Implicature OK

Re:
Metcalf's "OK: America's greatest word". Oxford University Press.

From wiki:

---- the implicature of 'OK':

""Okay" can fulfill functions at many level of discourse."

"At the ideational level it functions as an adjective or adverb (Bangerter and Clark, 2003), it signifies approval, acceptance and confirmation by the speaker (Condon, 1986; Merritt, 1984), and affirmatively responds to a question (Guthrie, 1997; Heisler, 1996)."

From the OED

OED:

adj
All correct, all right; satisfactory, good; well, in good health or order. In early use, occas. more intensively: outstanding, excellent. Now freq. in somewhat weakened sense: adequate, acceptable. OK by (someone): fine by (a person), acceptable to (a person). Chiefly predicative.
Fashionable, modish; prestigious, high-class.
Of a person: decent, trustworthy; congenial.
Appropriate, suitable; permissible, allowed. Freq. with for.
Of a person: comfortable, at ease, content, satisfied; reasonable, understanding. Usu. with about, with.
int
Expressing assent, concession, or approval, esp. with regard to a previous statement or question: yes, all right.
a. Appended as an interrogative to a clause, phrase, etc., in expectation of agreement or approval.
b. Brit. ——rules OK!: asserting the pre-eminence of a specified person or thing.
Introducing an utterance or as a conversational filler, typically without affirmative or concessive force, but rather as a means of drawing attention to what the speaker is about to say: well, so, right.
n
An indication of approval; an endorsement, authorization. Freq. in to give the OK (to).In early use chiefly with reference to the marking of a document, etc., with the letters ‘OK’.
adv
Satisfactorily, acceptably.
v
trans. To endorse, esp. by marking with the letters ‘OK’; to approve, agree to, sanction, or pass. Freq. in pa. pple.

"In this function it is frequently discussed as a third turn receipt by a current speaker (Bangerter and Clark, 2003; Guthrie, 1997; Beach, 1993)."

""Okay" has also been described as serving a variety of text-structural functions as a marker of information-state transitions."

"Several studies describe this function of okay, frequently, however, labeling the phenomenon differently (Levin and Gray, 1983; Merritt, 1984; Condon, 1986; Heisler, 1996; Rendle-Short, 2000; Swales and Malczewski, 2001; Bangerter and Clark, 2003)."

"Several studies subdivide this structural type of okay, usually, however, these subdivisions refer to the place where structural okay occurs or to the type of new section it opens up."

""Okay" functions as a pre-closing device (Schegloff and Sacks, 1973; Bangerter and Clark, 2003), it marks a return from a digression (Bangerter and Clark, 2003), functions as a text bracketing device (Rendle-Short, 2000), occurs in introductory or conclusion position (Levin and Gray, 1983), or as an attention getter at the beginning of an interaction (Heisler, 1996)."

"Finally "okay" and "alright" are frequently mentioned in their function of backchannel signal (Heisler, 1996; Swales and Malczewski, 2001)."[173]"

"The 1977 Tenerife airport disaster, in which 583 people were killed, was blamed in part on a misunderstranding between pilot and air traffic control over the intended sense of the word "OK". While the controller meant "understood, stand by", the pilot may have interpreted it as "approved, proceed". Standard control terminology excludes "OK" precisely to avoid such ambiguities."

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Etc.