[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 need choose WordNet sense index for "helps" in given context. We need output JSON only. Need disambiguate.

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 target "helps" means assists/ enables them to strike a friendly posture. Similar to "aid", "assist", maybe "be of use; facilitate". Sense options:
1. help%2:41:00:: give help or assistance; be of service; synonyms assist, aid; examples Everyone helped out during earthquake; Can you help me carry this table? This is transitive with person object and VP complement? "help me carry" is catenative. Sense: provide assistance. This fits "helps them strike a friendly posture". But need distinguish from sense 3 (be of use; facilitate), sense 6 (contribute to furtherance of), sense 8 (improve; change for the better).

WordNet senses for help verb:
- 2:41:00 help: give help or assistance; be of service; synonyms assist, aid.
- 2:29:00 help: improve the condition of; These pills will help the patient (health).
- 2:42:00 help: be of use; synonyms facilitate; This will help to prevent accidents.
- 2:42:08 help: cannot help (restraint).
- 2:34:00 help: serve food.
- 2:41:12 help: contribute to the furtherance of; This money will help the development of literacy.
- 2:34:04 help: take or use (helped herself to supplies).
- 2:30:13 help: improve; change for the better; New slipcovers will help old furniture.

The context: "helps them strike a friendly posture" - "help somebody do something": assist by doing service. That is sense 1. But let's examine sense 3 "be of use; facilitate; examples This will help to prevent accidents". It can also be transitive with non-person? The key difference: sense 1 is "give help or assistance; be of service" - subject is helper, object is beneficiary and possibly task. Sense 3 is "be of use" - subject is thing or action that is useful; object is something? Example "This will help to prevent accidents" (intransitive? with to-infinitive). Gloss: be of use. synonyms facilitate. Actually facilitate verb often transitive with process (e.g., "it facilitates X"). In our sentence "it helps them strike ..." subject "it" = the libel; object "them" = politicians; infinitive "strike ...". Could be sense 1 because object is person receiving assistance to do an action. But "be of use" could also have object? Hmm.

We need single best indexed sense. Let's deeply analyze WN examples and senses.

WordNet frames for help:
"v 8 senses". The eight senses likely align in order: 1 help, assist, aid; 2 help, aid (improve condition); 3 facilitate, help (be of use); 4 help oneself (can't help but); 5 serve, help (help to food); 6 help, facilitate? no; 7 avail oneself; 8 help (improve).

Let's get exact examples from WordNet:
1. *help%2:41:00::*: (v) help, assist, aid  "Everyone helped out during the earthquake"; "Can you help me carry this table?"; "She never helps around the house"
2. *help%2:29:00::*: (v) help, aid  "These pills will help the patient"
3. *help%2:42:00::*: (v) facilitate, help  "This will help to prevent accidents"
4. *help%2:42:08::*: (v) help oneself  "I can't help myself--I have to smoke"; "She could not help watching the sad spectacle"
5. *help%2:34:00::*: (v) serve, help  "I served him three times, and after that he helped himself"
6. *help%2:41:12::*: (v) help  "This money will help the development of literacy in developing countries"
7. *help%2:34:04::*: (v) avail, help  "She helped herself to some of the office supplies"
8. *help%2:30:13::*: (v) help  "New slipcovers will help the old living room furniture"

Now, sentence: "since it helps them strike a friendly posture". The thing (libel/political libel) helps them (politicians) to perform an action (strike posture). Which sense? Sense 1 examples include "Can you help me carry this table?" That is a person helping another person do a physical action, i.e., give assistance/assistance. But "help" in that case may mean give help (one may carry part of the load). In abstract context, a statement "helps politicians strike a friendly posture" means makes it easier / assists them in doing so. That aligns most with sense 1? But sense 3 "facilitate" might be more appropriate for abstract enabling. Let's compare sense 1 vs 3.

Sense 1: give help or assistance; be of service. It implies agent (helper) provides help to recipient. With an infinitival complement "help someone (to) do something". The subject can be non-person? Example not provided, but "Can you help me carry this table?" subject is person. Another example "Everyone helped out during the earthquake". "She never helps around the house". It often includes direct object person and task. WordNet frames maybe: somebody helps somebody, somebody helps somebody PP, somebody helps somebody to INF, somebody helps do something.

