I havent read any reviews or blogs or internet postings of anyone who has entered Jhnanas through the instruction set of AB.
Real jhana is a supernormal state. At least for monks, it is a transgression to reveal a supernormal state to the general public. Also, since jhana silences speech, it is doubtful a layman that has reached real jhana would announce it to people because it is simply contrary to jhana.
When a person, by having no interest whatsoever in sex & have no fear of aloneness (solitude), reaches jhana, the mind has the clarity to discern the common worldly person, attached to sex & ego, cannot reach jhana. Therefore, they would not declare to worldly people they have reached jhana. To do otherwise would be similar to trying to teach calculus to a monkey.
The link seems to be talking on similar lines but different language.
I doubt Gunaratana would teach the same as AB. I imagine Gunaratana would teach (Hindu) yogic (manipulative) practises from commentaries, such as the Visuddhimagga.
Is there a certified, peer reviewed instruction manual to entering Jnanas?
Only a relatively tiny proportion of Buddhists have attained real jhana. There is no such thing as "certified" by peer review. The only way to "certify" instructions is to compare them to the Pali suttas.
In brief, Ajahn Brahm, as written in his book, says his instructions based on "letting go" ("vossagga") are how the Buddha taught in SN 48.9 (SN 48.10 and MN 118).
Can you provide any other instruction manual link preferably if you have experienced it.
It is not proper to ask people to declare if they have experienced jhana. The path is based on the aspirations of the student rather than the attainments of the teacher. If a student has a worldly attitude, its unlikely they can reach jhana (because ego is too strong in the psyche).
This said, if you want to follow instructions other than Ajahn Brahm, I recommend to read the relevant posts on Buddhism Stack Exchange by the poster named Dhammadhatu.
In summary, AB's book is based on the following words of the Buddha found in SN 48.9, SN 48.10 and MN 118. Therefore, the AB method has been certified by the Lord Buddha.
And what is the faculty of concentration? There is the case where a monk, a disciple of the noble ones, making it his object to let go (vossagga),
attains concentration, attains singleness of mind. Quite withdrawn
from sensuality, withdrawn from unskillful mental qualities, he enters
& remains in the first jhana...
SN 48.9 Indriya-vibhanga Sutta
There is the case where a monk develops concentration as a factor for awakening dependent on seclusion, dependent on dispassion, dependent
on cessation, resulting in relinquishment (vossagga).
MN 118 Anapanasati Sutta
Simply put, Jhana states are stages of letting go. One cannot be attached to letting go. Just as one cannot be imprisoned by freedom.
The joy and happiness that arises with the beautiful breath is fueled
by the letting go of burdens such as past and future, internal
commentary and diversity of consciousness. Because it is a delight
born of letting go, it cannot produce attachment.
As for samadhi, an empty mind is the supreme samadhi, the supremely focused firmness of mind. The straining and striving sort of samadhi
isn't the real thing and the samadhi which aims at anything other than
non-clinging to the five khandas is micchasamadhi (wrong or perverted
samadhi). You should be aware that there is both micchasamadhi and
sammasamadhi (right or correct samadhi). Only the mind that is empty
of grasping at and clinging to 'I' and 'mine' can have the true and
perfect stability of sammasamadhi. One who has an empty mind has