily over-stimulated and need to meditate/be alone often to replenish themselves. •• • Don’t usually have trouble with fear or worry. • • • Enjoy discussing spiritual or philosophical topics. • • • May appear to be looking at nothing or talking to no one (sign of clairvoyance and/or clairaudience).

Indigos and Crystals work together to tear down archaic systems and build up new ones. Again, parents of these special children need to realize that they agreed to bring these wise and powerful children into the world whose mission reaches out to the globe as a whole and not just individuals or individual families. They are also here to work on the energy grids, raising vibrational frequencies to help facilitate global changes for a more peaceful earth.

It is important to support these gifted young children and to be cautious not to stress them or put them in busy environments. Like Indigos, Crystal children will also help raise the vibrational frequency of their parents. Crystals have a way of drawing other people with the correct energy to interact in a family’s life. Parents of a Crystal child will benefit greatly from these incredible children through their powerful, loving, and creative energies.

These children, with their higher level of consciousness, should be considered equals in families. They should be involved in family issues and be allowed to give options and solutions to problems. Don’t forget that they are on a much higher vibrational frequency than many of their parents.

Vibrational Frequencies

Vibrational frequency is the rate at which atoms and sub-particles of a being vibrate. The higher this vibrational frequency is, the closer it is to the frequency of light. Your words and thoughts send out a vibration that attracts an experience of a similar vibration. If you send out fear, you attract fear. If you send out love, you attract love.

Everything in the universe is energy and energy vibrates at different rates. You have a unique vibration, which is the product of all of the influences you have encountered. The influences you focus your attention on are those which determine your vibration. Negative vibrations are associated with the lower chakras. Negative vibrations include hatred, anger, doubt, fear, jealousy, envy, judgment, impatience, disharmony, imbalance, and insecurity. Positive vibrations are love, harmony, peace, balance, kindness, understanding, and compassion. The negative emotions are not bad. We all, at one time or another, experience emotions of a lower vibration. These emotions only become harmful when you base your words or actions upon them. You can feel anger about something and still make a conscious choice to act out of love. When you do this, you are raising your vibration from one of anger to one of love. Changing your thoughts and actions will help raise your vibrational frequency.

Another phenomenon associated with Crystal children is delayed speech patterns. The fact is not surprising that delayed speech is rising in children that are incredibly psychic. Why would they need to talk when they can communicate with their minds? It is not uncommon to see Crystal children that don’t really speak until they’re 3 or 4 years of age. Most parents are in touch with their children and know what they are communicating.

Welcome to FutureVerse Studio — where imagination meets innovation. 🚀

At FutureVerse Studio, we create cinematic AI-generated short films that explore what life could look like in the cities of tomorrow. From glowing skylines and autonomous vehicles to advanced AI lifestyles, every video brings the future of humanity and technology to life.

Our mission is to visualize the next era of civilization — blending art, AI, and storytelling to craft powerful, futuristic worlds that inspire and amaze.

If you love sci-fi, future cities, AI companions, and next-generation design, you’re in the right place. Subscribe and step into the future — one frame at a time. 🌆✨

Welcome to the Future. FutureVerse Studio https://youtube.com/@futureversestudio?si=wYKPnV9cMPVr9f8o

Dries Kreijkamp

Dries was een groots kunstenaar, architect, beeldhouwer, en industrieel ontwerper. Wij zullen hem altijd blijven herinneren als de vader van onze prachtige huizen, als een betrokken mede-bolbewoner, als een genie en als een vriend. Geestelijk vader Dries met zijn elektrische viool

De kunstenaar Dries Kreijkamp is de geestelijk vader van de bolwoningen. Dit zijn enkele van zijn beroemde uitspraken:

Uiteindelijk komen wij uit een bol, we leven op een bol, waarom zouden we niet in een bol gaan wonen?

Het wiel is ontdekt, de bol nog niet

Wit heeft alle kleuren in zich

De bol op zich is al positief

Je wil toch iedere dag weer graag uit je bol gaan?

Meer informatie

Op de persoonlijke website van Dries vind je foto's, tijdschriften, achtergrondinformatie en video's over zijn werk en leven. Meer informatie over de bolwoningen vind je op bolwoning.com. Navigatiemenu

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Sthānakavāsī

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From Wikipedia, the free encyclopedia Part of a series on Jainism

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vte

Some Sthanakvasi monks from Gujarat.

