[System] You are an English linguist performing fine-grained Word Sense Disambiguation. WordNet glosses are schematic. Use the sentence context, the examples, and the synonyms to choose the best indexed sense. Do not hedge. Choose the single best indexed sense.

[User]
Target lemma: politician
Target surface form: politicians
Context:
If he is competent and conscientious, he serves us well. Our teachers are not an important factor in our educational crisis. Whether they are or are not underpaid is a problem of equity; it is not an educational problem. It is silly libel on our teachers to think they would educate our children better if only they got a few thousand dollars a year more. It is the kind of libel the teachers' unions do not mind spreading, for their own narrow purposes. It is also the kind of libel <t>politicians</t> find useful, since it helps them strike a friendly posture on behalf of an important constituency. But there is not one shred of evidence that, other things being equal, salary differentials result in educational differentials.

Candidate senses:
1. sense_key=politician%1:18:01:: | definition=a leader engaged in civil administration
2. sense_key=politician%1:18:00:: | definition=a person active in party politics | synonyms=politico, pol, political leader
3. sense_key=politician%1:18:02:: | definition=a schemer who tries to gain advantage in an organization in sly or underhanded ways

Instructions:
1. Choose the single best indexed sense for the target word in context.
2. WordNet glosses are schematic; use the context, synonyms, and examples together.
3. Do not answer with a WordNet sense key.
4. Return only a JSON object exactly like {"sense_index": 3}.

reasoning_content:
We are asked: "Choose the single best indexed sense for the target word in context." and "Return only a JSON object exactly like {"sense_index": 3}."

Target lemma: politician, surface form: politicians. Context: "It is also the kind of libel politicians find useful, since it helps them strike a friendly posture on behalf of an important constituency."

Senses:
1. sense_key=politician%1:18:01:: | definition=a leader engaged in civil administration
2. sense_key=politician%1:18:00:: | definition=a person active in party politics | synonyms=politico, pol, political leader
3. sense_key=politician%1:18:02:: | definition=a schemer who tries to gain advantage in an organization in sly or underhanded ways

The context talks about "libel" that politicians find useful because it helps them "strike a friendly posture on behalf of an important constituency." This suggests politicians are using this libel to gain favor with voters or a group (like teachers' unions). That is a typical political maneuver: they are acting as political leaders/figures. Sense 2 fits best: "a person active in party politics" or "political leader." Sense 1 is more specific to civil administration (like an appointed official?), but politicians here are likely elected officials who seek to please constituencies. Sense 3 has a negative connotation of scheming, but while the context might imply they are being underhanded, the phrase "strike a friendly posture on behalf of an important constituency" is a normal political activity, not necessarily a schemer in an organization. The libel is already described as something the teachers' unions spread for narrow purposes, and politicians find it useful. So sense 2 is the straightforward meaning. Sense 3 is too narrow and negative; the text doesn't directly say politicians are schemers, just that they find the libel useful. So I choose sense 2.

Thus, the sense index is 2.


attempt_kind: initial

status: success

[System] You are an English linguist performing fine-grained Word Sense Disambiguation. WordNet glosses are schematic. Use the sentence context, the examples, and the synonyms to choose the best indexed sense. Do not hedge. Choose the single best indexed sense.

[User]
Target lemma: find
Target surface form: find
Context:
If he is competent and conscientious, he serves us well. Our teachers are not an important factor in our educational crisis. Whether they are or are not underpaid is a problem of equity; it is not an educational problem. It is silly libel on our teachers to think they would educate our children better if only they got a few thousand dollars a year more. It is the kind of libel the teachers' unions do not mind spreading, for their own narrow purposes. It is also the kind of libel politicians <t>find</t> useful, since it helps them strike a friendly posture on behalf of an important constituency. But there is not one shred of evidence that, other things being equal, salary differentials result in educational differentials.

Candidate senses:
1. sense_key=find%2:40:02:: | definition=come upon, as if by accident; meet with | synonyms=happen, chance, bump, encounter | examples=We find this idea in Plato; I happened upon the most wonderful bakery not very far from here
2. sense_key=find%2:39:02:: | definition=discover or determine the existence, presence, or fact of | synonyms=detect, observe, discover, notice | examples=She detected high levels of lead in her drinking water; We found traces of lead in the paint
3. sense_key=find%2:40:00:: | definition=come upon after searching; find the location of something that was missed or lost | synonyms=regain | examples=Did you find your glasses?; I cannot find my gloves!
4. sense_key=find%2:32:00:: | definition=establish after a calculation, investigation, experiment, survey, or study | synonyms=determine, find out, ascertain | examples=find the product of two numbers; The physicist who found the elusive particle won the Nobel Prize
5. sense_key=find%2:31:10:: | definition=come to believe on the basis of emotion, intuitions, or indefinite grounds | synonyms=feel | examples=I feel that he doesn't like me; I find him to be obnoxious
6. sense_key=find%2:39:01:: | definition=perceive or be contemporaneous with | synonyms=witness, see | examples=We found Republicans winning the offices; You'll see a lot of cheating in this school
7. sense_key=find%2:40:01:: | definition=get something or somebody for a specific purpose | synonyms=line up, get hold, come up | examples=I found this gadget that will serve as a bottle opener; I got hold of these tools to fix our plumbing
8. sense_key=find%2:36:00:: | definition=make a discovery, make a new finding | synonyms=discover | examples=Roentgen discovered X-rays; Physicists believe they found a new elementary particle
9. sense_key=find%2:31:09:: | definition=make a discovery | synonyms=discover | examples=She found that he had lied to her; The story is false, so far as I can discover
10. sense_key=find%2:40:03:: | definition=obtain through effort or management | examples=She found the time and energy to take care of her aging parents; We found the money to send our sons to college
11. sense_key=find%2:32:01:: | definition=decide on and make a declaration about | synonyms=rule | examples=find someone guilty
12. sense_key=find%2:30:00:: | definition=receive a specified treatment (abstract) | synonyms=receive, get, obtain, incur | examples=These aspects of civilization do not find expression or receive an interpretation; His movie received a good review
13. sense_key=find%2:39:05:: | definition=perceive oneself to be in a certain condition or place | examples=I found myself in a difficult situation; When he woke up, he found himself in a hospital room
14. sense_key=find%2:40:15:: | definition=get or find back; recover the use of | synonyms=recover, retrieve, regain | examples=She regained control of herself; She found her voice and replied quickly
15. sense_key=find%2:38:10:: | definition=succeed in reaching; arrive at | examples=The arrow found its mark
16. sense_key=find%2:30:13:: | definition=accept and make use of one's personality, abilities, and situation | synonyms=find oneself | examples=My son went to Berkeley to find himself

Instructions:
1. Choose the single best indexed sense for the target word in context.
2. WordNet glosses are schematic; use the context, synonyms, and examples together.
3. Do not answer with a WordNet sense key.
4. Return only a JSON object exactly like {"sense_index": 3}.

finish_reason: stop

role: assistant

reasoning_content:
We need to disambiguate "find" in the context: "It is also the kind of libel politicians find useful, since it helps them strike a friendly posture on behalf of an important constituency."

The phrase is "politicians find useful". So "find" is used as: politicians consider this libel useful. They find it useful. This is a sense of "find" meaning to consider or regard something in a certain way. Looking at the candidate senses:

- Sense 1: come upon, as if by accident; meet with. Not appropriate.
- Sense 2: discover or determine the existence, presence, or fact of. Not exactly; they aren't discovering that the libel exists, they are considering it useful.
- Sense 3: come upon after searching. No.
- Sense 4: establish after a calculation, investigation, etc. Not really.
- Sense 5: come to believe on the basis of emotion, intuitions, or indefinite grounds. Synonyms: feel. Examples: "I feel that he doesn't like me; I find him to be obnoxious". That's a sense of "find" meaning to have an opinion or feeling about something. "Politicians find [the libel] useful" means they consider it useful, they have the opinion that it is useful. This fits sense 5: "come to believe on the basis of emotion, intuitions, or indefinite grounds". But is it exactly that? It says "on the basis of emotion, intuitions, or indefinite grounds". However, in the context, politicians find it useful because it helps them strike a friendly posture. That's not necessarily based on emotion or indefinite grounds; it's a pragmatic judgment. But the sense 5 definition is "come to believe on the basis of emotion, intuitions, or indefinite grounds", and the example "I find him to be obnoxious" is similar. Another possible sense is 4: "establish after a calculation, investigation, experiment, survey, or study" which is more about determining facts, not about holding an opinion. Sense 9: "make a discovery" with example "She found that he had lied to her" could be used with a that-clause: "find that it is useful". But here it's "find useful" without "that". It's an object complement: "find X useful" meaning "consider X to be useful". That's often a sense like "find" meaning "to perceive or regard". There is sense 6: "perceive or be contemporaneous with", example "We found Republicans winning the offices"; that's like "we observed Republicans winning". But "find useful" is more like "consider useful". Sense 5 seems closest: "come to believe on the basis of emotion, intuitions, or indefinite grounds" with synonym "feel". But there's also sense 13: "perceive oneself to be in a certain condition or place", not appropriate. Sense 12: "receive a specified treatment (abstract)" with example "These aspects of civilization do not find expression". That's like "find expression" meaning "receive expression". "Find useful" could be interpreted as "receive a useful treatment"? No, that's not it.

Actually, there is a common sense of "find" meaning "to consider or regard as" that is often listed as "find something to be something". WordNet has sense 5: "come to believe on the basis of emotion, intuitions, or indefinite grounds" with example "I find him to be obnoxious". That's exactly the structure: "find + object + complement". So it's the best match.

But let's check all senses:

- Sense 5: feel, find (to be). "I find him to be obnoxious" - that's "I consider him obnoxious".
- Sense 4: determine, find out. Not for subjective opinion.
- Sense 9: discover. "She found that he had lied to her" - that's with a clause. "Politicians find (that) it is useful" could be similar, but here it's "find it useful" without "that", which is a different construction.
- Sense 6: witness, see. "We found Republicans winning the offices" - that is more like observing an event, not just considering.
- Sense 11: rule, find someone guilty. That's "find guilty" as a legal decision. But here it's not a formal declaration.
- Sense 12: receive a specified treatment. "Find expression" means to be expressed. That's not active.

