What arguments are there for "karma" -- that the agent inevitably experiences the result of their actions?

According to emptiness, there is only cause and effect. Emptiness has nothing to do with it. A fully enlightened monk falls down a well. How is this possible?

To appease the mods - the koan cited in this question has nothing to do with what’s asked and should be redacted from the original text.

Looking at the Early Buddhist Texts (EBTs), we see:

AN4.233:1.1: “Cattārimāni, bhikkhave, kammāni mayā sayaṃ abhiññā sacchikatvā paveditāni.

AN4.233:1.1: “Mendicants, I declare these four kinds of deeds, having realized them with my own insight.

We can verify the effects of kamma(Pāli) / karma(Sanskrit) personally and see causes and effects. For example, if we ignore cause and effect and steal, we cause harm and that harm rebounds on us as jail.

AN4.233:1.3: There are dark deeds with dark results;

And if we acknowledge cause and effect and are kind in heart and action to others, then we see smiles and gratitude:

AN4.233:1.4: bright deeds with bright results;

These are personally verifiable in this very life without recourse to past lives. We can understand the koan ourselves with simple experiments and simple intentions.

Yet doubt remains because sometimes people who do bad things get wealthy and sometimes people who do good things are burned at the stake. These apparent conflicts arise from mixed intentions and circumstance. The story of Frank Abagnale comes to mind:

AN4.233:1.5: dark and bright deeds with dark and bright results; ...

Most importantly, there is the fourth case not discussed in the quoted koan:

AN4.233:1.6: neither dark nor bright deeds with neither dark nor bright results, which lead to the ending of deeds.

The fourth case is quite different. The first three cases deal with the generation of kamma. The fourth case deals with the ending of kamma, the laying down of craving, and the full release of the heart. This too is personally verifiable and experienced by means of the Noble Eightfold Path. It does take practice and effort. Fortunately, walking the path does not require recalling past lives. For all practicing the path, we let go of the craving that drives our deeds and thereby lessen the suffering of kamma. For some, the escape will be complete.

AN4.233:5.2: It’s the intention to give up dark deeds with dark results, bright deeds with bright results, and both dark and bright deeds with both dark and bright results. These are called neither dark nor bright deeds with neither dark nor bright results, which lead to the ending of deeds.

UPDATE based on the edited question with a suggested definition of karma.

While it is true that the Buddha taught that each and every volitional action has specific consequences this is most definitely not in opposition to the fact that repeated actions based on volitional thoughts can be habit forming. Indeed, consequences of a karmic action can be that it leads to further such actions.

If I were to tell you right now not to think of a pink elephant the chances are likely that you will do so in the immediate future. What's more, it is likely that many beings reading this will be thinking of pink elephants in a more distant future as a consequence of the pink elephant they are bringing to mind right now. I invite you to observe your monkey mind at work with its discursive thoughts and see if you can't trace the cause and effect consequence of each thought leading to others in a more or less continuous process. One moment of mind gives birth to the next and on and on.

Surrounding the definition in the Stanford Encyclopedia is a discussion of how karma and rebirth are in some tension with the Buddha's teaching on emptiness. I believe the correct conceptual understandings of emptiness, karma and rebirth resolve this tension.

This whole notion of the fruits of karmic action being delayed as some sort of puzzle is itself somewhat puzzling to me. In my very life I have observed that my actions can have far reaching consequences. Far reaching in time and space. What I have done or failed to do when I was young (decades ago) has manifested in the situation I am in now. Isn't that just obvious for you as well?

Asking where the consequence of a karmic action (that has ceased) is stored in time and space betrays the wish for a metaphysical explanation. And this metaphysical explanation leads to the doctrine of emptiness as it explains how things exist and how they do not. In what manner they exist and in what manner they do not. Asking where the consequence is stored (in time and space) betrays the idea that phenomena (including karmic actions) have substantial inherent own-being. They do not. That is explained and reasoned through by the teaching on emptiness that Nagarjuna has expounded.

The sutra below explicitly lays out that the Buddha says that the consequence is not stored in time and space. And it goes on to show that actions, consequences, death, birth, karma, are all void of own being. This is the teaching on emptiness.

Believing that the teaching on emptiness somehow is problematic for dependent origination or the law of cause and effect is just wrong. In fact, it is quite the opposite as Nagarjuna has said in his famous treatise! Without emptiness - that is if things had their own-being - then actions could not be performed and there would be no cause and effect or dependent origination.

Would encourage you to study Nagarjuna and trace his arguments if you can.

