Let's have some fun...
I haven't thought this all the way through so I may change my consideration, but, for the moment, I'm very leery of this question being useful. We see the question (posed rhetorically) a lot, often mid-squabble. It's kinda an expression of sheer scepticism that can be used to thwart any attempt to come to a conclusion. We also see it associated to a list (Ron's ?) of 4 Types of Audiophiles, one being those who seek reproduction true to what is on the recording, or some such.
Microstrip's formulation (above) taken from Dave C's cue asks about the artists' intent. This is somewhat problematic because intent is difficult to gauge through listening. If they're still around, we could ask performers - "does this recording exhibit what you intended?" Suppose they say 'yes' or 'no' - what does that tell us? That the recording is faithful to their idea of what they wanted it be? Huh? What does that tell us?
Inspired by remembering that Descarte's scepticism ("How do I know that I exist?) was ultimately the cause of his certainty (cogito ergo sum), I'll rashly answer the question. :-O
We start with the notion that at such-and-such a time and place the XYZ Orchestra of the Air along with The 4th Street Belmont Singers performed Brahm's Schicksalslied Op.54 and that was captured by microphones, etc. and put on tape.
There was an act of recording; the verb. But is that 'the recording' ? If it is, all the scepticism boils down to saying we cannot relive the past, so we can't really know. Even if we could, that's not the recording of a performance, it is the performance.
Is the so-called 'master tape' the recording? No, it's a magnetic tape on a metal reel. Even if you hold it close to your ear you won't hear the Song of Destiny. Not even a pre-echo.
I reject the notion that "the recording" exists as some kind of timeless objective Platonic Form that is The True Recording, that it is something we can never truly know, something that at best we can only grasp as 'shadows' of the recording. This seems to be the angle where the question is coming from.
Music is performance art. It exists in time and is transient. A recording must be performed to hear music. It moves from the potential (media) to the actual through time - when the recording is performed, when the record is played. Every time you play a record you hear exactly what is on the recording.
IME it all depends on your source hardware and software. A good piece of software, wether tape, lp or cd played back on good to very good systems should give a human being a pretty decent and engaging facsimile of the original event. The next step up is superior and exceptional software either lp or if you're lucky enough tape, will transport one even closer to that event. Then playback that superior lp on a properly setup Beyond level turntable like the American Sound AS-2000 with a system to match and one will be attending that venue. This isn't about 1:1 reproduction of the event, we're not test equipment set up to receive rudimentary data via a cable and assign numerical values, we receive data through extremely sophisticated sensory equipment and process it internally through an incredible nervous system then internalize it using other senses and emotion. There's a lot of hidden information in tiny grooves of grooves of a record which most people haven't heard nor are aware that it exists until one hears that record played on something like the AS-2000. Human beings are very capable of consuming and processing this micro information, it's what we need to build a near complete picture of the event with our nervous system. This is what matters, we can process the data and recreate reality if all the information is present, even if altered. Artists or engineers intent is irrelevant it's the level of their competency that matters, a good musician will deliver the goods and a good engineer will record it all even with some alteration.
David