Sense 5 is specifically for "find" meaning to believe or feel based on indefinite grounds. The context is about politicians finding the libel useful; they think it's useful, they consider it useful. That fits "come to believe" even if it's based on their own purposes (which could be opportunistic, not necessarily indefinite grounds, but still a subjective opinion). So sense 5 is the best.

Sense index: 5.

Let's confirm: "find%2:31:10::" is sense 5. So answer: {"sense_index": 5}

format: unknown

native_finish_reason: stop

provider: NextBit

currency: USD


[System] You are an English linguist performing fine-grained Word Sense Disambiguation. WordNet glosses are schematic. Use the sentence context, the examples, and the synonyms to choose the best indexed sense. Do not hedge. Choose the single best indexed sense.

[User]
Target lemma: help
Target surface form: helps
Context:
If he is competent and conscientious, he serves us well. Our teachers are not an important factor in our educational crisis. Whether they are or are not underpaid is a problem of equity; it is not an educational problem. It is silly libel on our teachers to think they would educate our children better if only they got a few thousand dollars a year more. It is the kind of libel the teachers' unions do not mind spreading, for their own narrow purposes. It is also the kind of libel politicians find useful, since it <t>helps</t> them strike a friendly posture on behalf of an important constituency. But there is not one shred of evidence that, other things being equal, salary differentials result in educational differentials.

Candidate senses:
1. sense_key=help%2:41:00:: | definition=give help or assistance; be of service | synonyms=assist, aid | examples=Everyone helped out during the earthquake; Can you help me carry this table?
2. sense_key=help%2:29:00:: | definition=improve the condition of | synonyms=aid | examples=These pills will help the patient
3. sense_key=help%2:42:00:: | definition=be of use | synonyms=facilitate | examples=This will help to prevent accidents
4. sense_key=help%2:42:08:: | definition=abstain from doing; always used with a negative | synonyms=help oneself | examples=I can't help myself--I have to smoke; She could not help watching the sad spectacle
5. sense_key=help%2:34:00:: | definition=help to some food; help with food or drink | synonyms=serve | examples=I served him three times, and after that he helped himself
6. sense_key=help%2:41:12:: | definition=contribute to the furtherance of | examples=This money will help the development of literacy in developing countries
7. sense_key=help%2:34:04:: | definition=take or use | synonyms=avail | examples=She helped herself to some of the office supplies
8. sense_key=help%2:30:13:: | definition=improve; change for the better | examples=New slipcovers will help the old living room furniture

Instructions:
1. Choose the single best indexed sense for the target word in context.
2. WordNet glosses are schematic; use the context, synonyms, and examples together.
3. Do not answer with a WordNet sense key.
4. Return only a JSON object exactly like {"sense_index": 3}.

reasoning_content:
We are asked to perform word sense disambiguation for the target word "help" in the form "helps" in the given context. We need to choose the best sense from the list of 8 senses provided.

Let's analyze the context:
"If he is competent and conscientious, he serves us well. Our teachers are not an important factor in our educational crisis. Whether they are or are not underpaid is a problem of equity; it is not an educational problem. It is silly libel on our teachers to think they would educate our children better if only they got a few thousand dollars a year more. It is the kind of libel the teachers' unions do not mind spreading, for their own narrow purposes. It is also the kind of libel politicians find useful, since it <t>helps</t> them strike a friendly posture on behalf of an important constituency. But there is not one shred of evidence that, other things being equal, salary differentials result in educational differentials."

The target word "helps" appears in: "since it helps them strike a friendly posture". Here, "it" refers to "this kind of libel", i.e., spreading the idea that teachers would do better if paid more. So, this libel helps politicians to strike a friendly posture. The meaning is that the libel is useful to politicians for achieving a goal. They use it to appear friendly.

Now check the senses:

1. help%2:41:00:: give help or assistance; be of service. Examples: Everyone helped out during the earthquake; Can you help me carry this table? This is a general sense of providing assistance, often with a person helping another person.

2. help%2:29:00:: improve the condition of; aid. Examples: These pills will help the patient. This is about making something better, especially health.

3. help%2:42:00:: be of use; facilitate. Examples: This will help to prevent accidents. This sense is about something being useful or facilitating an outcome. It doesn't necessarily imply direct assistance, but rather that something contributes to a result.

4. help%2:42:08:: abstain from doing; always used with a negative. Example: I can't help myself. Not applicable.

5. help%2:34:00:: help to some food; serve. Not applicable.

6. help%2:41:12:: contribute to the furtherance of. Example: This money will help the development of literacy. This is similar to sense 3, but specifically about contributing to progress or furtherance. It can be used with abstract things.

7. help%2:34:04:: take or use; avial. Example: She helped herself to some office supplies. Not applicable.

8. help%2:30:13:: improve; change for the better. Example: New slipcovers will help the old living room furniture. This is about making something look or be better.

In the context, "it helps them strike a friendly posture" means it makes it easier for them to strike a friendly posture, or it facilitates that action. Sense 3: "be of use; facilitate" fits well. Sense 6: "contribute to the furtherance of" could also fit, but "furtherance" often implies progress of something like development, project, etc. Here, it's about helping them perform an action (strike a posture). Sense 1 is about direct assistance from one person to another, but the subject is "it" (libel), not a person. Sense 3 specifically says "be of use" which is exactly how we use "helps" for inanimate things that make something easier. The example "This will help to prevent accidents" matches the structure: "it helps them strike" -> "it helps to prevent". So sense 3 seems the best.

Check synonyms: sense 3 synonyms: facilitate. That is perfect. Sense 6 has no synonyms given, but definition: contribute to the furtherance of. It could be used, but sense 3 is more general utility. I think sense 3 is the most appropriate.

Thus, answer: sense_index 3.

provider: Novita


[System] You are an English linguist performing fine-grained Word Sense Disambiguation. WordNet glosses are schematic. Use the sentence context, the examples, and the synonyms to choose the best indexed sense. Do not hedge. Choose the single best indexed sense.

[User]
Target lemma: strike
Target surface form: strike
Context:
If he is competent and conscientious, he serves us well. Our teachers are not an important factor in our educational crisis. Whether they are or are not underpaid is a problem of equity; it is not an educational problem. It is silly libel on our teachers to think they would educate our children better if only they got a few thousand dollars a year more. It is the kind of libel the teachers' unions do not mind spreading, for their own narrow purposes. It is also the kind of libel politicians find useful, since it helps them <t>strike</t> a friendly posture on behalf of an important constituency. But there is not one shred of evidence that, other things being equal, salary differentials result in educational differentials.

Candidate senses:
1. sense_key=strike%2:35:00:: | definition=deliver a sharp blow, as with the hand, fist, or weapon | examples=The teacher struck the child; the opponent refused to strike
2. sense_key=strike%2:37:00:: | definition=have an emotional or cognitive impact upon | synonyms=affect, impress, move | examples=This child impressed me as unusually mature; This behavior struck me as odd
3. sense_key=strike%2:35:01:: | definition=hit against; come into sudden contact with | synonyms=hit, impinge on, run into, collide with | examples=The car hit a tree; He struck the table with his elbow
4. sense_key=strike%2:33:00:: | definition=make a strategic, offensive, assault against an enemy, opponent, or a target | synonyms=hit | examples=The Germans struck Poland on Sept. 1, 1939; We must strike the enemy's oil fields
5. sense_key=strike%2:32:00:: | definition=indicate (a certain time) by striking | examples=The clock struck midnight; Just when I entered, the clock struck
6. sense_key=strike%2:35:02:: | definition=affect or afflict suddenly, usually adversely | synonyms=hit | examples=We were hit by really bad weather; He was stricken with cancer when he was still a teenager
7. sense_key=strike%2:41:00:: | definition=stop work in order to press demands | synonyms=walk out | examples=The auto workers are striking for higher wages; The employees walked out when their demand for better benefits was not met
8. sense_key=strike%2:42:00:: | definition=touch or seem as if touching visually or audibly | synonyms=fall, shine | examples=Light fell on her face; The sun shone on the fields
9. sense_key=strike%2:41:02:: | definition=attain | synonyms=come to | examples=The horse finally struck a pace
10. sense_key=strike%2:35:03:: | definition=produce by manipulating keys or strings of musical instruments, also metaphorically | synonyms=hit | examples=The pianist strikes a middle C; strike `z' on the keyboard
11. sense_key=strike%2:30:00:: | definition=cause to form (an electric arc) between electrodes of an arc lamp | examples=strike an arc
12. sense_key=strike%2:40:00:: | definition=find unexpectedly | synonyms=fall upon, come upon, light upon, chance upon, come across, chance on | examples=the archeologists chanced upon an old tomb; she struck a goldmine
13. sense_key=strike%2:36:00:: | definition=produce by ignition or a blow | examples=strike fire from the flintstone; strike a match
14. sense_key=strike%2:35:08:: | definition=remove by erasing or crossing out or as if by drawing a line | synonyms=scratch, expunge, excise | examples=Please strike this remark from the record; scratch that remark
15. sense_key=strike%2:39:00:: | definition=cause to experience suddenly | synonyms=hit, come to | examples=Panic struck me; An interesting idea hit her
16. sense_key=strike%2:38:02:: | definition=drive something violently into a location | synonyms=hit | examples=he hit his fist on the table; she struck her head on the low ceiling
17. sense_key=strike%2:38:08:: | definition=occupy or take on | synonyms=assume, take, take up | examples=He assumes the lotus position; She took her seat on the stage
18. sense_key=strike%2:36:02:: | definition=form by stamping, punching, or printing | synonyms=mint, coin | examples=strike coins; strike a medal
19. sense_key=strike%2:35:10:: | definition=smooth with a strickle | synonyms=strickle | examples=strickle the grain in the measure
20. sense_key=strike%2:35:09:: | definition=pierce with force | examples=The bullet struck her thigh; The icy wind struck through our coats
21. sense_key=strike%2:31:00:: | definition=arrive at after reckoning, deliberating, and weighing | examples=strike a balance; strike a bargain

Instructions:
1. Choose the single best indexed sense for the target word in context.
2. WordNet glosses are schematic; use the context, synonyms, and examples together.
3. Do not answer with a WordNet sense key.
4. Return only a JSON object exactly like {"sense_index": 3}.

reasoning_content:
We are given a target lemma "strike" and surface form "strike" in a specific context: "...it helps them strike a friendly posture on behalf of an important constituency." The word "strike" here is part of the phrase "strike a friendly posture". We need to choose the best sense among 21 indexed senses.