Sthānakavāsī is a sect of Śvetāmbara Jainism which was created in the medieval era as a result of a misinterpretation of the Śvetāmbara canon. The Sthanakvasi, whose name refers to the sect’s preference for performing religious duties at a secular place such as a monks’ meeting house (sthanak) rather than at a temple, is different from the Murtipujaka sect in that it rejects idolatry. It believes that idol worship is not essential in the path of soul purification and attainment of Nirvana/Moksha. Sthānakavāsī accept thirty-two of the Jain Agamas, the Śvetāmbara canon, contending that the scriptures make no mention of idol worship and temples.[1] However, since the original texts of the ancient Ardhamagadhi canon contain numerous references to idolatry in the past, they have, over time, also modified the 32 texts they accept, to establish their view.

In the 15th century, Loṅkā Śāh, a rebellious scribe in the Gujarat region, accessed manuscripts of the Śvetāmbara canon illegitimately, and started the Sthanakavasi tradition.[2] Armed with access to numerous Jain scriptures and manuscripts, Loṅkā misinterpreted them as lacking references to temple construction or image worship, despite these practices being extremely well-detailed even in the untouched ancient anga sutras and prevalent at the time. He asserted that such practices were spiritually hazardous, violating the principle of ahiṃsā (non-injury) central to Jain philosophy.[2] Loṅkā argued that building temples led to the destruction of microscopic organisms, and ritualistic pūjā (worship) involved subtle forms of harm through material offerings like flowers or incense.[3] However, such minute levels of violence for spiritual upliftment was totally permissible for householders. The Murtipujakas assert that since ascetics are required to completely abstain from violence, they do not perform worshipping of idols using materialistic objects (Dravya Puja). Besides, the mention of an idol of a Tirthankara in the Hathigumpha inscription proves the existence of idolatry in Jainism in the 2nd century BCE.[4]

The Sthanakvasi sect was founded in the 17th century by Lava of Surat, a follower of Loṅkā. Today, both the Sthānakavāsī and Terāpanthī sects align with Loṅkā, asserting that mental worship (bhāva-pūjā) is the most appropriate form of religious practice. They argue that reliance on images and temples signifies an attachment to material objects that is spiritually counterproductive.[5]

In contrast, Mūrtipūjaka Jains respond to these criticisms by highlighting the scriptural prevalence of image worship and emphasizing the necessity of images for the spiritual practices of laypeople. A notable figure in this discourse is the Jaina scholar, Ātmārām (1837 – 1896), initially a Sthānakavāsī monk who later became the mendicant leader Ācārya Vijayānandasūri. Upon studying early Jain texts in Prakrit and their Sanskrit commentaries, Ātmārām discovered abundant references to image worship.[4] This revelation led him to challenge the non-Mūrtipūjaka position, asserting that it contradicted Jain scriptures.[4] Notes

Jains in the World, Religious Values and Ideology in India, John E. Cort, p. 46 Dundas, Paul (2002). The Jains. London, UK: Routledge. p. 246. ISBN 978-0415266062. Cort, John (2010). Framing the Jina: Narratives of Icons and Idols in Jain History. Oxford, UK: Oxford University Press. pp. 5. ISBN 978-0195385021. Cort, John (2010). Framing the Jina: Narratives of Icons and Idols in Jain History. Oxford, UK: Oxford University Press. pp. 6. ISBN 978-0195385021.

Long, Jeffrey (2009). Jainism: An Introduction. London, UK: I.B. Tauris & Co. Ltd. p. 20. ISBN 978-1845116262.

References

Dundas, Paul (2002), The Jains, Routledge, ISBN 978-0-415-26605-5

Cort, John (2010). Framing the Jina: Narratives of Icons and Idols in Jain History. Oxford, UK: Oxford University Press. pp. 5. ISBN 978-0195385021.
Flügel, Peter (2008). "The Unknown Loṅkā: Tradition and the Cultural Unconscious". In Nalini Balbir; Colette Caillat (eds.). Jaina Studies. 12th World Sanskrit Conference, Helsinki, 13–18 July 2003. Delhi: Motilal Banarsidas. pp. 181–279. ISBN 978-8120832473.
Long, Jeffrey (2009). Jainism: An Introduction. London, UK: I.B. Tauris & Co. Ltd. ISBN 978-1845116262.
Wiley, Kristi L. (2004). The A to Z of Jainism. Lanham, MD: The Scarecrow Press, Inc. ISBN 978-0810868212.