Sense 3: be of use; facilitate. Gloss "be of use" synonyms facilitate. Example "This will help to prevent accidents". Subject is thing/action. The frame could be "something helps (to) do something" / "something helps something". It emphasizes being useful, enabling, contributing. In "it helps them strike a friendly posture", subject is "it" (the libel) which is a thing/claim. It enables them to perform. This may be sense 3. But sense 3's example "This will help to prevent accidents" shows subject = measure/thing, infinitival complement = occurrence/action. It does not show a person object. However, "help them strike" with person object is more in line with sense 1.

Let's look at sense 6: contribute to the furtherance of; example "This money will help the development of literacy". Subject thing (money), object noun phrase (development). Not "person doing action". Could be possible: "it helps them strike..." i.e., contributes to furtherance of their striking posture. But sense 6 likely requires a noun phrase object and not animate beneficiary + VP. So not sense 6.

Sense 8: improve; change for the better; example slipcovers help old furniture. Not fit.

Sense 3 vs 1 subtle. In WSD tasks, "help" with animate object ("help me carry") is sense 1; inanimate object action is sense 3? Check WordNet definitions and mapping in training may differentiate by direct object type. Let's search memory of SemCor/WN use. For "help", examples:
- "The Russian Orthodox Church has helped..."? Might be sense 6? Hard.
- "It may help to ..." often sense 3.
- "helped them to escape" likely sense 1? Let's think.

The "help somebody (to) do something" construction with direct object human could be both sense 1 and 3? WordNet sense 3 includes "facilitate". The verb facilitate is transitive or intransitive? WN sense 3 "be of use" synonyms facilitate. If you say "it helps them strike a friendly posture", you are saying "it facilitates their striking a friendly posture." In that case, object is a gerund phrase underlying; "them strike" is not just person but event. But direct object "them" makes it sense 1 give service.

Let's examine examples in official WordNet for sense 1: "Can you help me carry this table?" Here subject = person, object = animate pronoun, infinitive. Exactly parallel to sentence: subject = inanimate "it", object = animate "them", infinitive. So sense 1 can have subject inanimate? Maybe yes. Example includes animate person though. But sense 1's definition is broad "give help or assistance; be of service". This can apply to things too? "This tool helps me open jars." Is that sense 1 or sense 3? Without checking, "This book will help you understand the subject" could be sense 1? Hmm.

Distinguishing by definition:
- Sense 1: "give help or assistance; be of service". Involves an entity serving/helping. If subject is a tool or a statement, it "gives help" by being useful. But sense 3 specifically "be of use" is for things being useful. In lexical semantics, sense 1 often personal: one entity assists another. Sense 3 entities are useful, facilitate. Yet the examples of sense 1 also around house, earthquake; sense 3 example inanimate "This will help to prevent accidents".

The target "helps" has subject "it" (the libel) and object "them". The semantic frame "X helps Y Z" with Y as beneficiary and Z as action is very common. In WordNet, which sense lists this construction? Let's check if sense 3 frames include "Somebody ----s somebody INFINITIVE". Could sense 3 take a person object? Maybe not. Let's recall VerbNet/FrameNet? WordNet lexical file help-v has frames for all senses. GLE:
help (sense 1) frame: Somebody ----s somebody, Somebody ----s somebody with something, Somebody ----s somebody INFINITIVE.
help (sense 3) frame: Something ----s somebody, Something ----s somebody to INFINITIVE? Actually "facilitate" has frames: Somebody ----s something, Somebody ----s PP, Somebody ----s somebody, Something ----s something. Hmm.