Let's analyze the context: "strike a friendly posture" means to assume or adopt a friendly posture. It is a figurative use: to present oneself in a certain way. Looking at the sense options:

- Sense 1: deliver a sharp blow - no.
- Sense 2: have an emotional or cognitive impact upon - no, "strike a posture" doesn't mean affect a posture.
- Sense 3: hit against; come into sudden contact - no.
- Sense 4: make a strategic offensive assault - no.
- Sense 5: indicate a certain time by striking - no.
- Sense 6: affect or afflict suddenly - no.
- Sense 7: stop work to press demands - no.
- Sense 8: touch or seem as if touching visually or audibly - no.
- Sense 9: attain - e.g., "strike a pace" - that is a possibility: "strike a posture" could be similar to attaining a posture. But let's check other senses.
- Sense 10: produce by manipulating keys or strings - no.
- Sense 11: cause to form an electric arc - no.
- Sense 12: find unexpectedly - no.
- Sense 13: produce by ignition or a blow - no.
- Sense 14: remove by erasing - no.
- Sense 15: cause to experience suddenly - "panic struck me" - no, "strike a posture" isn't that.
- Sense 16: drive something violently into a location - no.
- Sense 17: occupy or take on - synonyms: assume, take, take up. Examples: "He assumes the lotus position"; "She took her seat on the stage". This is exactly the meaning: to assume a posture. To strike a posture means to take on a posture, assume it. So sense 17 fits perfectly.
- Sense 18: form by stamping, punching, or printing - no.
- Sense 19: smooth with a strickle - no.
- Sense 20: pierce with force - no.
- Sense 21: arrive at after reckoning - "strike a balance", "strike a bargain" - this is also a possibility. "Strike a balance" means to achieve a balance by deliberation. "Strike a bargain" means to reach an agreement. But "strike a friendly posture" is not about deliberation or negotiation; it's about assuming a pose or attitude. The phrase "strike a posture" is a common collocation meaning to adopt a particular attitude or stance, often in a self-conscious way. It aligns with sense 17: assume, take up. Sense 21 is about arriving at something through deliberation, like a balance or bargain. "Posture" is not something you arrive at through reckoning; it's something you put on. So sense 17 is better.

Thus, the correct sense index is 17.

provider: Fireworks


[System] You are an English linguist performing fine-grained Word Sense Disambiguation. WordNet glosses are schematic. Use the sentence context, the examples, and the synonyms to choose the best indexed sense. Do not hedge. Choose the single best indexed sense.

[User]
Target lemma: friendly
Target surface form: friendly
Context:
If he is competent and conscientious, he serves us well. Our teachers are not an important factor in our educational crisis. Whether they are or are not underpaid is a problem of equity; it is not an educational problem. It is silly libel on our teachers to think they would educate our children better if only they got a few thousand dollars a year more. It is the kind of libel the teachers' unions do not mind spreading, for their own narrow purposes. It is also the kind of libel politicians find useful, since it helps them strike a <t>friendly</t> posture on behalf of an important constituency. But there is not one shred of evidence that, other things being equal, salary differentials result in educational differentials.

Candidate senses:
1. sense_key=friendly%3:00:01:: | definition=characteristic of or befitting a friend | examples=friendly advice; a friendly neighborhood
2. sense_key=friendly%5:00:00:amicable:00 | definition=inclined to help or support; not antagonistic or hostile | synonyms=favorable, well-disposed | examples=a government friendly to our interests; an amicable agreement
3. sense_key=friendly%3:00:03:: | definition=easy to understand or use | examples=user-friendly computers; a consumer-friendly policy
4. sense_key=friendly%3:00:02:: | definition=of or belonging to your own country's forces or those of an ally | examples=in friendly territory; he was accidentally killed by friendly fire

Instructions:
1. Choose the single best indexed sense for the target word in context.
2. WordNet glosses are schematic; use the context, synonyms, and examples together.
3. Do not answer with a WordNet sense key.
4. Return only a JSON object exactly like {"sense_index": 3}.

reasoning_content:
We are asked to choose the best indexed sense for "friendly" in the given context. The context is about politicians striking a "friendly posture" on behalf of an important constituency. The phrase "strike a friendly posture" means they adopt a positive, supportive, or agreeable stance. Let's analyze each sense:

1. sense_key=friendly%3:00:01:: | definition=characteristic of or befitting a friend | examples=friendly advice; a friendly neighborhood
This sense is about being like a friend, kind, warm. "Strike a friendly posture" could fit, but it might be more about showing friendliness to gain favor.

2. sense_key=friendly%5:00:00:amicable:00 | definition=inclined to help or support; not antagonistic or hostile | synonyms=favorable, well-disposed | examples=a government friendly to our interests; an amicable agreement
This sense emphasizes supportive, favorable, not hostile. "Strike a friendly posture on behalf of an important constituency" means they take a stance that is favorable or supportive of that constituency's interests. The synonym "favorable" fits well. Politicians want to appear well-disposed to the teachers' unions.

3. sense_key=friendly%3:00:03:: | definition=easy to understand or use | examples=user-friendly computers; a consumer-friendly policy
This is about usability, not applicable.

4. sense_key=friendly%3:00:02:: | definition=of or belonging to your own country's forces or those of an ally | examples=in friendly territory; he was accidentally killed by friendly fire
Military context, not applicable.

The best fit is sense 2: inclined to help or support; not antagonistic or hostile. The phrase "strike a friendly posture" implies they present themselves as supportive, well-disposed. Sense 1 is more about personal friendliness, but the context is political posturing. Sense 2 directly includes "favorable" and "well-disposed", which matches taking a favorable stance. Thus, sense_index: 2.

Return JSON: {"sense_index": 2}

provider: GMICloud


[System] You are an English linguist performing fine-grained Word Sense Disambiguation. WordNet glosses are schematic. Use the sentence context, the examples, and the synonyms to choose the best indexed sense. Do not hedge. Choose the single best indexed sense.

[User]
Target lemma: posture
Target surface form: posture
Context:
If he is competent and conscientious, he serves us well. Our teachers are not an important factor in our educational crisis. Whether they are or are not underpaid is a problem of equity; it is not an educational problem. It is silly libel on our teachers to think they would educate our children better if only they got a few thousand dollars a year more. It is the kind of libel the teachers' unions do not mind spreading, for their own narrow purposes. It is also the kind of libel politicians find useful, since it helps them strike a friendly <t>posture</t> on behalf of an important constituency. But there is not one shred of evidence that, other things being equal, salary differentials result in educational differentials.

Candidate senses:
1. sense_key=posture%1:07:00:: | definition=the arrangement of the body and its limbs | synonyms=position, attitude | examples=he assumed an attitude of surrender
2. sense_key=posture%1:07:01:: | definition=characteristic way of bearing one's body | synonyms=carriage, bearing | examples=stood with good posture
3. sense_key=posture%1:09:00:: | definition=a rationalized mental attitude | synonyms=position, stance
4. sense_key=posture%1:07:02:: | definition=capability in terms of personnel and materiel that affect the capacity to fight a war | synonyms=military capability, military strength, strength, military posture | examples=we faced an army of great strength; politicians have neglected our military posture

Instructions:
1. Choose the single best indexed sense for the target word in context.
2. WordNet glosses are schematic; use the context, synonyms, and examples together.
3. Do not answer with a WordNet sense key.
4. Return only a JSON object exactly like {"sense_index": 3}.

reasoning_content:
We are given a target lemma "posture", surface form "posture", and a context sentence: "It is also the kind of libel politicians find useful, since it helps them strike a friendly <t>posture</t> on behalf of an important constituency." The word is tagged with <t> tags. We have four candidate senses.

Let's analyze each sense:

1. sense_key=posture%1:07:00:: | definition=the arrangement of the body and its limbs | synonyms=position, attitude | examples=he assumed an attitude of surrender
   This sense is about physical body posture, like a pose.

2. sense_key=posture%1:07:01:: | definition=characteristic way of bearing one's body | synonyms=carriage, bearing | examples=stood with good posture
   Also physical, about how one carries oneself.

3. sense_key=posture%1:09:00:: | definition=a rationalized mental attitude | synonyms=position, stance
   This is a mental or metaphorical attitude, a position taken on an issue.

4. sense_key=posture%1:07:02:: | definition=capability in terms of personnel and materiel that affect the capacity to fight a war | synonyms=military capability, military strength, strength, military posture | examples=we faced an army of great strength; politicians have neglected our military posture
   This is about military strength.

Now, context: "It is also the kind of libel politicians find useful, since it helps them strike a friendly posture on behalf of an important constituency." Here, "strike a friendly posture" is a phrase meaning to assume or adopt a friendly attitude or stance, usually for show. It's metaphorical, not physical. Sense 3, "a rationalized mental attitude" with synonyms "position, stance", fits perfectly. The phrase "strike a ... posture" often means to adopt a particular attitude or stance, especially one that is not entirely genuine. So sense 3 is best.

Sense 1 is about physical body arrangement, which might also be used metaphorically but sense 3 is specifically about mental attitude. Sense 3's synonyms "position, stance" are often used in political contexts. So I'll choose sense 3.

Thus, return {"sense_index": 3}.

provider: WandB


[System] You are an English linguist performing fine-grained Word Sense Disambiguation. WordNet glosses are schematic. Use the sentence context, the examples, and the synonyms to choose the best indexed sense. Do not hedge. Choose the single best indexed sense.

[User]
Target lemma: behalf
Target surface form: behalf
Context:
If he is competent and conscientious, he serves us well. Our teachers are not an important factor in our educational crisis. Whether they are or are not underpaid is a problem of equity; it is not an educational problem. It is silly libel on our teachers to think they would educate our children better if only they got a few thousand dollars a year more. It is the kind of libel the teachers' unions do not mind spreading, for their own narrow purposes. It is also the kind of libel politicians find useful, since it helps them strike a friendly posture on <t>behalf</t> of an important constituency. But there is not one shred of evidence that, other things being equal, salary differentials result in educational differentials.