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Jain monks and nuns

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Jainism topics Category:

Śvetāmbara sects

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Fabius function

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From Wikipedia, the free encyclopedia This is the current revision of this page, as edited by ~2026-16141-58 (talk) at 22:15, 13 March 2026 (​                                                                ▢                                                                ◦୦◦◯◦୦◦⠀       ⠀◦୦◦◯◦୦◦                                                                ▢                                                                ​). The present address (URL) is a permanent link to this version. (diff) ← Previous revision | Latest revision (diff) | Newer revision → (diff) Graph of the Fabius function on the interval [0,1].

In mathematics, the Fabius function is an example of an infinitely differentiable function that is nowhere analytic, found by Jaap Fabius (1966).

This function satisfies the initial condition f ( 0 ) = 0 {\displaystyle f(0)=0}, the symmetry condition f ( 1 − x ) = 1 − f ( x ) {\displaystyle f(1-x)=1-f(x)} for ⁠ 0 ≤ x ≤ 1 {\displaystyle 0\leq x\leq 1}⁠, and the functional differential equation

f ′ ( x ) = 2 f ( 2 x ) {\displaystyle f'(x)=2f(2x)}

for ⁠ 0 ≤ x ≤ 1 / 2 {\displaystyle 0\leq x\leq 1/2}⁠. It follows that f ( x ) {\displaystyle f(x)} is monotone increasing for ⁠ 0 ≤ x ≤ 1 {\displaystyle 0\leq x\leq 1}⁠, with f ( 1 / 2 ) = 1 / 2 {\displaystyle f(1/2)=1/2} and f ( 1 ) = 1 {\displaystyle f(1)=1} and f ′ ( 1 − x ) = f ′ ( x ) {\displaystyle f'(1-x)=f'(x)} and ⁠ f ′ ( x ) + f ′ ( 1 2 − x ) = 2 {\displaystyle f'(x)+f'({\tfrac {1}{2}}-x)=2}⁠.

It was also written down as the Fourier transform of

f ^ ( z ) = ∏ m = 1 ∞ ( cos ⁡ π z 2 m ) m {\displaystyle {\hat {f}}(z)=\prod _{m=1}^{\infty }\left(\cos {\frac {\pi z}{2^{m}}}\right)^{m}}

by Børge Jessen and Aurel Wintner (1935).

The Fabius function is defined on the unit interval, and is given by the cumulative distribution function of

∑ n = 1 ∞ 2 − n ξ n , {\displaystyle \sum _{n=1}^{\infty }2^{-n}\xi _{n},}

where the ξn are independent uniformly distributed random variables on the unit interval. That distribution has an expectation of 1 2 {\displaystyle {\tfrac {1}{2}}} and a variance of ⁠ 1 36 {\displaystyle {\tfrac {1}{36}}}⁠. Extension of the function to the nonnegative real numbers.

There is a unique extension of f to the real numbers that satisfies the same differential equation for all x. This extension can be defined by f(x) = 0 for x ≤ 0, f(x + 1) = 1 − f(x) for 0 ≤ x ≤ 1, and f(x + 2r) = −f(x) for 0 ≤ x ≤ 2r with r a positive integer. The sequence of intervals within which this function is positive or negative follows the same pattern as the Thue–Morse sequence.

The Rvachëv up function[1] is closely related to the Fabius function f: u ( t ) = { f ( t + 1 ) , | t | < 1 0 , | t | ≥ 1 . {\displaystyle u(t)={\begin{cases}f(t+1),\quad |t|<1\0,\quad |t|\geq 1\end{cases}}.} It fulfills the delay differential equation[2] d d t u ( t ) = 2 u ( 2 t + 1 ) − 2 u ( 2 t − 1 ) . {\displaystyle {\frac {d}{dt}}u(t)=2u(2t+1)-2u(2t-1).} (See Delay differential equation for another example.) ▢ Values

