Which is a certified/authentic guide to entering Jhnanas?

Is there a certified, peer reviewed instruction manual to entering Jnanas?

The answer is yes and no.

There are some universalities but when one comes to applying a particular approach devised by another person there will always be an element of experimentation, or at least there should be if one isn't getting results. Once you've realized the hindrances and let go the rest is mostly self-directed intuitive feeling-around-in-the-dark.

You could start with learning about your five mental hindrances. Once you see how they hinder your progression it becomes natural to let them go. A lot of people want to skip this part, then discover that they cannot reach jhana because they don't have the knowledge of the hindrances. It save a huge amount of time to go through these meticulously. There are times where hindrances don't occur and this can be capitalized on but I would always suggest you develop knowledge of how your hindrances arise in your sessions. Through this knowledge one can traverse those difficulties and navigate across the undulating contours of the meditative terrain.

Even with this, it isn't a one-size-fits all approach. We all have different things happening with the mind. You will only learn by examining yourself carefully.

Avarana Sutta

Mahasatipatthana Sutta (Section on Hindrances)

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

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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

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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.

Ajahn Brahmavamso

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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 correct samadhi.

Ajahn Buddhadasa

First, without being explicitly jhana, to get the citta into samadhi, like here https://suttacentral.net/an10.2/en/sujato http://obo.genaud.net/dhamma-vinaya/ati/sn/05_mv/sn05.55.040.than.ati.htm#p1 there is, before, 'sukhaṃ vediyati'', meaning pleasant vedana or ''sukkha''. Before the pleasant vedana, there is ''kāyo passambhati'', which is a tranquil body. Before, the tranquil body, there is ''pītimanassa'' which is mano having piti. Before mano has piti, there is ''Pamuditassa'', which is the experience of joy (of being moral and rejecting thought of delight on kama and ill will, which makes you keep the 5 precepts and all those rules about morality). Before the joy, there is a lack of regrets.

This stuff about eagerness for renunciation, seeing drawbacks, and nirodha is the discriminating factor between a success and a failure to reach sotapanna or arhanthood through the jhanas, http://obo.genaud.net/dhamma-vinaya/ati/an/04_fours/an04.178.than.ati.htm#p1

Like the buddha said about him, https://suttacentral.net/an9.41/en/sujato, he claimed that renunciation of sensuality was good, but his citta was not '' confident'' in it. And as usual, the citta is not inclined towards renunciation due to a lack of seeing a danger in sensuality. Once he saw this danger, he managed to get the jhanas.

Now explicitly for the jhanas. First there is a whole vagga about jhanas http://obo.genaud.net/backmatter/indexes/sutta/sn/03_kv/idx_34_jhanasamyutta.htm

second, the usual way to enter the first jhana is to be ''aloof from sense-desires, aloof from unprofitable states,'' from the typical formulation http://www.buddha-vacana.org/formulae/4jhana.html#1-cl and the buddha says that samasamadhi is precisely those jhanas http://www.buddha-vacana.org/sutta/samyutta/maha/sn45-008.html#sammasamadhi

so the situation where somebody is ''aloof from sense-desires, aloof from unprofitable states,'' should stem form the joy and lack of regrets from being moral and seeing drawbacks of cravings for and delight in sensuality.