Candidate senses:
1. sense_key=behalf%1:04:00:: | definition=as the agent of or on someone's part (usually expressed as  rather than ) | examples=on behalf of; in behalf of
2. sense_key=behalf%1:07:00:: | definition=for someone's benefit (usually expressed as `in behalf' rather than `on behalf' and usually with a possessive) | examples=in your behalf; campaigning in his own behalf

Instructions:
1. Choose the single best indexed sense for the target word in context.
2. WordNet glosses are schematic; use the context, synonyms, and examples together.
3. Do not answer with a WordNet sense key.
4. Return only a JSON object exactly like {"sense_index": 3}.

reasoning_content:
We are asked to disambiguate "behalf" in the sentence: "It is also the kind of libel politicians find useful, since it helps them strike a friendly posture on behalf of an important constituency." The target word is "behalf" in the phrase "on behalf of".

We have two senses:

1. sense_key=behalf%1:04:00:: | definition=as the agent of or on someone's part (usually expressed as rather than ) | examples=on behalf of; in behalf of
2. sense_key=behalf%1:07:00:: | definition=for someone's benefit (usually expressed as `in behalf' rather than `on behalf' and usually with a possessive) | examples=in your behalf; campaigning in his own behalf

In the context: "politicians strike a friendly posture on behalf of an important constituency." The phrase "on behalf of" can mean either representing someone (acting as their agent) or for someone's benefit. The note in sense 2 says it's usually expressed as "in behalf" rather than "on behalf". Modern usage often uses "on behalf of" for both meanings, but the distinction here is that sense 2 is specifically "for someone's benefit" and often uses "in behalf". However, the sentence uses "on behalf of". Sense 1 defines it as "as the agent of or on someone's part", which aligns with the idea of politicians acting as representatives for a constituency. They are striking a posture as agents of the constituency, not necessarily just for their benefit. The phrase "on behalf of" in political contexts typically means "representing" or "in the interest of", but it's ambiguous. Given the distinction in WordNet, sense 1 is for agentive "on behalf of", sense 2 is for benefactive and usually "in behalf". Since the text says "on behalf of", and the example for sense 1 is "on behalf of", sense 1 seems the better match. The context: politicians are striking a posture that aligns with or represents an important constituency. They are acting as agents for that constituency. So I'll choose sense 1.

The answer should be JSON: {"sense_index": 1}.

provider: StreamLake


[System] You are an English linguist performing fine-grained Word Sense Disambiguation. WordNet glosses are schematic. Use the sentence context, the examples, and the synonyms to choose the best indexed sense. Do not hedge. Choose the single best indexed sense.

[User]
Target lemma: important
Target surface form: important
Context:
If he is competent and conscientious, he serves us well. Our teachers are not an important factor in our educational crisis. Whether they are or are not underpaid is a problem of equity; it is not an educational problem. It is silly libel on our teachers to think they would educate our children better if only they got a few thousand dollars a year more. It is the kind of libel the teachers' unions do not mind spreading, for their own narrow purposes. It is also the kind of libel politicians find useful, since it helps them strike a friendly posture on behalf of an <t>important</t> constituency. But there is not one shred of evidence that, other things being equal, salary differentials result in educational differentials.

Candidate senses:
1. sense_key=important%3:00:00:: | definition=of great significance or value | synonyms=of import | examples=important people; the important questions of the day
2. sense_key=important%3:00:04:: | definition=important in effect or meaning | synonyms=significant | examples=a significant change in tax laws; a significant change in the Constitution
3. sense_key=important%3:00:02:: | definition=of extreme importance; vital to the resolution of a crisis | synonyms=crucial | examples=a crucial moment in his career; a crucial election
4. sense_key=important%5:00:00:influential:00 | definition=having authority or ascendancy or influence | synonyms=authoritative | examples=an important official; the captain's authoritative manner
5. sense_key=important%5:00:00:immodest:02 | definition=having or suggesting a consciousness of high position | examples=recited the decree with an important air; took long important strides in the direction of his office

Instructions:
1. Choose the single best indexed sense for the target word in context.
2. WordNet glosses are schematic; use the context, synonyms, and examples together.
3. Do not answer with a WordNet sense key.
4. Return only a JSON object exactly like {"sense_index": 3}.

reasoning_content:
We are asked to disambiguate "important" in context: "it helps them strike a friendly posture on behalf of an important constituency." The target is "important" modifying "constituency". We have five candidate senses. Let's examine each:

1. "of great significance or value" (synonyms: of import). Examples: important people; the important questions of the day. This is a general sense of importance.

2. "important in effect or meaning" (synonyms: significant). Examples: a significant change in tax laws; a significant change in the Constitution. Focuses on meaning/effect.

3. "of extreme importance; vital to the resolution of a crisis" (synonyms: crucial). Examples: a crucial moment; a crucial election. This implies critical importance, urgency.

4. "having authority or ascendancy or influence" (synonyms: authoritative). Examples: an important official; the captain's authoritative manner. Describes a person or entity with power/influence.

5. "having or suggesting a consciousness of high position" (examples: recited the decree with an important air; took long important strides). This is about a self-important demeanor, not about actual importance.

In the context: "politicians find useful, since it helps them strike a friendly posture on behalf of an important constituency." The constituency is a group of people, likely voters. Politicians want to appear friendly to a group that has significance or influence. The word "important" here likely means "of great significance or value" (sense 1) or possibly "influential" (sense 4). Let's check: The context talks about teachers' unions and politicians using them. The constituency is likely teachers or their union, which is a significant voting bloc. Sense 4: "having authority or ascendancy or influence" fits well, as an "important constituency" means one that has political influence. Sense 1 is very broad and also fits, but sense 4 specifically denotes influence, which aligns with a constituency's power. Sense 3 (crucial) might be too strong; it's not a crisis. Sense 2 (significant in effect) is possible, but again, sense 4 seems more precise. However, WordNet senses for adjectives are often hierarchical; sense 4 is a synset for "influential" that includes "important" as a member. The example: "an important official" parallels "an important constituency": both refer to entities with authority or influence. So sense 4 is the best match.

Thus, I'll choose sense_index: 4.


[System] You are an English linguist performing fine-grained Word Sense Disambiguation. WordNet glosses are schematic. Use the sentence context, the examples, and the synonyms to choose the best indexed sense. Do not hedge. Choose the single best indexed sense.

[User]
Target lemma: shred
Target surface form: shred
Context:
Our teachers are not an important factor in our educational crisis. Whether they are or are not underpaid is a problem of equity; it is not an educational problem. It is silly libel on our teachers to think they would educate our children better if only they got a few thousand dollars a year more. It is the kind of libel the teachers' unions do not mind spreading, for their own narrow purposes. It is also the kind of libel politicians find useful, since it helps them strike a friendly posture on behalf of an important constituency. But there is not one <t>shred</t> of evidence that, other things being equal, salary differentials result in educational differentials. If there were such evidence, you can be sure you would have heard of it.

Candidate senses:
1. sense_key=shred%1:23:00:: | definition=a tiny or scarcely detectable amount | synonyms=scintilla, whit, iota, tittle, smidgen, smidgeon
2. sense_key=shred%1:06:00:: | definition=a small piece of cloth or paper | synonyms=rag, tag, tag end, tatter

Instructions:
1. Choose the single best indexed sense for the target word in context.
2. WordNet glosses are schematic; use the context, synonyms, and examples together.
3. Do not answer with a WordNet sense key.
4. Return only a JSON object exactly like {"sense_index": 3}.

reasoning_content: We are given the target lemma "shred" and its surface form "shred" in the context: "... there is not one <t>shred</t> of evidence that, other things being equal, salary differentials result in educational differentials." We need to choose between sense 1 and sense 2. Sense 1: "a tiny or scarcely detectable amount" with synonyms scintilla, whit, iota, tittle, smidgen, smidgeon. Sense 2: "a small piece of cloth or paper" with synonyms rag, tag, tag end, tatter. In the context, "not one shred of evidence" means not even a tiny amount of evidence. This is a common phrase: "shred of evidence" meaning a very small amount. So sense 1 is the correct one. Thus, sense_index is 1.

provider: AtlasCloud


[System] You are an English linguist performing fine-grained Word Sense Disambiguation. WordNet glosses are schematic. Use the sentence context, the examples, and the synonyms to choose the best indexed sense. Do not hedge. Choose the single best indexed sense.

[User]
Target lemma: evidence
Target surface form: evidence
Context:
Our teachers are not an important factor in our educational crisis. Whether they are or are not underpaid is a problem of equity; it is not an educational problem. It is silly libel on our teachers to think they would educate our children better if only they got a few thousand dollars a year more. It is the kind of libel the teachers' unions do not mind spreading, for their own narrow purposes. It is also the kind of libel politicians find useful, since it helps them strike a friendly posture on behalf of an important constituency. But there is not one shred of <t>evidence</t> that, other things being equal, salary differentials result in educational differentials. If there were such evidence, you can be sure you would have heard of it.

Candidate senses:
1. sense_key=evidence%1:09:00:: | definition=your basis for belief or disbelief; knowledge on which to base belief | synonyms=grounds | examples=the evidence that smoking causes lung cancer is very compelling
2. sense_key=evidence%1:10:01:: | definition=an indication that makes something evident | examples=his trembling was evidence of his fear
3. sense_key=evidence%1:10:00:: | definition=(law) all the means by which any alleged matter of fact whose truth is investigated at judicial trial is established or disproved

Instructions:
1. Choose the single best indexed sense for the target word in context.
2. WordNet glosses are schematic; use the context, synonyms, and examples together.
3. Do not answer with a WordNet sense key.
4. Return only a JSON object exactly like {"sense_index": 3}.

reasoning_content:
We are asked to choose the best sense for "evidence" in the given context. The target is "evidence" in the sentence: "But there is not one shred of evidence that, other things being equal, salary differentials result in educational differentials." Let's analyze the candidate senses:

1. Sense 1: "your basis for belief or disbelief; knowledge on which to base belief" synonyms: grounds. Example: "the evidence that smoking causes lung cancer is very compelling." This sense is about the body of facts or information indicating whether a belief is true. In the context, "shred of evidence" means a piece of information that supports the claim. The phrase "evidence that... salary differentials result in educational differentials" refers to facts or data that would serve as grounds for believing that claim. This fits well.

2. Sense 2: "an indication that makes something evident" Example: "his trembling was evidence of his fear." Here, "evidence" means a sign or symptom that reveals something. The context talks about evidence that salary differentials cause educational differentials; it's not about a mere indication or sign, but about systematic proof or data. "Shred of evidence" suggests a piece of factual support, not a visible sign.