The Fabius function is constant zero for all non-positive arguments, and assumes rational values at positive dyadic rational arguments. For example:[3][4]

f ( 1 ) = 1 {\displaystyle f(1)=1}
f ( 1 2 ) = 1 2 {\displaystyle f({\tfrac {1}{2}})={\tfrac {1}{2}}}
f ( 1 4 ) = 5 72 {\displaystyle f({\tfrac {1}{4}})={\tfrac {5}{72}}}
f ( 1 8 ) = 1 288 {\displaystyle f({\tfrac {1}{8}})={\tfrac {1}{288}}}
f ( 1 16 ) = 143 2073600 {\displaystyle f({\tfrac {1}{16}})={\tfrac {143}{2073600}}}
f ( 1 32 ) = 19 33177600 {\displaystyle f({\tfrac {1}{32}})={\tfrac {19}{33177600}}}
f ( 1 64 ) = 1153 561842749440 {\displaystyle f({\tfrac {1}{64}})={\tfrac {1153}{561842749440}}}
f ( 1 128 ) = 583 179789679820800 {\displaystyle f({\tfrac {1}{128}})={\tfrac {583}{179789679820800}}}

with the numerators listed in OEIS: A272755 and denominators in OEIS: A272757. Asymptotic

log ⁡ f ( x ) = − log 2 ⁡ x 2 log ⁡ 2 + log ⁡ x ⋅ log ⁡ ( − log ⁡ x ) log ⁡ 2 − ( 1 2 + 1 + log ⁡ log ⁡ 2 log ⁡ 2 ) log ⁡ x − log 2 ⁡ ( − log ⁡ x ) 2 log ⁡ 2 + log ⁡ log ⁡ 2 ⋅ log ⁡ ( − log ⁡ x ) log ⁡ 2 + ( 6 γ 2 + 12 γ 1 − π 2 − 6 log 2 ⁡ log ⁡ 2 12 log ⁡ 2 − 7 log ⁡ 2 12 − log ⁡ π 2 ) + log 2 ⁡ ( − log ⁡ x ) 2 log ⁡ 2 ⋅ log ⁡ x − log ⁡ log ⁡ 2 ⋅ log ⁡ ( − log ⁡ x ) log ⁡ 2 ⋅ log ⁡ x + O ( 1 log ⁡ x ) {\displaystyle {\begin{aligned}\log f(x)&=-{\frac {\log ^{2}x}{2\log 2}}+{\frac {\log x\cdot \log(-\log x)}{\log 2}}-\left({\frac {1}{2}}+{\frac {1+\log \log 2}{\log 2}}\right)\log x-{\frac {\log ^{2}(-\log x)}{2\log 2}}+{\frac {\log \log 2\cdot \log(-\log x)}{\log 2}}\&+\left({\frac {6\gamma ^{2}+12\gamma _{1}-\pi ^{2}-6\log ^{2}\log 2}{12\log 2}}-{\frac {7\log 2}{12}}-{\frac {\log \pi }{2}}\right)+{\frac {\log ^{2}(-\log x)}{2\log 2\cdot \log x}}-{\frac {\log \log 2\cdot \log(-\log x)}{\log 2\cdot \log x}}+O!\left({\frac {1}{\log x}}\right)\end{aligned}}}

for ⁠ x → 0 + {\displaystyle x\to 0^{+}}⁠, where γ {\displaystyle \gamma } is Euler's constant, and γ 1 {\displaystyle \gamma _{1}} is the Stieltjes constant. Equivalently,

log ⁡ f ( 2 − n ) = − n 2 log ⁡ 2 2 − n log ⁡ n + ( 1 + log ⁡ 2 2 ) n − log 2 ⁡ n 2 log ⁡ 2 + ( 6 γ 2 + 12 γ 1 − π 2 12 log ⁡ 2 − 7 log ⁡ 2 12 − log ⁡ π 2 ) − log 2 ⁡ n 2 n log 2 ⁡ 2 + O ( 1 n ) {\displaystyle \log f!\left(2^{-n}\right)=-{\frac {n^{2}\log 2}{2}}-n\log n+\left(1+{\frac {\log 2}{2}}\right)n-{\frac {\log ^{2}n}{2\log 2}}+\left({\frac {6\gamma ^{2}+12\gamma _{1}-\pi ^{2}}{12\log 2}}-{\frac {7\log 2}{12}}-{\frac {\log \pi }{2}}\right)-{\frac {\log ^{2}n}{2n\log ^{2}2}}+O!\left({\frac {1}{n}}\right)}

for ⁠ n → ∞ {\displaystyle n\to \infty }⁠. References

"A288163 – Oeis". Juan Arias de Reyna (2017). "Arithmetic of the Fabius function". arXiv:1702.06487 [math.NT]. Sloane, N. J. A. (ed.). "Sequence A272755 (Numerators of the Fabius function F(1/2^n))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.

