How does Brahman become JagatkaaraNam? Shiva and Vishnu Purana non-difference

In the Shiva Purana is a stuti by Vishnu and Brahmaa addressed to Shiva:
https://sa.wikisource.org/s/xlj

त्वमेव निर्गुणस्सत्योऽनंतोऽनंतपराक्रमः ।।
सगुणश्च सन्निवेशः प्रकृतेः पुरुषात्परः ।। ३३ ।।
You alone are NirguNa, Satya, Eternal, Infinite and of measureless power. You are Saguna too, transcending the Prakriti and Purusha (jiva).
रजसा सृष्टिसमये त्वं ब्रह्मा सृष्टिकृत्प्रभो ।।
सत्त्वेन पालने विष्णुस्त्रिभुवावनकारकः ।। ३४ ।।
Owing to Rajoguna, at the time of creation, you are Brahmaa, the Creator, O Lord. By assuming Sattvaguna, you alone are Vishnu, protecting the three worlds. 
तमसा प्रलये रुद्रो जगत्संहारकारकः ।।
निस्त्रैगुण्ये शिवाख्यातस्तुर्य्यो ज्योतिःस्वरूपकः ।। ३५ ।।  

By Tamoguna, at pralaya, you are Rudra, the destroyer. Beyond the three gunas, you are the Turya called Shiva, Pure Consciousness.
This is in consonance with the Mandukya upanishad 7th mantra which teaches Brahman as the Chaturtham. Turiya, beyond the entire creation where alone the three gunas operate.  Turiya is Nirguna Brahman.  
त्रयाणां जनकः   त्रिगुणातीत निर्व्यग्र त्रिदेवजनक प्रभो ।। २७ ।।  
This verse says: tri-deva-janaka which means: You, Turiya Shiva, are the source of the Trimurtis.  
We have the same idea taught in the Vishnu Purana too: 

From Vishnu Purana:

In the Vishnu Purana, at the very beginning, we have this message that tells us in no uncertain terms that the cosmic functions such as creation and destruction are ‘really’ that of Brahman. The functions require the operation of guna-s and thereby it is only Brahman, assuming the appropriate gunas indulges in those functions:  

जुषन् रजो गुणं तत्र स्वयं विश्वेश्वरो हरिः  ।

ब्रह्माभूत्वास्य जगतो विसृष्टौ संप्रवर्तते  ॥ १,२.६१ ॥

सृष्टं च पात्यनुयुगं यावत्कल्पविकल्पना  ।

सत्त्वभृद्भगवान्विष्णुरप्रमेयपराक्रमः  ॥ १,२.६२ ॥

By attaching himself to Rajo guna, and himself having become Brahma, Vishnu (Brahman/Ishwara) engages in the creation of the world. And assuming the Sattva guna, Vishnu himself of mighty power engages in maintaining the created world. [the particle ‘bhrt’ after sattva in the above verse teaches that Brahman ‘assumes’ sattvaguna. This is a strong refutation of the unvedic idea that Vishnu is ‘always of sattva guna.’ For, the Vedanta teaches that Brahman is beyond all gunas, even sattva.]

तमोद्रेकी च कल्पान्ते रुद्ररूपी जर्नादनः  ।

मैत्रेयाखिलभूतानि भक्षयत्यतिदारूणः  ॥ १,२.६३ ॥

भक्षयित्वा च भूतानि जगत्येकार्णवीकृते  ।

नागपर्यङ्कशयने शेते च परमेश्वरः  ॥ १,२.६४ ॥

At the end of the Kalpa, Janardana of Rudra-form, who is of immense Tamas, O Maitreya, gobbles up the entire creation. And having made the world one mass, Parameshwara rests on the serpent-couch. [Sridhara Swamin says here: Parameshwara sleeps in his mula svarupa of brahma, shiva, etc. avatara.  Thus Brahma, Vishnu and Shiva are only avataras of Brahman, no different from Rama, Krishna, Narasimha, etc., a concept that is anathema for those theological schools that hold a Vishnu that is absolutely distinct from the ‘jivas’  that are Brahma and Shiva is the Para Brahman.]

Here the Purana clearly says it is Vishnu alone, owing to immense Tamas, has become Rudra. This also is a refutation of the theological schools’ idea that Vishnu is different from Brahma and Rudra. Such laughable ideas have no place in the Vedanta/Vishnu Purana.

प्रबुद्धश्च पुनः सृष्टिं करोति ब्रह्मरूपधृक् ॥ १,२.६५ ॥

सृष्टिस्थित्यन्तकरणीं ब्रह्मविष्णुशिवात्मिकाम्  ।

स संज्ञां याति भगवानेक एव जनार्दनः  ॥ १,२.६६ ॥

The Purana confirms the idea by reiterating that again, at the beginning of the next cycle, Brahman (Vishnu), taking up the form of Brahma, engages in creation. Thus, One Lord, Janardana, alone gets the names of Brahma, Vishnu and Shiva.  This is what is stated by Sureshwara in the Brihadaranya Vartika. This idea is also inimical to theological schools as they cannot tolerate Vishnu  (a finite deity) being also Brahma and Rudra. They come up with childish ideas as ‘these statements mean ‘Vishnu is antaryami of Brahma and Shiva.’ They fail to understand that if one Janardana has to get three names owing to different functions, upadhis, then Janardana has to be the antaryami of Vishnu also. Because even this function is also only an assumed one, assuming sattva guna, which is not the native guna of Janardana. This is what is taught in the above lines. Sridhara Swamin continues; ब्रह्मादिरूपाणि च तद्व्यतिरिक्तानि न भवन्ति इत्येतदाह – सृष्टिस्थित्यन्तकरणीं.  The VP says: the forms such as Brahma, Vishnu and Shiva are not distinct from Janardana by the verse: सृष्टिस्थित्यन्तकरणीं… 

Thus, we have evidence for Turiya Shiva and Turiya Vishnu in the works of Veda Vyasa.

Om Tat Sat