Let's find actual WordNet data from memory or derive. WordNet help senses lexical IDs:
1. help%2:41:00:: (41 is social?) Frames: ? Examples as above.
3. help%2:42:00:: (42 is verb.communication? Wait 42 is ? WordNet lexicographer file classes: 29 = verb.body, 30 = verb.change, 34 = verb.consumption, 41 = verb.social, 42 = verb.competition? Actually 42 is verb.competition? Hmm. help%2:42:00:: belongs to verb.competition? That's odd; "be of use" maybe in verb.social? Not sure. Lexical files: 29 body, 30 change, 31 cognition, 32 communication, 33 competition, 34 consumption, 35 contact, 36 creation, 37 emotion, 38 motion, 39 perception, 40 possession, 41 social, 42 stative, 43 weather. Wait 42 is verb.stative? Let me recall: Princeton WordNet lexnames: noun.Tops, noun.act, noun.animal, ..., adj.all; verb: verb.body (29), verb.change (30), verb.cognition (31), verb.communication (32), verb.competition (33), verb.consumption (34), verb.contact (35), verb.creation (36), verb.emotion (37), verb.motion (38), verb.perception (39), verb.possession (40), verb.social (41), verb.stative (42), verb.weather (43). So sense 1 is social (41), sense 3 is stative (42). Ah! Sense 3 "be of use" = stative, subject thing/state, object process/activity. Sense 1 is social (helping). So subject "it" (libel) as something that helps politicians strike posture - is it stative (be of use) or social? It's an abstract entity being useful to somebody, enabling an action. Lexical file stative includes relations like "benefit, facilitate, help"? If subject is "it" and meaning "be of use", then sense 3 seems apt.

But the direct object "them" is a person; can stative "help" take a person object? Example "This memo will help you"? I think that's commonly sense 1 or 3. Let's examine usage of "help" in sense 3 definition "be of use; facilitate". The synonym facilitate transitive often takes a process object (facilitate the negotiation) but can take person? Not typical. However WordNet example "This will help to prevent accidents" is intransitive-ish. Could have object "to prevent accidents".

In SemCor, "help" annotated? Since I cannot search internet, use reasoning. The sentence from the user likely drawn from a corpus with gold WN tags. Need choose index. It might be from a WSD benchmark. Let's identify source. The paragraph talks about teachers not being an important factor in educational crisis, salary differentials etc. It sounds like an editorial article. Could be from "American Purpose" maybe. The word "helps" in phrase "helps them strike a friendly posture" could be from an opinion piece. In a WSD test set (e.g., English all-words). The candidates listed include indices 1-8, and instructions. We need decide index.

Could be gold sense index perhaps 1. Let's see which sense best matches "politicians find useful, since it helps them strike a friendly posture". The phrase "find useful" points to sense 3 "be of use"? It is useful to them, helps them. In WordNet, sense 3 "be of use" = useful. But sense 1 "be of service" similar. Let's analyze more thoroughly.

Wordnet Key difference: Sense 1 has direct object as "someone", and implies agent intentionally provides help. Sense 3 has subject as something and means "be of use / facilitate", can be: "something helps (someone) to do something". But example provided for sense 3 lacks person object. The synonym "facilitate" is sense 3. The phrase "it helps them strike a friendly posture" = it facilitates them in striking... Since subject is inanimate and emphasis on being useful, I lean sense 3. But the frame with animate object is more typical of sense 1. Hmm.

Let's examine the candidate examples included in prompt. They may give clues. Sense 1 examples: "Everyone helped out during the earthquake; Can you help me carry this table?" Both involve direct assistance, physical or human. Sense 3 examples: "This will help to prevent accidents". It shows an inanimate subject and infinitival complement. Sense 6 example: "This money will help the development of literacy..." Inanimate subject + noun object. Sense 8 example: "New slipcovers will help the old living room furniture" inanimate subject + inanimate object.

Our sentence: subject "it" (a statement) + object "them" (politicians) + infinitive "strike". None of the examples exactly match. Which example's sense accepts an animate object + VP? Sense 1. But does the subject need to be animate? Not necessarily; but social verb frames usually have animate agent. However "help" as social can also have inanimate subject: "this dictionary helps me find definitions." In SemCor maybe tagged as sense 1? Actually "dictionary" helps = be of service. But sense 3 "be of use" too.

