Are there in universe references to technologies utilized in the Star Trek TNG series that were discovered during Star Trek TOS? For instance, android tech? Norman 1 from the "I, Mudd" episode should have been a treasure trove of data.
Spock gathering data?
Norman X?
No, there is no sign of any of the technologies that Kirk discovered on his legendary voyages. These missing technologies are the elephant in the room in any discussion of post-Kirk Star Trek. Consider that V'ger was at least the eleventh machine intelligence Kirk encountered. Others include:
Leaving aside the cybernetics breakthroughs and unlimited time travel possibilities, Kirk also discovered substances that amplify psi abilities (Plato's Stepchildren), accelerate time (Wink of an Eye), and turn crones into beautiful women (Mudd's Women). There was a truth machine (Court Martial, Wolf in the Fold). There was the Kelvan technology, including their superfast warp drive and human-to-styrofoam-to-human encoding (By Any Other Name). There was the IQ boosting "Teacher" technology of the Eymorgs (Spock's Brain). Just Flint's bag of tricks --- cybernetics, miniaturization, stasis, instantaneous transport (Requiem For Methuselah) --- could have jump-started whole industries.
If we are to accept that these events are part of the Star Trek canon, then the conspicuous absence of all these technologies in the 24th century Federation must be by design. My favorite pet theory is that there is some sort of technology police like Larry Niven's ARM that quietly squirrels away the dangerous knowledge to keep it from destabilizing society. There is some support for this theory to be found in the Star Trek: Voyager episode "The Omega Directive", where Kirk-era information about warp-destroying omega particles was shown to be suppressed by Starfleet.
During Kirk's era, AI Is A Crapshoot (Often, at least):
More than likely, this turned Federation scientists away from true AI for a long time. Even in the TNG era, Soong created Data and his other androids independently of Starfleet and the Federation. (Besides, in most of these cases, Kirk destroyed the evidence and there was nothing to study.)
There is another possibility, though. It took over two hundred years for Starfleet to start making Holodecks after they first encountered that technology. Some of what Kirk found is probably still in research and development.
This is a scientific discovery rather than an exploratory/archeological discovery that is probably more what the OP implicitly wanted. But considering the top answer says no examples I'll add something.
One of the innovations in the 1987 TNG writers guide (page 36 or pdf page 42 in my file) is a mention that Dilithium can be re-crystallised and crystals don't have significant problems anymore. Implicitly avoiding a rehash of TOS style scarcity episodes. (Which leaves room for problematic holodecks!)
How can dilithium be re-crystallised in the 24th century? From a necessity is the mother of invention time travel incident. A klingon bird of prey's dilithium crystals degraded from the stress of traveling to the 1980s to bring humpback whales back to the future.
Note gamma rays are high energy photons.
TNG Relics http://www.chakoteya.net/NextGen/230.htm
SCOTT: The Captain wanted to try a cold start of the warp engines. I told him that without a proper phase lock it would take at least thirty minutes You canna change the laws of physics, I told him, but he wouldn't believe me, so I had to come up with a new engine start-up routine. Do you know that your dilithium crystals are going to fracture?
LAFORGE: We recomposite the crystals while they're still inside the articulation frame. Look, Mister Scott, I'd love to explain everything to you, but the Captain wants this spectrographic analysis done by thirteen hundred hours.
From TNG Technical Manual Section 5.2 Matter/Antimatter Reaction Injectors
(See last sentence)
THE ROLE OF DILITHIUM The key element in the efficient use of M/A reactions is the dilithium crystal. This is the only material known to Federation science to be nonreactive with antimatter when subjected to a high-frequency electromagnetic (EM) field in the megawatt range, rendering it "porous" to antihydrogen. Dilithium permits the antihydrogen to pass directly through its crystalline structure without actually touching it, owing to the field dynamo effect created in the added iron atoms. The longer form of the crystal name is the forced-matrix formula 2<5>6dilithium 2<:>1 diallosilicate 1:9:1 heptoferranide. This highly complex atomic structure is based on simpler forms discovered in naturally occurring geological layers of certain planetary systems. It was for many years deemed irreproducible by known or predicted vapor-deposition methods, until breakthroughs in nuclear epitaxy and antieutectics allowed the formation of pure, synthesized dilithium for starship and conventional powerplant use, through theta-matrix compositing techniques utilizing gamma radiation bombardment.