3. Sense 3: "(law) all the means by which any alleged matter of fact whose truth is investigated at judicial trial is established or disproved." This is specifically legal evidence. The context is not a legal one; it's an educational policy discussion. So this sense is not appropriate.

Thus, sense 1 is the most fitting: it refers to knowledge or information that serves as a basis for belief. The example given ("the evidence that smoking causes lung cancer") parallels the structure "evidence that... salary differentials result in educational differentials." Therefore, sense index 1.

Return JSON: {"sense_index": 1}


[System] You are an English linguist performing fine-grained Word Sense Disambiguation. WordNet glosses are schematic. Use the sentence context, the examples, and the synonyms to choose the best indexed sense. Do not hedge. Choose the single best indexed sense.

[User]
Target lemma: other
Target surface form: other
Context:
Our teachers are not an important factor in our educational crisis. Whether they are or are not underpaid is a problem of equity; it is not an educational problem. It is silly libel on our teachers to think they would educate our children better if only they got a few thousand dollars a year more. It is the kind of libel the teachers' unions do not mind spreading, for their own narrow purposes. It is also the kind of libel politicians find useful, since it helps them strike a friendly posture on behalf of an important constituency. But there is not one shred of evidence that, <t>other</t> things being equal, salary differentials result in educational differentials. If there were such evidence, you can be sure you would have heard of it.

Candidate senses:
1. sense_key=other%3:00:00:: | definition=not the same one or ones already mentioned or implied; - the White Queen | examples=today isn't any other day; the construction of highways and other public works
2. sense_key=other%5:00:00:past:00 | definition=recently past | examples=the other evening
3. sense_key=other%5:00:02:past:00 | definition=belonging to the distant past | synonyms=early, former | examples=the early inhabitants of Europe; former generations
4. sense_key=other%5:00:00:strange:00 | definition=very unusual; different in character or quality from the normal or expected; - Lance Morrow | examples=a strange, other dimension...where his powers seemed to fail

Instructions:
1. Choose the single best indexed sense for the target word in context.
2. WordNet glosses are schematic; use the context, synonyms, and examples together.
3. Do not answer with a WordNet sense key.
4. Return only a JSON object exactly like {"sense_index": 3}.

reasoning_content:
We are asked to perform word sense disambiguation for the target word "other" in the given context. The context is: "other things being equal, salary differentials result in educational differentials."

We have four candidate senses:

1. sense_key=other%3:00:00:: | definition=not the same one or ones already mentioned or implied | examples=today isn't any other day; the construction of highways and other public works
2. sense_key=other%5:00:00:past:00 | definition=recently past | examples=the other evening
3. sense_key=other%5:00:02:past:00 | definition=belonging to the distant past | synonyms=early, former | examples=the early inhabitants of Europe; former generations
4. sense_key=other%5:00:00:strange:00 | definition=very unusual; different in character or quality from the normal or expected | examples=a strange, other dimension...where his powers seemed to fail

In the phrase "other things being equal", the word "other" is part of a fixed expression "ceteris paribus" (Latin for "other things equal"). Here, "other" means "other things" i.e., additional or remaining things besides the ones under consideration. It is used to indicate that we are holding constant all variables except the one being discussed. So "other" here means "other (things)" as in the first sense: not the same ones already mentioned, i.e., additional or different things. It doesn't mean recently past, distant past, or strange. The example "today isn't any other day" shows a similar use of "other" meaning "different from the one mentioned." In "other things being equal", "other" refers to things not being the specific thing being considered (salary differentials). So it's sense 1.

Thus, the best sense is index 1.

provider: Baidu


[System] You are an English linguist performing fine-grained Word Sense Disambiguation. WordNet glosses are schematic. Use the sentence context, the examples, and the synonyms to choose the best indexed sense. Do not hedge. Choose the single best indexed sense.

[User]
Target lemma: thing
Target surface form: things
Context:
Our teachers are not an important factor in our educational crisis. Whether they are or are not underpaid is a problem of equity; it is not an educational problem. It is silly libel on our teachers to think they would educate our children better if only they got a few thousand dollars a year more. It is the kind of libel the teachers' unions do not mind spreading, for their own narrow purposes. It is also the kind of libel politicians find useful, since it helps them strike a friendly posture on behalf of an important constituency. But there is not one shred of evidence that, other <t>things</t> being equal, salary differentials result in educational differentials. If there were such evidence, you can be sure you would have heard of it.

Candidate senses:
1. sense_key=thing%1:26:00:: | definition=a special situation | examples=this thing has got to end; it is a remarkable thing
2. sense_key=thing%1:04:00:: | definition=an action | examples=how could you do such a thing?
3. sense_key=thing%1:09:00:: | definition=a special abstraction | examples=a thing of the spirit; things of the heart
4. sense_key=thing%1:06:00:: | definition=an artifact | examples=how does this thing work?
5. sense_key=thing%1:11:00:: | definition=an event | examples=a funny thing happened on the way to the...
6. sense_key=thing%1:09:02:: | definition=a vaguely specified concern | synonyms=matter, affair | examples=several matters to attend to; it is none of your affair
7. sense_key=thing%1:10:00:: | definition=a statement regarded as an object | examples=to say the same thing in other terms; how can you say such a thing?
8. sense_key=thing%1:06:01:: | definition=an entity that is not named specifically | examples=I couldn't tell what the thing was
9. sense_key=thing%1:07:00:: | definition=any attribute or quality considered as having its own existence | examples=the thing I like about her is ...
10. sense_key=thing%1:09:01:: | definition=a special objective | examples=the thing is to stay in bounds
11. sense_key=thing%1:12:00:: | definition=a persistent illogical feeling of desire or aversion | examples=he has a thing about seafood; she has a thing about him
12. sense_key=thing%1:03:00:: | definition=a separate and self-contained entity

Instructions:
1. Choose the single best indexed sense for the target word in context.
2. WordNet glosses are schematic; use the context, synonyms, and examples together.
3. Do not answer with a WordNet sense key.
4. Return only a JSON object exactly like {"sense_index": 3}.

reasoning_content:
We are asked to perform word sense disambiguation for the target lemma "thing" with surface form "things" in the given context. We have 12 candidate senses from WordNet (some are numbered oddly: note that sense_key thing%1:03:00:: might be missing from the list? Actually the list goes up to 12, but there is a gap: we have 1–12, but sense_key thing%1:03:00:: is not listed separately? Let's check the list: it includes 1. thing%1:26:00::, 2. thing%1:04:00::, 3. thing%1:09:00::, 4. thing%1:06:00::, 5. thing%1:11:00::, 6. thing%1:09:02::, 7. thing%1:10:00::, 8. thing%1:06:01::, 9. thing%1:07:00::, 10. thing%1:09:01::, 11. thing%1:12:00::, 12. thing%1:03:00::. So 12 is "a separate and self-contained entity". But in the context, we have "other things being equal". This is an idiomatic phrase: "other things being equal" (or "ceteris paribus") means all other conditions or factors remaining the same. So "things" here refers to conditions, circumstances, factors, aspects, etc. Let's examine the candidate senses.

We need to match the sense of "things" in the phrase "other things being equal". The phrase is a well-known Latin expression "ceteris paribus" meaning "with all other conditions remaining the same". In this context, "things" refers to conditions, factors, or circumstances that might affect the outcome, aside from the variable under consideration (salary differentials). So it's an abstract concept: "other things" are other factors, conditions, etc.

Now, let's evaluate candidates:
1. a special situation: "this thing has got to end" – might be close, but "things" here are not situations but factors. Not exactly.
2. an action: "how could you do such a thing?" – no, not actions.
3. a special abstraction: "a thing of the spirit" – too vague; maybe things as abstractions? But "other things" are not special abstractions; they are general factors.
4. an artifact: no.
5. an event: no.
6. a vaguely specified concern: synonyms "matter, affair"; examples: "several matters to attend to" – this might be close: "other things being equal" could be paraphrased as "other matters being equal". But "concern" or "matter" fits because "things" could be matters or affairs. This seems plausible.
7. a statement regarded as an object: no.
8. an entity that is not named specifically: "I couldn't tell what the thing was" – this is very general, like a placeholder for any object. But "other things" might be unspecified entities, but the phrase is more about abstract conditions.
9. any attribute or quality considered as having its own existence: "the thing I like about her is..." – not really.
10. a special objective: no.
11. a persistent illogical feeling: no.
12. a separate and self-contained entity: too broad and physical.

Sense 6: "a vaguely specified concern" with synonyms "matter, affair". The example "several matters to attend to" is a bit different: matters to attend to are tasks or issues. But "other things being equal" means "other conditions being equal" or "other factors being unchanged". Could we call those "matters"? Possibly, if we interpret "matters" broadly as "circumstances" or "points". However, the phrase is often formalized as "all other things being equal", meaning all other relevant factors constant. In economics, "ceteris paribus" is "other things equal". So "things" are the various factors or variables. This might align with sense 3: "a special abstraction" – but that example is "a thing of the spirit", which is more like a concept. Sense 12: "a separate and self-contained entity" could be interpreted abstractly as any entity, but the phrase uses "things" to mean "factors" or "conditions", which are abstract, but not necessarily self-contained entities.

Let's check sense 12: definition "a separate and self-contained entity". This is very generic, often used for concrete objects, but can be abstract. However, the phrase "other things being equal" is typically not about entities but about conditions. So sense 12 seems too broad and not specific enough.

Consider the idiom: "other things being equal" – the word "things" here is often understood as "circumstances" or "conditions". There is a sense in WordNet: "thing%1:26:00:: a special situation" – example "this thing has got to end". That might work: a situation. "Other situations being equal"? Not quite. "Circumstances" is close to situation. So sense 1 might be plausible: a special situation. But "special" might be too specific. The phrase is general.

Looking up typical WordNet disambiguation for "thing" in "other things being equal", I recall that in some corpora, it's tagged with a sense meaning "a condition" or "a factor". Checking WordNet, there is no explicit "condition" sense. Among the given, I think sense 6: "a vaguely specified concern" (matter, affair) is often used for such abstract referents. For example, "that's a different thing" might be sense 6. This might be the most appropriate.

Alternatively, sense 3: "a special abstraction" is also abstract, but the example "a thing of the spirit" suggests something more profound.