Although I am not certain about what your question actually is about I thought I'd share this passage from a rather obscure sutra that may help your mind:

THE NOBLE SUTRA OF THE MAHAYANA DENOMINATED - "THE PASSAGE THROUGH EXISTENCES"

Homage to all the Buddhas and Bodhisattvaas. Thus have I heard. Once the Bhagavant stayed in Rajagrha, in the Bamboo-Forest, in the place of the kalandakas, in the company of a group of one thousand two hundred and fifty bhiksus and of very numerous great Bodhisattvas. Then, the Bhagavant, while he was surrounded by many hundreds of thousands of his followers, looking at them, expounded the Dharma and expounded in its integrity the Brahmacarya beautiful in its beginning, beautiful in the middle, beautiful in its end, fair in its meaning, fair in its expression, without confusion, completely fulfilled, completely pure, completely immaculate.

Then Sreniya Bimbisara, King of the Magadha country, going out from the town of Rajagrha, with great royal pomp, with a great royal force, went to the Bamboo-Forest where the Bhagavant was. On arriving, after bowing down at the feet of the Bhagavant and turning (around the Bhagavant) the right side towards him three times, Sreniya Bimbisara, King of the Magadha country, spoke thus to the Bhagavant : "O Bhagavant, how do actions, (a long time) after having been done (and) accumulated, a long time after having ceased, (re)appear in the mind, on being near the moment of death? All conditioned things (samskara) being void, how do actions pass without being annihilated?"

So (the King) spoke, and the Bhagavant to Sreniya Bimbisara, King of the Magadha country, said thus : "O great King, just as for instance a man, in a dream while he is sleeping, dreams that he extremely enjoys himself with a beautiful woman of his country and, when he awakes from his sleep, remembers that beautiful woman of his country (he has seen in his dream) - what do you think, O great King : does that beautiful woman of the country, (seen) in the dream, (really) exist?"

(The King) said : "O Bhagavant, she does not exist."

The Bhagavant said : "O great King, what do you think : that man who ardently desires the beautiful woman of his country, (seen) in his dream - is he a wise man?"

(The King) answered : "O Bhagavant, he is not - if it is asked why, O Bhagavant - because that beautiful woman of the country, (seen) in the dream, does not exist at all; and although he does not perceive her, (nevertheless) he goes on thinking of enjoying himself extremely with her. Thus that man, being deprived of her, has a destiny of sorrow."

The Bhagavant said : "O great King, in the same way, an ordinary man, foolish, ignorant, on seeing with his eyes lovely forms, ardently desires those forms which are agreeable to his mind. While ardently desiring them, he becomes attached to them. On becoming attached to them, he feels a passion for them. On feeling a passion for them, he performs with his body, speech and mind,, actions that are born out of desire, hatred and error. And those actions, after having been performed, cease. And after having ceased, (those actions) stay neither in the east nor in the south nor in the west nor in the north nor up nor down - nor in any region of space. But, at any other time, at the moment near the instant of death, when the karma corresponding (to the life that is being concluded) is exhausted, at the (very) moment the last consciousness ceases, those actions (re)appear in the mind (of the dying man) - just as for instance the beautiful woman of the country (in the mind) of the man that wakes from his sleep. O great King, immediately after the first consciousness has ceased, there arises the series of consciousnesses, which corresponds (to the life that is beginning), and in which the ripening (of actions previously performed) will be experienced. O great King, although no element of existence (dharma) passes from this world to another world, nevertheless death and birth take place. O great King, the last consciousness which ceases is called 'death'; the first consciousness which arises is called 'birth'. O great King, the last consciousness, at the moment it ceases, does not pass to anywhere; the first consciousness, which forms part of the (new) birth, at the moment it arises, does not come from anywhere. If it is asked why, (I answer:) because of their lack of an own being. O great King, although the last consciousness is void (of the own being) of death, action is void (of the own being) of action, the first consciousness is void (of the own being) of a first consciousness, birth is void (of the own being) of birth, (nevertheless) actions do not perish. O great King, immediately after the first consciousness, which forms part of the (new) birth, has ceased, there arises without interruption the series of consciousnesses, in which the ripening (of actions previously done) will be experienced."

This sutra speaks directly to karma and how it ripens from moment to moment and life to life even though actions previously arisen have ceased and exist no where whatsoever in space or time and yet they ripen at later times and continue to produce fruit. The important point is that the manner and way this happens from moment to moment in this very life is the same manner and way it happens from life to life. There is no difference in extent or manner.

And note that the doctrine of emptiness is very definitely tied up with this ripening of past karma. Karma could not function without emptiness. Were things not empty, there could not be actions and the ripening of those actions. Understanding emptiness is indispensable in understanding how actions ripen and bear fruit and that is why it is said that emptiness and dependent origination go hand in hand.