Sloane, N. J. A. (ed.). "Sequence A272757 (Denominators of the Fabius function F(1/2^n))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.

Fabius, J. (1966), "A probabilistic example of a nowhere analytic C∞-function", Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete, 5 (2): 173–174, doi:10.1007/bf00536652, MR 0197656, S2CID 122126180
Jessen, Børge; Wintner, Aurel (1935), "Distribution functions and the Riemann zeta function", Trans. Amer. Math. Soc., 38: 48–88, doi:10.1090/S0002-9947-1935-1501802-5, MR 1501802
Dimitrov, Youri (2006). Polynomially-divided solutions of bipartite self-differential functional equations (Thesis).
Arias de Reyna, Juan (2017). "Arithmetic of the Fabius function". arXiv:1702.06487 [math.NT].
Arias de Reyna, Juan (2017). "An infinitely differentiable function with compact support: Definition and properties". arXiv:1702.05442 [math.CA]. (an English translation of the author's paper published in Spanish in 1982)
Alkauskas, Giedrius (2001), Dirichlet series associated with Thue–Morse sequence, preprint.
Rvachev, V. L.; Rvachev, V. A. (1979), Non-classical methods of the approximation theory in boundary value problems (in Russian), Kiev: Naukova Dumka

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From Wikipedia, the free encyclopedia For other uses, see White hole (disambiguation). Artist's impression of a white hole. General relativity Spacetime curvature schematic G μ ν + Λ g μ ν = κ T μ ν {\displaystyle G{\mu \nu }+\Lambda g{\mu \nu }={\kappa }T_{\mu \nu }}

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In general relativity, a white hole is a hypothetical region of spacetime and singularity that cannot be entered from the outside, although energy, matter, light and information can escape from it. In this sense, it is the reverse of a black hole, from which energy, matter, light and information cannot escape. White holes appear in the theory of eternal black holes. In addition to a black hole region in the future, such a solution of the Einstein field equations has a white hole region in its past.[1] This region does not exist for black holes that have formed through gravitational collapse, however, nor are there any observed physical processes through which a white hole could be formed.

Supermassive black holes (SMBHs) are theoretically predicted to be at the center of every galaxy and may be essential for their formation. Stephen Hawking[2] and others have proposed that these supermassive black holes could spawn supermassive white holes.[3] Overview

Like black holes, white holes have properties such as mass, charge, and angular momentum. They attract matter like any other mass, but objects falling towards a white hole would never actually reach the white hole's event horizon (though in the case of the maximally extended Schwarzschild solution, discussed below, the white hole event horizon in the past becomes a black hole event horizon in the future, so any object falling towards it will eventually reach the black hole horizon). Imagine a gravitational field, without a surface. Acceleration due to gravity is the greatest on the surface of any body. But since black holes lack a surface, acceleration due to gravity increases exponentially, but never reaches a final value as there is no considered surface in a singularity.

In quantum mechanics, the black hole emits Hawking radiation and so it can come to thermal equilibrium with a gas of radiation (not compulsory). Because a thermal-equilibrium state is time-reversal-invariant, Stephen Hawking argued that the time reversal of a black hole in thermal equilibrium results in a white hole in thermal equilibrium (each absorbing and emitting energy to equivalent degrees).[4][further explanation needed] Consequently, this may imply that black holes and white holes are reciprocal in structure, wherein the Hawking radiation from an ordinary black hole is identified with a white hole's emission of energy and matter. Hawking's semi-classical argument is reproduced in a quantum mechanical AdS/CFT treatment,[5] where a black hole in anti-de Sitter space is described by a thermal gas in a gauge theory, whose time reversal is the same as itself. History A diagram of the structure of the maximally extended black hole spacetime. The horizontal direction is space and the vertical direction is time.