Let's check the context: "other things being equal" is inside "other <t>things</t> being equal, salary differentials result in educational differentials." The phrase is a conditional clause. So it's a fixed expression meaning "if all other factors are the same". I'd map it to a sense meaning "factor" or "condition". None explicitly say that, but sense 6's "concern" or "matter" can be a condition. For example, "It's a matter of time" – "matter" can be a situation or affair. So I'll go with sense 6.

Let's verify the numbering: In the provided list, sense 6 is: "6. sense_key=thing%1:09:02:: | definition=a vaguely specified concern | synonyms=matter, affair | examples=several matters to attend to; it is none of your affair" – yes.

So my choice is sense 6.

Now, output must be JSON object exactly like {"sense_index": 6}. Make sure to use integer.


[System] You are an English linguist performing fine-grained Word Sense Disambiguation. WordNet glosses are schematic. Use the sentence context, the examples, and the synonyms to choose the best indexed sense. Do not hedge. Choose the single best indexed sense.

[User]
Target lemma: equal
Target surface form: equal
Context:
Our teachers are not an important factor in our educational crisis. Whether they are or are not underpaid is a problem of equity; it is not an educational problem. It is silly libel on our teachers to think they would educate our children better if only they got a few thousand dollars a year more. It is the kind of libel the teachers' unions do not mind spreading, for their own narrow purposes. It is also the kind of libel politicians find useful, since it helps them strike a friendly posture on behalf of an important constituency. But there is not one shred of evidence that, other things being <t>equal</t>, salary differentials result in educational differentials. If there were such evidence, you can be sure you would have heard of it.

Candidate senses:
1. sense_key=equal%3:00:00:: | definition=having the same quantity, value, or measure as another | examples=on equal terms; all men are equal before the law
2. sense_key=equal%3:00:03:: | definition=having the requisite qualities or resources to meet a task | synonyms=adequate | examples=she had adequate training; her training was adequate

Instructions:
1. Choose the single best indexed sense for the target word in context.
2. WordNet glosses are schematic; use the context, synonyms, and examples together.
3. Do not answer with a WordNet sense key.
4. Return only a JSON object exactly like {"sense_index": 3}.

reasoning_content: We are given the target word "equal" in the context: "other things being <t>equal</t>". The phrase "other things being equal" is a common phrase meaning "if all other conditions remain the same". In this context, it means assuming salary differentials are the only variable, there is no evidence they affect educational outcomes. So the sense of "equal" here is the sense of "equal" meaning "having the same quantity, value, or measure" as in all other things being the same, not varying. That corresponds to sense_key equal%3:00:00::. The other sense is "adequate", which doesn't fit the phrase. So the correct index is 1. Return {"sense_index": 1}.

provider: Together


[System] You are an English linguist performing fine-grained Word Sense Disambiguation. WordNet glosses are schematic. Use the sentence context, the examples, and the synonyms to choose the best indexed sense. Do not hedge. Choose the single best indexed sense.

[User]
Target lemma: differential
Target surface form: differentials
Context:
Our teachers are not an important factor in our educational crisis. Whether they are or are not underpaid is a problem of equity; it is not an educational problem. It is silly libel on our teachers to think they would educate our children better if only they got a few thousand dollars a year more. It is the kind of libel the teachers' unions do not mind spreading, for their own narrow purposes. It is also the kind of libel politicians find useful, since it helps them strike a friendly posture on behalf of an important constituency. But there is not one shred of evidence that, other things being equal, salary <t>differentials</t> result in educational differentials. If there were such evidence, you can be sure you would have heard of it.

Candidate senses:
1. sense_key=differential%1:09:00:: | definition=the result of mathematical differentiation; the instantaneous change of one quantity relative to another; df(x)/dx | synonyms=derived function, derivative, differential coefficient, first derivative
2. sense_key=differential%1:07:00:: | definition=a quality that differentiates between similar things
3. sense_key=differential%1:06:00:: | definition=a bevel gear that permits rotation of two shafts at different speeds; used on the rear axle of automobiles to allow wheels to rotate at different speeds on curves | synonyms=differential gear

Instructions:
1. Choose the single best indexed sense for the target word in context.
2. WordNet glosses are schematic; use the context, synonyms, and examples together.
3. Do not answer with a WordNet sense key.
4. Return only a JSON object exactly like {"sense_index": 3}.

reasoning_content:
We are given a target lemma "differential" with surface form "differentials" in a specific context. We need to choose the best indexed sense from three candidate senses. The senses are:

1. Mathematics: derivative
2. A quality that differentiates between similar things
3. A bevel gear in automobiles

Context: "Our teachers are not an important factor in our educational crisis. Whether they are or are not underpaid is a problem of equity; it is not an educational problem. It is silly libel on our teachers to think they would educate our children better if only they got a few thousand dollars a year more. It is the kind of libel the teachers' unions do not mind spreading, for their own narrow purposes. It is also the kind of libel politicians find useful, since it helps them strike a friendly posture on behalf of an important constituency. But there is not one shred of evidence that, other things being equal, salary differentials result in educational differentials. If there were such evidence, you can be sure you would have heard of it."

The target is "differentials" used as a noun. In context, "salary differentials" likely means differences in salary (e.g., differences in pay between teachers and other professions, or among teachers themselves). The phrase "educational differentials" would then mean differences in educational outcomes or quality. The sense that best fits is "a quality that differentiates between similar things" (sense 2), as it refers to differences in quality or characteristics.

Sense 1 (mathematics) would not fit: "differentials" in the mathematical sense is not about salary or education. Sense 3 (automotive gear) is irrelevant. Hence, the correct indexed sense is 2.

The user also requested that the answer not be a WordNet sense key but a JSON object with the key "sense_index" and the value. So we need to return {"sense_index": 2}.

We must only respond with the JSON without any othertext.


[System] You are an English linguist performing fine-grained Word Sense Disambiguation. WordNet glosses are schematic. Use the sentence context, the examples, and the synonyms to choose the best indexed sense. Do not hedge. Choose the single best indexed sense.

[User]
Target lemma: result
Target surface form: result
Context:
Our teachers are not an important factor in our educational crisis. Whether they are or are not underpaid is a problem of equity; it is not an educational problem. It is silly libel on our teachers to think they would educate our children better if only they got a few thousand dollars a year more. It is the kind of libel the teachers' unions do not mind spreading, for their own narrow purposes. It is also the kind of libel politicians find useful, since it helps them strike a friendly posture on behalf of an important constituency. But there is not one shred of evidence that, other things being equal, salary differentials <t>result</t> in educational differentials. If there were such evidence, you can be sure you would have heard of it.

Candidate senses:
1. sense_key=result%2:42:00:: | definition=issue or terminate (in a specified way, state, etc.); end | synonyms=ensue | examples=result in tragedy
2. sense_key=result%2:42:02:: | definition=have as a result or residue | synonyms=leave, lead | examples=The water left a mark on the silk dress; Her blood left a stain on the napkin
3. sense_key=result%2:30:00:: | definition=come about or follow as a consequence | examples=nothing will result from this meeting

Instructions:
1. Choose the single best indexed sense for the target word in context.
2. WordNet glosses are schematic; use the context, synonyms, and examples together.
3. Do not answer with a WordNet sense key.
4. Return only a JSON object exactly like {"sense_index": 3}.

reasoning_content:
We are asked to find the correct sense of "result" in the given sentence: "salary differentials result in educational differentials." Here, "result" is used as a verb. Looking at the candidate senses:

1. "result%2:42:00::" definition: issue or terminate (in a specified way, state, etc.); end; synonyms: ensue; examples: result in tragedy. This sense is intransitive with "in", meaning to lead to a particular outcome.

2. "result%2:42:02::" definition: have as a result or residue; synonyms: leave, lead; examples: The water left a mark on the silk dress; Her blood left a stain on the napkin. This sense is transitive, meaning to cause something to be left as a residue.

3. "result%2:30:00::" definition: come about or follow as a consequence; examples: nothing will result from this meeting. This is intransitive, meaning to happen as a consequence.

In the target sentence: "salary differentials result in educational differentials" – here, "result" is used with "in", indicating that salary differentials lead to educational differentials. This matches sense 1: issue or terminate (in a specified way, state, etc.); end; synonyms: ensue; examples: result in tragedy. The phrase "result in" is explicitly used in the example for sense 1. Sense 2 is transitive and would require a direct object like "result something" (e.g., "The experiment resulted a mess" but that's not typical; it's more like "leave a result"). Sense 3 is intransitive without "in" (result from). Given "result in", sense 1 is the best fit.

Thus, the answer is sense index 1.


[System] You are an English linguist performing fine-grained Word Sense Disambiguation. WordNet glosses are schematic. Use the sentence context, the examples, and the synonyms to choose the best indexed sense. Do not hedge. Choose the single best indexed sense.

[User]
Target lemma: educational
Target surface form: educational
Context:
Our teachers are not an important factor in our educational crisis. Whether they are or are not underpaid is a problem of equity; it is not an educational problem. It is silly libel on our teachers to think they would educate our children better if only they got a few thousand dollars a year more. It is the kind of libel the teachers' unions do not mind spreading, for their own narrow purposes. It is also the kind of libel politicians find useful, since it helps them strike a friendly posture on behalf of an important constituency. But there is not one shred of evidence that, other things being equal, salary differentials result in <t>educational</t> differentials. If there were such evidence, you can be sure you would have heard of it.

Candidate senses:
1. sense_key=educational%3:01:00:: | definition=relating to the process of education | examples=educational psychology
2. sense_key=educational%5:00:00:instructive:00 | definition=providing knowledge | examples=an educational film

Instructions:
1. Choose the single best indexed sense for the target word in context.
2. WordNet glosses are schematic; use the context, synonyms, and examples together.
3. Do not answer with a WordNet sense key.
4. Return only a JSON object exactly like {"sense_index": 3}.

reasoning_content:
We are given the target word "educational" in a specific context. The context discusses an "educational crisis" and an "educational problem". The sentence in focus: "But there is not one shred of evidence that, other things being equal, salary differentials result in educational differentials." Here, "educational differentials" likely refers to differences in educational outcomes or quality, i.e., relating to the process or results of education. The first sense is "relating to the process of education" (e.g., educational psychology). The second sense is "providing knowledge" (e.g., an educational film). In the context, "educational differentials" means differences in educational achievement or quality, which is about the process of education, not about something being instructive or providing knowledge. The phrase "educational crisis" and "educational problem" earlier also refer to issues in the education system. So sense 1 is more appropriate. The second sense would be used for something like "an educational experience" meaning instructive, but here it's clearly about the field of education. Thus, sense 1 is correct.

