Do the Gospel stories faithfully fall within what relevant witnesses were saying?

Specialists in onomastic studies have catalogued over 3,000 names from tomb inscriptions and similar writings around 1st century Palestine. That's a lot. And as a result, we now know that the very specific Jewish names and name-ratios of in 1st century Palestine precisely matches the combined names and name-ratios in the four Gospels and the book of Acts (a robust sample size).

This is relevant because the name-ratio correspondance to onomastic studies is easy to explain if the material in the Gospels and Acts is witness-based, that is to say, if the witness-sources were simply recounting the genuinely random names of people involved in authentic historical episodes. By contrast, no other explanation can easily explain this correspondence. (For example, even liars perfectly located in AD 30 Palestine would be unlikely to conjure up a genuine random sampling of names that gets the ratios right, and for legend-makers outside of Palestine it would be straightforwardly impossible [for example the name-ratios in Egypt at this time are completely different]).¹ Moreover, since Jewish names pervade the Gospels and Acts, this correspondence is a statement on the Gospels and Acts as a whole, so if any real number of fabricated stories were even mixed in with the Gospels and Acts, this correspondence could be put in jeopardy.

The Gospels abound in stories which we can—for reasons internal to the story itself— conclude came ultimately from the testimony of one or more witnesses.

This is relevant because it means mechanisms were in place which resulted in authentic witness-testimony abounding in the Gospels. By contrast, while there may be evidence of some flexibility in story-telling side-details, there is no example-based evidence of mechanisms operating in Gospel construction which would lead us to think seriously fabricated Jesus-biography was incorporated. Extrapolating from these two results, we can infer that probably most or all of the Gospel material is witness-based and not fabricated.

Rather than deviating from what the relevant witnesses themselves would’ve said, did the Jesus biography circulated by early Christians align with what eyewitnesses remembered and testified to?

This is relevant because the Gospels depended on sources for virtually all of their content, and if witness-based Jesus-bio predominated in this era, then that means the Gospel authors would’ve likely included witness-based stories even without putting in any work to check; i.e. it would have been harder for them to find and relay a false legend, even if they tried.

Rather than just writing down willy-nilly whatever the heart, the gospel authors tended to diligently ground or confirm their material in the testimony of witnesses, either interviewing them directly or taking extra steps to ensure their content properly traces back to a witness (for example, by interviewing and running content by friends or relatives who would know the truth).

This is relevant because it essentially entails that the Gospel traditions (i.e. the Jesus-bio which the Gospel authors ultimately incorporated into the gospels) echoed what witnesses said and/or were saying.

Whether the Gospel stories originated prior to the Gospels being written or not, when they did form, they formed in an honest way, rather than as the result of someone inventing them; the content is not legendary.

This is relevant because, if the content is not legendary, then that leaves few or no other ways the Gospel traditions could have entered into circulation. The hypothesis that the content simply formed from witnesses remembering Jesus and talking about it stands strongest.

Most Jesus biography that was reported in the gospels faithfully falls within what the Jerusalem church was saying and circulating.

This is relevant if the Jerusalem church’s Jesus-bio is a subset of witness testimony (e.g. it is where the apostles and major witnesses resided). So, there is a transitive relation here: if the Gospels' content is a subset of the Jerusalem church's, and the Jerusalem church's teachings on Jesus is a subset of what witnesses were saying, then by transitivity the Gospels content is a subset of what witnesses were saying.

The historical claims in the Gospels are usually or always historically accurate.

This is relevant because it is best explained by its having conformed to witness testimony rather than chance or any other competing explanation.