....Such a mapping function could exist within a highly restricted subset of the set of all possible conductive objects. ...........
If I'm not mistaken, your entire post is basically nothing more than what used to be called : "Ring enhancement programs". Because every since TID was introduced to the market (starting in 1982), it became no secret that you could play the "Las Vegas Odds". And notch IN certain zones, and notch OUT certain zones.
Because, for example, if you were to test a random 1,000 gold rings (like, let's say your friend owned a jewelry store, so you could spend an entire night air sampling each one). Let's say you made meticulous notes of each one's TID #. Then let's say you went to a typical junky blighted park, entered into "relic mindset mode" and dug : 1,000 aluminum junk items. Then you spent all night sampling the TID #s of these recurring typical aluminum junk park items.
THEN AFTER YOU'VE DONE THE ABOVE COMPUTER SPREAD SHEETS, then yes : You would indeed notice that there are TID # ranges where it's most likely to be trash . And other #'s with a higher degree of gold rings in that zone.
FOR EXAMPLE : Very few gold rings read down in the foil range. Unless you're talking very dainty ladies rings. Of which perhaps only 5% of the 1000 gold rings fall into that TID range. Contrast to 50% of the aluminum you dug might fall into that range. Hence presto: You knock out those ranges. And for example you knock out nickels' exact TID #, since : Odds are , it will be a nickel AND NOT GOLD (since perhaps only 5% of rings fell *exactly* on that #). And you would knock out beaver tail round tabs (of the most common recurring soft-drink). Because go figure, those are the bane of detecting. And perhaps only 20% of the gold rings fell in that range.
However, you open up all the other #'s, and perhaps that still accounts for 50% of the rings (since men's fatties read well above round tab). This was called "Ring Enhancement programs". And several wrote them (after these type studies), that users were supposed to program in to their Spectrum, XLT, Eagle, Teknetics, etc....
But the devil was in the details : YOU WILL STILL MISS GOLD RINGS AND YOU WILL STILL DIG A BOATLOAD OF TRASH. And if you're in an area where lawnmowers made can slaw out of aluminum cans, then : You can kiss these programs goodbye. You can chuck them out the window. Same for place where BBQ's go on (parks with campfires, BBQs, etc...) . Because those molten aluminum turds READ ALL OVER THE RANGE.
And sure as heck, someone's bound to try to claim that : That they can combine ring-enhancement programs , with sound characteristics (claiming gold is mellower or rounder or softer, etc....) . Here's what you do to solve this person's problem : You merely invite them out to the nearest blighted urban turfed park. Turn them loose. And : You will hear the sound of crickets. You will immediately cure them of their notion.