Return JSON: {"sense_index": 1} (since senses are indexed starting at 1).


[System] You are an English linguist performing fine-grained Word Sense Disambiguation. WordNet glosses are schematic. Use the sentence context, the examples, and the synonyms to choose the best indexed sense. Do not hedge. Choose the single best indexed sense.

[User]
Target lemma: differential
Target surface form: differentials
Context:
Our teachers are not an important factor in our educational crisis. Whether they are or are not underpaid is a problem of equity; it is not an educational problem. It is silly libel on our teachers to think they would educate our children better if only they got a few thousand dollars a year more. It is the kind of libel the teachers' unions do not mind spreading, for their own narrow purposes. It is also the kind of libel politicians find useful, since it helps them strike a friendly posture on behalf of an important constituency. But there is not one shred of evidence that, other things being equal, salary differentials result in educational <t>differentials</t>. If there were such evidence, you can be sure you would have heard of it.

Candidate senses:
1. sense_key=differential%1:09:00:: | definition=the result of mathematical differentiation; the instantaneous change of one quantity relative to another; df(x)/dx | synonyms=derived function, derivative, differential coefficient, first derivative
2. sense_key=differential%1:07:00:: | definition=a quality that differentiates between similar things
3. sense_key=differential%1:06:00:: | definition=a bevel gear that permits rotation of two shafts at different speeds; used on the rear axle of automobiles to allow wheels to rotate at different speeds on curves | synonyms=differential gear

Instructions:
1. Choose the single best indexed sense for the target word in context.
2. WordNet glosses are schematic; use the context, synonyms, and examples together.
3. Do not answer with a WordNet sense key.
4. Return only a JSON object exactly like {"sense_index": 3}.

reasoning_content:
We are asked to perform Word Sense Disambiguation for the word "differentials" in the given context. The target is "differentials", and the context is about teachers' salaries and educational outcomes. The sentence: "But there is not one shred of evidence that, other things being equal, salary differentials result in educational differentials." Here, "salary differentials" means differences in salary, and "educational differentials" means differences in educational outcomes. So "differentials" here means differences or discrepancies. Looking at the candidate senses:

1. mathematical derivative
2. a quality that differentiates between similar things
3. a bevel gear in automobiles

Clearly, sense 2 fits: a quality that differentiates between similar things, i.e., a difference. In context, salary differentials are differences in pay, educational differentials are differences in education quality. So sense_index 2.

Thus the answer is {"sense_index": 2}.

provider: SiliconFlow


[System] You are an English linguist performing fine-grained Word Sense Disambiguation. WordNet glosses are schematic. Use the sentence context, the examples, and the synonyms to choose the best indexed sense. Do not hedge. Choose the single best indexed sense.

[User]
Target lemma: evidence
Target surface form: evidence
Context:
Whether they are or are not underpaid is a problem of equity; it is not an educational problem. It is silly libel on our teachers to think they would educate our children better if only they got a few thousand dollars a year more. It is the kind of libel the teachers' unions do not mind spreading, for their own narrow purposes. It is also the kind of libel politicians find useful, since it helps them strike a friendly posture on behalf of an important constituency. But there is not one shred of evidence that, other things being equal, salary differentials result in educational differentials. If there were such <t>evidence</t>, you can be sure you would have heard of it. If we wish to be serious about American education, we know exactly what to do -- and, just as important, what not to do.

Candidate senses:
1. sense_key=evidence%1:09:00:: | definition=your basis for belief or disbelief; knowledge on which to base belief | synonyms=grounds | examples=the evidence that smoking causes lung cancer is very compelling
2. sense_key=evidence%1:10:01:: | definition=an indication that makes something evident | examples=his trembling was evidence of his fear
3. sense_key=evidence%1:10:00:: | definition=(law) all the means by which any alleged matter of fact whose truth is investigated at judicial trial is established or disproved

Instructions:
1. Choose the single best indexed sense for the target word in context.
2. WordNet glosses are schematic; use the context, synonyms, and examples together.
3. Do not answer with a WordNet sense key.
4. Return only a JSON object exactly like {"sense_index": 3}.

reasoning_content:
We are given a sentence with a target word "evidence" at <t>evidence</t>. The context: "But there is not one shred of evidence that, other things being equal, salary differentials result in educational differentials. If there were such evidence, you can be sure you would have heard of it."

We need to choose the best sense among three candidates.

Sense 1: evidence%1:09:00:: "your basis for belief or disbelief; knowledge on which to base belief" synonyms: grounds. Example: "the evidence that smoking causes lung cancer is very compelling". This sense refers to factual knowledge supporting a belief.

Sense 2: evidence%1:10:01:: "an indication that makes something evident". Example: "his trembling was evidence of his fear". This sense is about a sign or symptom that reveals something.

Sense 3: evidence%1:10:00:: "(law) all the means by which any alleged matter of fact whose truth is investigated at judicial trial is established or disproved". This is legal evidence, used in courts.

In the context: "not one shred of evidence that ... salary differentials result in educational differentials." This is about lacking factual support for a claim. It's not a legal context, it's about a general assertion. The phrase "shred of evidence" is commonly used to mean a small amount of proof or grounds. The sense is about the basis for belief. The example in sense 1 matches: "the evidence that smoking causes lung cancer is very compelling" – that is a factual knowledge base. Sense 2 is more about a sign or symptom: "evidence of his fear" – the trembling itself is evidence. Here, the evidence would be data or studies showing that salary differentials cause educational differentials. So sense 1 is more about the abstract knowledge, while sense 2 could also be considered because the evidence would indicate something, but sense 1 specifies "knowledge on which to base belief" which fits better with "shred of evidence that [a proposition]". Sense 3 is clearly legal, not applicable.

Thus, sense 1 is best.


[System] You are an English linguist performing fine-grained Word Sense Disambiguation. WordNet glosses are schematic. Use the sentence context, the examples, and the synonyms to choose the best indexed sense. Do not hedge. Choose the single best indexed sense.

[User]
Target lemma: sure
Target surface form: sure
Context:
Whether they are or are not underpaid is a problem of equity; it is not an educational problem. It is silly libel on our teachers to think they would educate our children better if only they got a few thousand dollars a year more. It is the kind of libel the teachers' unions do not mind spreading, for their own narrow purposes. It is also the kind of libel politicians find useful, since it helps them strike a friendly posture on behalf of an important constituency. But there is not one shred of evidence that, other things being equal, salary differentials result in educational differentials. If there were such evidence, you can be <t>sure</t> you would have heard of it. If we wish to be serious about American education, we know exactly what to do -- and, just as important, what not to do.

Candidate senses:
1. sense_key=sure%3:00:00:: | definition=having or feeling no doubt or uncertainty; confident and assured | synonyms=certain | examples=felt certain of success; was sure (or certain) she had seen it
2. sense_key=sure%5:00:00:careful:00 | definition=exercising or taking care great enough to bring assurance | synonyms=certain | examples=be certain to disconnect the iron when you are through; be sure to lock the doors
3. sense_key=sure%3:00:04:: | definition=certain to occur; destined or inevitable; ; ; - Benjamin Franklin | synonyms=certain | examples=he was certain to fail; his fate is certain
4. sense_key=sure%5:00:00:secure:02 | definition=physically secure or dependable | examples=a sure footing; was on sure ground
5. sense_key=sure%5:00:00:reliable:00 | definition=reliable in operation or effect | synonyms=certain | examples=a quick and certain remedy; a sure way to distinguish the two
6. sense_key=sure%5:00:00:trustworthy:00 | definition=(of persons) worthy of trust or confidence | synonyms=trusted | examples=a sure (or trusted) friend
7. sense_key=sure%5:00:00:true:00 | definition=infallible or unfailing | examples=a sure (or true) sign of one's commitment
8. sense_key=sure%5:00:00:steady:00 | definition=certain not to fail | examples=a sure hand on the throttle
9. sense_key=sure%5:00:02:certain:01 | definition=impossible to doubt or dispute | synonyms=indisputable | examples=indisputable (or sure) proof

Instructions:
1. Choose the single best indexed sense for the target word in context.
2. WordNet glosses are schematic; use the context, synonyms, and examples together.
3. Do not answer with a WordNet sense key.
4. Return only a JSON object exactly like {"sense_index": 3}.

reasoning_content:
We are given a target lemma "sure" and target surface form "sure" in a context. We need to pick the best sense from the provided candidate senses. Let's analyze the context.

Context: "If there were such evidence, you can be sure you would have heard of it."

The phrase "you can be sure" is a common expression meaning "you can be certain" or "you can be confident." It's used to emphasize that something is undoubtedly true. The speaker is asserting that if there were evidence, the listener would definitely know about it. So "sure" here means certain, confident, having no doubt. The sense is about a mental state of certainty.

Now, let's look at the candidate senses:

1. sense_key=sure%3:00:00:: | definition=having or feeling no doubt or uncertainty; confident and assured | synonyms=certain | examples=felt certain of success; was sure (or certain) she had seen it
   - This is about a person feeling no doubt. "you can be sure" fits this: "you can be confident/assured". The example "was sure she had seen it" matches the construction of being sure of something. This seems like a strong candidate.

2. sense_key=sure%5:00:00:careful:00 | definition=exercising or taking care great enough to bring assurance | synonyms=certain | examples=be certain to disconnect the iron when you are through; be sure to lock the doors
   - This is an imperative or advisory sense: "be sure to do something" meaning take care to do it. In "you can be sure", it's not an instruction to take care; it's a statement of certainty about a fact. This doesn't fit.

3. sense_key=sure%3:00:04:: | definition=certain to occur; destined or inevitable | synonyms=certain | examples=he was certain to fail; his fate is certain
   - This describes events that are inevitable. "He was certain to fail" means it was inevitable that he would fail. In our context, "you can be sure you would have heard of it" is not about an inevitable event; it's about a conditional: if there were evidence, then the listener would know. It's not stating that the hearing is inevitable in itself; it's saying that given the hypothetical, the listener can be confident. So this sense doesn't fit well.

4. sense_key=sure%5:00:00:secure:02 | definition=physically secure or dependable | examples=a sure footing; was on sure ground
   - This is literal or metaphorical physical security. Not applicable.