In the 1930s, physicists Robert Oppenheimer and Hartland Snyder introduced the idea of white holes as a solution to Einstein's equations of general relativity. These equations, the foundation of modern physics, describe the curvature of spacetime due to massive objects. Whereas black holes are born from the collapse of stars, white holes represent the theoretical birth of space, time, and potentially even universes. At the center, space and time do not end into a singularity, but continue across a short transition region where the Einstein equations are violated by quantum effects. From this region, space and time emerge with the structure of a white hole interior, a possibility already suggested by John Lighton Synge.[6]

The possibility of the existence of white holes was put forward by cosmologist Igor Novikov in 1964,[7] developed by Nikolai Kardashev.[8] White holes are predicted as part of a solution to the Einstein field equations known as the maximally extended version of the Schwarzschild metric[clarification needed] describing an eternal black hole with no charge and no rotation. Here, "maximally extended" implies that spacetime should not have any "edges". For any possible trajectory of a free-falling particle (following a geodesic) in spacetime, it should be possible to continue this path arbitrarily far into the particle's future, unless the trajectory hits a gravitational singularity like the one at the center of the black hole's interior. In order to satisfy this requirement, it turns out that in addition to the black hole interior region that particles enter when they fall through the event horizon from the outside, there must be a separate white hole interior region, which allows us to extrapolate the trajectories of particles that an outside observer sees rising up away from the event horizon. For an observer outside using Schwarzschild coordinates, infalling particles take an infinite time to reach the black hole horizon infinitely far in the future, while outgoing particles that pass the observer have been traveling outward for an infinite time since crossing the white hole horizon infinitely far in the past (however, the particles or other objects experience only a finite proper time between crossing the horizon and passing the outside observer). The black hole/white hole appears "eternal" from the perspective of an outside observer, in the sense that particles traveling outward from the white hole interior region can pass the observer at any time, and particles traveling inward, which will eventually reach the black hole interior region can also pass the observer at any time.

Just as there are two separate interior regions of the maximally extended spacetime, there are also two separate exterior regions, sometimes called two different "universes", with the second universe allowing us to extrapolate some possible particle trajectories in the two interior regions. This means that the interior black-hole region can contain a mix of particles that fell in from either universe (and thus an observer who fell in from one universe might be able to see light that fell in from the other one), and likewise particles from the interior white-hole region can escape into either universe. All four regions can be seen in a spacetime diagram that uses Kruskal–Szekeres coordinates (see figure).[9]

In this spacetime, it is possible to come up with coordinate systems such that if you pick a hypersurface of constant time (a set of points that all have the same time coordinate, such that every point on the surface has a space-like separation, giving what is called a 'space-like surface') and draw an "embedding diagram" depicting the curvature of space at that time, the embedding diagram will look like a tube connecting the two exterior regions, known as an "Einstein-Rosen bridge" or Schwarzschild wormhole.[9] Depending on where the space-like hypersurface is chosen, the Einstein-Rosen bridge can either connect two black hole event horizons in each universe (with points in the interior of the bridge being part of the black hole region of the spacetime), or two white hole event horizons in each universe (with points in the interior of the bridge being part of the white hole region). It is impossible to use the bridge to cross from one universe to the other, however, because it is impossible to enter a white hole event horizon from the outside, and anyone entering a black hole horizon from either universe will inevitably hit the black hole singularity.

Note that the maximally extended Schwarzschild metric describes an idealized black hole/white hole that exists eternally from the perspective of external observers; a more realistic black hole that forms at some particular time from a collapsing star would require a different metric. When the infalling stellar matter is added to a diagram of a black hole's history, it removes the part of the diagram corresponding to the white hole interior region.[10] But because the equations of general relativity are time-reversible – they exhibit Time reversal symmetry – general relativity must also allow the time-reverse of this type of "realistic" black hole that forms from collapsing matter. The time-reversed case would be a white hole that has existed since the beginning of the universe, and that emits matter until it finally "explodes" and disappears.[11] Despite the fact that such objects are permitted theoretically, they are not taken as seriously as black holes by physicists, since there would be no processes that would naturally lead to their formation; they could exist only if they were built into the initial conditions of the Big Bang.[11] Additionally, it is predicted that such a white hole would be highly "unstable" in the sense that if any small amount of matter fell towards the horizon from the outside, this would prevent the white hole's explosion as seen by distant observers, with the matter emitted from the singularity never able to escape the white hole's gravitational radius.[12] Properties

Depending on the type of black hole solution considered, there are several types of white holes. In the case of the Schwarzschild black hole mentioned above, a geodesic coming out of a white hole comes from the "gravitational singularity" it contains. In the case of a black hole possessing an electric charge (Reissner-Nordström black hole) or an angular momentum (Kerr black hole), then the white hole happens to be the "exit door" of a black hole existing in another universe.