Q: How do the Three Proofs apply to provide validity of the Dai-Gohonzon?
A: First the Documentary Proof:

Nichiren defined the Gohonzon as: the great object of veneration in the whole world. He wrote “Believe in the Gohonzon, the supreme object of worship in Jambudvipa." (Writings of Nichiren Daishonin, p. 386)

He inscribed various Gohonzons for his immediate followers for their own practice at that time. But by inscribing these individual Gohonzons, Nichiren still did not fulfil the “Great Desire” of the Juryo chapter of the Lotus Sutra, to provide “all people” with the means for attaining Buddhahood. The Buddha of the Juryo Chapter’s Great Desire concerned all people:
“Mai ji sa ze nen. I ga ryo shujo. Toku nyumu-jo do. Soku joju busshin."

"At all times I think to myself
How can I cause living beings
To gain entry into the unsurpassed way 
and quickly acquire the body of a Buddha.”
(from the Lotus Sutra, end of the 16th Chapter)
This Great Desire of the Buddha is perfectly embodied in the doctrine of the Dai-Gohonzon, a “Gohonzon for all people” as the Object of Veneration, inscribed by Nichiren for future generation. The Dai-Gohonzon is in complete accord with the Lotus Sutra and with Nichiren’s teachings.

Nichiren was very clear at declaring that the purpose of his advent was inscribing the Gohonzon:  "... I will inscribe the treasure tower especially for you. This is the reason for my advent in this world” (Writings of Nichiren Daishonin, p. 300). 

But even after he inscribed tens of Gohonzons “especially for” individual believers, he did not consider his purpose of advent to be fulfilled yet until the year 1279, the year of inscribing the Dai-Gohonzon for all humanity. Nichiren clearly refers to "fulfilling his purpose" only in 1279 in his letter “Persecutions Befalling the Sage,” where he stated 

“Now in the second year of Koan (1279), it is twenty-seven years since I first proclaimed the true teaching at Seicho-ji temple.… The Buddha fulfilled the purpose of his advent in a little over forty years; T'ien-t'ai took about thirty years, and Dengyo, some twenty years. I have spoken repeatedly of the indescribable persecutions they suffered during those years. For me it took twenty-seven years, and the persecutions I faced during this period are well known to you all.” 
(Writings of Nichiren Daishonin, p. 996)
Most of the 120 Gohonzons available today were inscribed before 1279, the year which he declared as the year of fulfilling the purpose of his advent, and the year of inscribing the Dai-Gohonzon for all humanity. 

This work has been compiled by individual SGI members and is solely our personal opinion, based on years of practice and study.