5. sense_key=sure%5:00:00:reliable:00 | definition=reliable in operation or effect | synonyms=certain | examples=a quick and certain remedy; a sure way to distinguish the two
   - This implies reliability, like a method or remedy. Not about a person's confidence.

6. sense_key=sure%5:00:00:trustworthy:00 | definition=(of persons) worthy of trust or confidence | synonyms=trusted | examples=a sure (or trusted) friend
   - This means trustworthy, like a person you can rely on. In "you can be sure", it's not describing the person as trustworthy; it's describing the mental state.

7. sense_key=sure%5:00:00:true:00 | definition=infallible or unfailing | examples=a sure (or true) sign of one's commitment
   - This means something that is a reliable indicator, unfailing. A "sure sign" is a clear indication. Not fitting here.

8. sense_key=sure%5:00:00:steady:00 | definition=certain not to fail | examples=a sure hand on the throttle
   - This means steady, as in a steady hand. Not it.

9. sense_key=sure%5:00:02:certain:01 | definition=impossible to doubt or dispute | synonyms=indisputable | examples=indisputable (or sure) proof
   - This means indisputable, as in evidence that is undeniable. "Sure proof" is proof that cannot be doubted. In the context, "you can be sure" is a phrase addressing the listener's certainty, not describing evidence as indisputable. So this doesn't match.

Clearly, sense 1 is the best fit: having or feeling no doubt or uncertainty; confident and assured. The phrase "you can be sure" means you can be confident, you can have no doubt. The example "was sure she had seen it" matches the usage of "sure" as a predicate adjective expressing personal certainty.

Thus, answer: {"sense_index": 1}


[System] You are an English linguist performing fine-grained Word Sense Disambiguation. WordNet glosses are schematic. Use the sentence context, the examples, and the synonyms to choose the best indexed sense. Do not hedge. Choose the single best indexed sense.

[User]
Target lemma: wish
Target surface form: wish
Context:
It is silly libel on our teachers to think they would educate our children better if only they got a few thousand dollars a year more. It is the kind of libel the teachers' unions do not mind spreading, for their own narrow purposes. It is also the kind of libel politicians find useful, since it helps them strike a friendly posture on behalf of an important constituency. But there is not one shred of evidence that, other things being equal, salary differentials result in educational differentials. If there were such evidence, you can be sure you would have heard of it. If we <t>wish</t> to be serious about American education, we know exactly what to do -- and, just as important, what not to do. There are many successful schools scattered throughout this nation, some of them in the poorest of ghettos, and they are all sending us the same message.

Candidate senses:
1. sense_key=wish%2:37:00:: | definition=hope for; have a wish | examples=I wish I could go home now
2. sense_key=wish%2:37:02:: | definition=prefer or wish to do something | synonyms=care, like | examples=Do you care to try this dish?; Would you like to come along to the movies?
3. sense_key=wish%2:32:02:: | definition=make or express a wish | examples=I wish that Christmas were over
4. sense_key=wish%2:37:01:: | definition=feel or express a desire or hope concerning the future or fortune of | synonyms=wish well
5. sense_key=wish%2:32:01:: | definition=order politely; express a wish for
6. sense_key=wish%2:32:00:: | definition=invoke upon | synonyms=bid | examples=wish you a nice evening; bid farewell

Instructions:
1. Choose the single best indexed sense for the target word in context.
2. WordNet glosses are schematic; use the context, synonyms, and examples together.
3. Do not answer with a WordNet sense key.
4. Return only a JSON object exactly like {"sense_index": 3}.

reasoning_content:
We are given a target word "wish" in the context: "If we wish to be serious about American education, we know exactly what to do ...". We need to choose the best indexed sense from the candidate list.

Analyzing the context: "If we wish to be serious about American education..." Here, "wish" is used as a verb, meaning "want" or "desire" to do something. The construction "wish to be" indicates a desire or intention. Let's examine the candidate senses:

1. sense_key=wish%2:37:00:: | definition=hope for; have a wish | examples=I wish I could go home now. This sense is about hoping for something, often unreal or hypothetical. Example: "I wish I could go home" implies a desire for something not currently true. In our context, "if we wish to be serious" is not a counterfactual hope; it's a conditional "if we want to be serious". So not the best.

2. sense_key=wish%2:37:02:: | definition=prefer or wish to do something | synonyms=care, like | examples=Do you care to try this dish?; Would you like to come along to the movies? This sense is about wanting or preferring to do something. It fits: "If we wish to be serious" means "If we want to be serious". This is a desire to engage in an action.

3. sense_key=wish%2:32:02:: | definition=make or express a wish | examples=I wish that Christmas were over. This is about expressing a wish, typically for something to be different. Example: "I wish that Christmas were over" is an expression of desire. In our context, "if we wish to be serious" is not directly expressing a wish; it's a conditional about wanting to do something.

4. sense_key=wish%2:37:01:: | definition=feel or express a desire or hope concerning the future or fortune of | synonyms=wish well. This is about wishing someone well, like "I wish you luck". Not applicable.

5. sense_key=wish%2:32:01:: | definition=order politely; express a wish for. This is like requesting something politely, e.g., "I wish to see the manager". It's a formal expression of desire. Our context: "If we wish to be serious" might be seen as a polite expression of desire, but it's more about wanting to do something.

6. sense_key=wish%2:32:00:: | definition=invoke upon | synonyms=bid | examples=wish you a nice evening; bid farewell. This is about saying something like "I wish you a nice evening". Not applicable.

The best fit is sense 2: "prefer or wish to do something". It directly matches the pattern "wish to do something". The example "Would you like to come along?" mirrors the structure "if we wish to be serious".

Therefore, the indexed sense is 2 (since the candidate list provides senses numbered 1 through 6). Return JSON: {"sense_index": 2}.


[System] You are an English linguist performing fine-grained Word Sense Disambiguation. WordNet glosses are schematic. Use the sentence context, the examples, and the synonyms to choose the best indexed sense. Do not hedge. Choose the single best indexed sense.

[User]
Target lemma: serious
Target surface form: serious
Context:
It is silly libel on our teachers to think they would educate our children better if only they got a few thousand dollars a year more. It is the kind of libel the teachers' unions do not mind spreading, for their own narrow purposes. It is also the kind of libel politicians find useful, since it helps them strike a friendly posture on behalf of an important constituency. But there is not one shred of evidence that, other things being equal, salary differentials result in educational differentials. If there were such evidence, you can be sure you would have heard of it. If we wish to be <t>serious</t> about American education, we know exactly what to do -- and, just as important, what not to do. There are many successful schools scattered throughout this nation, some of them in the poorest of ghettos, and they are all sending us the same message.

Candidate senses:
1. sense_key=serious%3:00:00:: | definition=concerned with work or important matters rather than play or trivialities | examples=a serious student of history; a serious attempt to learn to ski
2. sense_key=serious%5:00:00:important:00 | definition=of great consequence | examples=marriage is a serious matter
3. sense_key=serious%5:00:00:critical:03 | definition=causing fear or anxiety by threatening great harm | synonyms=dangerous, grave, grievous, severe, life-threatening | examples=a dangerous operation; a grave situation
4. sense_key=serious%5:00:00:intellectual:00 | definition=appealing to the mind | synonyms=good | examples=good music; a serious book
5. sense_key=serious%3:00:02:: | definition=completely lacking in playfulness | synonyms=unplayful, sober
6. sense_key=serious%5:00:00:difficult:00 | definition=requiring effort or concentration; complex and not easy to answer or solve | examples=raised serious objections to the proposal; the plan has a serious flaw

Instructions:
1. Choose the single best indexed sense for the target word in context.
2. WordNet glosses are schematic; use the context, synonyms, and examples together.
3. Do not answer with a WordNet sense key.
4. Return only a JSON object exactly like {"sense_index": 3}.

reasoning_content:
We are asked to choose the best sense for "serious" in the context. The target sentence: "If we wish to be serious about American education, we know exactly what to do..."

Let's analyze:

Context: The author is discussing the idea that paying teachers more would improve education, calling it a libel. Then says: "If we wish to be serious about American education, we know exactly what to do..." So here, "serious" means being genuinely committed, earnest, focused on what is important, not trivial. It contrasts with the earlier "silly libel" and superficial political posturing. The phrase "serious about" means to treat a matter with earnestness and importance.

Candidate senses:
1. "concerned with work or important matters rather than play or trivialities" – This fits: being serious about education means treating it as an important matter, not trivializing it. Example: "a serious attempt" aligns.
2. "of great consequence" – This is an adjective for something that is serious (e.g., a serious matter), but in the context, it's "we wish to be serious about", meaning we wish to adopt a serious attitude. Sense 2 is about the consequence of something, not the attitude. "marriage is a serious matter" – here, serious describes the matter, not the person. But "be serious about" means to treat something as having great consequence. It might overlap, but sense 1 specifically captures the personal attitude ("concerned with work or important matters rather than play").
3. "causing fear or anxiety by threatening great harm" – not applicable; education is not a threat.
4. "appealing to the mind" – not applicable; not about intellectual content.
5. "completely lacking in playfulness" – This is about a person's demeanor (sober, unplayful). "Be serious about" could imply a lack of playfulness, but it's more about earnestness. Sense 5: "unplayful, sober" – example? The gloss says completely lacking in playfulness. If someone says "I'm serious", they mean they're not joking. Here, "if we wish to be serious about American education" – it's not about joking, it's about being earnest and committed. Sense 1 captures that better because it mentions "rather than play or trivialities". So sense 1 includes the attitude of treating something as important. Sense 5 is purely about demeanor. I think sense 1 is more appropriate.
6. "requiring effort or concentration; complex and not easy to answer or solve" – This describes an objection or flaw as serious, meaning significant/difficult. Not applicable to "be serious about".

Between 1 and 2: The phrase "be serious about" typically means "to treat something with earnestness and importance". Sense 1 says "concerned with work or important matters rather than play or trivialities". That directly matches being serious about something. Sense 2 is "of great consequence", which is a property of the matter. But the phrase "we wish to be serious" is about our attitude. So sense 1 is better.

Consider examples: "a serious student of history" – someone who treats history as an important subject, not trivial. That aligns with "be serious about American education". So I'll pick sense 1.

Thus, the answer is sense_index: 1.