Transcript of Star Trek IV http://www.chakoteya.net/movies/movie4.html
KIRK: I can't believe we've come this far only to be stopped by this! Is there no way to re-crystallise dilithium? SCOTT: Sorry, sir. We can't even do that in the twenty-third century. SPOCK: Admiral, there may be a twentieth century possibility. KIRK: Explain. SPOCK: If memory serves, there was a dubious flirtation with nuclear fission reactors resulting in toxic side effects. By the beginning of the fusion era, these reactors had been replaced, but at this time, we may be able to find some. KIRK: I thought you said they were toxic. SPOCK: We could construct a device to collect their high-energy photons safely. These photons could then be injected into the dilithium chamber, causing crystalline restructure. ...Theoretically. KIRK: Where would we find these reactors, ...theoretically? SPOCK: Nuclear power was widely used in naval vessels.
The android mechanical technology discovered by Kirk in "What Are Little Girls made Of?", "I,Mudd", and "Return to Tomorrow" was probably in Databases and Dr. Soong certainly made use of them. The difference between the androids shown in TOS and Data is in the positronic brain-which Soong tried to perfect with Lore--and failed. He succeeded with Data. He probably reasoned that the human condition is so complex that he decided to give Data the ability to figure it out FOR HIMSELF rather than try to duplicate it. That was the big mistake he made with Lore (similar to the mistake Dr. Daystrom made with M-5. Both M-5 and Lore were flawed--and as as a result-they became psychotic.) As to holodeck technology--THAT came from the Kalandan Computer in "That Which Survives"(what was LEFT of it after being blasted by a phaser!). It was already being used in a couple of years in "The Practical Joker" (and if you accept STAR TREK CONTINUES as canon-in "Pilgrim Of Eternity).
According to the theory that most episodes of episodic TV shows happen in alternate universes of their own, separate from the alternate universes of the other episodes, it would be probable that the next generation era shows are not sequels to the episodes where such discoveries were made.
Which TNG era episodes are known to be sequels to TOS era episodes?
Voyager "Flashback" and TNG "Unification" are sequels to The Undiscovered Country but what previous movies and episodes is The Undiscovered Country a sequel to?
Spock says he's been dead before, which probably makes it a sequel to II, III, & IV. In Final Frontier Kirk says he lost a brother but got him back again. So Final Frontier seems to be a sequel to "Operation Annihilate!" and II, III, & IV. Star Trek II: The Wrath of Khan is a sequel to "Space Seed".
In "I, Mudd" Chekov doesn't recognize Harry Mudd, implying Checkov was not aboard soon enough to experiemce or hear about "Mudd's Women". In "The Deadly Years" Chekov's reaction to corbomite implies he was aboard soon enough to experience or hear about "The Corbomite Maneuver". So "The Deadly Years" and "The Corbomite Maneuver" should be in an alternate universe where Chekov came aboard much sooner than in the alternate universe of "Mudd's Women" and "I, Mudd".
Since Chekov and Khan recognize each other in Star Trek II: The Wrath of Khan, "Space Seed" and Star Trek II: The Wrath of Khan should be in an alternate universe here Chekov joins the crew earlier than in some others, possibly the alternate universe of "The Deadly Years" and "The Corbomite Maneuver".
TNG "The Naked Now" is a sequel to TOS "The Naked Time".
DS9 "Trials and Tribble-ations" is a sequel to "Arena" and to "The Trouble with Tribbles" Which mentions the Organian peace Treaty and so seems to be a sequel to "Errand of Mercy".
TNG "Relics" Scotty mentions events in "Wolf in the Fold", "Elaan of Troyius", and "The Naked Time".
So "Encounter at Farpoint" and all later episodes of TNG, DS9, and VOY should be sequels to the two pilot shows "The Cage" and "Where No Man Has Gone Before" plus "The Corbomite Maneuver", "Space Seed", "The Naked Time", "Wolf in the Fold", "Elaan of Troyius", "Operation Annihilate!", "The Deadly Years", "Errand of Mercy", "The Trouble with Tribbles", "Arena", Star Trek II: The Wrath of Khan, Star Trek III: The Search For Spock, Star Trek IV: The Voyage Home, Star Trek V: The Final Frontier, and Star Trek VI: The Undiscovered Country.
But I don't seen any reason to make TNG, DS9, and VOY sequels to episodes where radical new technologies are discovered that are never developed and used even a century later.