Let's look up in memory WordNet's own words: For help v.1: "give help or assistance; be of service" e.g. "Can you help me carry this table?" "She never helps around the house". For help v.3: "be of use; 'This will help to prevent accidents'" The distinction: v.1 requires a human (or agent) helper; v.3 is more about something being useful. The subject "it" refers to "this kind of libel" (a statement/type of claim). Does a libel "give help or assistance"? It does not intentionally help; it is useful for the politicians. This is more "be of use, facilitate". But the object "them" complicates.

Could sense 6 "contribute to the furtherance of" capture? Example "This money will help the development of literacy". If we rephrase: "This libel helps them strike a friendly posture" = contributes to the furtherance of their ability to strike a friendly posture. However sense 6 definition specifically "contribute to the furtherance of" with NP object; examples not involving animate + infinitive. The WN sense 6 maybe includes frames: Somebody ----s something; Something ----s something. The object in our sentence is not an action noun but pronoun + infinitival clause. So sense 6 unlikely.

Could sense 1 be correct due to "help SO (to) do"? Let's search mental data from SemCor. Sentence "a realignment that would help the Republicans win the House" — likely tagged help%2:41:00::? Because Republicans are animate persons. Sense 1 includes "help me carry table". On the other hand, "This chart will help you understand" might be tagged help%2:42:00:: (be of use). But if object is person, perhaps still sense 1 because frame "somebody helps somebody to INF". However sense 3 frame maybe "something helps somebody" too? Let's see.

Let's inspect WordNet lexical relations maybe sense 3 is similar to "facilitate". In WordNet, "help%2:42:00::" synonyms: "facilitate". For "facilitate", usage examples: "facilitate the development of a process". It can be "The new ramp will facilitate the entry of wheelchairs". The object typically a process/noun, not animate. But you can "facilitate someone"? possible but rare.

Given the user examples omitted person object for sense 3 likely because sense 3 doesn't take that frame. So target with person object "them" is sense 1. But subject "it" inanimate, but sense 1 can apply to abstracts? Let's consider WordNet examples: sense 1 examples all have animate subjects? Not necessarily: "The new policy helped reduce unemployment"? That might be sense 3.

Let's think from the perspective of the author of this task. They list candidate senses with definitions and examples. They expect model to compare context to examples and synonyms. The target sentence has "helps them strike a friendly posture." The most similar example is sense 1 "Can you help me carry this table?" (help + person + verb) vs sense 3 "This will help to prevent accidents" (thing + to-infinitive without person) vs sense 6 "This money will help the development" (thing + noun). The syntactic frame with a person beneficiary + bare infinitive is classic sense 1. So likely answer sense_index: 1.

Could it be sense 3 because synonyms include "facilitate" and it's object is inanimate event "strike a friendly posture"? But there is a person object; still the event is the goal. Hmm.

Let's analyze semantic roles: In "help them strike a posture", "them" is the helped entity; the infinitive "strike a friendly posture" is the helped action. In sense 1, the helper contributes assistance to the doer in achieving action. In sense 3, the thing makes the event easier. Since the politicians themselves are striking the posture; the libel helps them (aids them) to strike it. It's social assistance (it serves/supports their political action). Could be sense 1. If the libel were making the action easier (not necessarily helping the people) we'd say "helps to strike a friendly posture". But here we have "helps them". Thus sense 1.

But let's not jump. Let's examine WordNet sense 1 definition "give help or assistance; be of service". Does it have a sense of 'be of service' that can apply to anything? In WN, "be of service" is a phrase. Sense 1's second gloss = "be of service". Wait sense 3's gloss is also "be of use". Sense 1 be of service: e.g., "Everyone helped out" (they provided service). Sense 3 be of use: e.g., "This will help to prevent accidents". So distinction = service vs use. Abstract libel "is of service" to politicians? It is useful/serviceable. Could be sense 1. But sense 3 focuses on use.

Could there be a possible sense 6 "contribute to the furtherance of"? Let's parse: "it helps them strike a friendly posture". If we restructure as "it helps [their striking a friendly posture]" with "them" as specifier of gerund, sense 6 could apply. But syntactically "help somebody (to) do something" is a different subcategorization. WN sense 6 likely doesn't have infinitival complement. So no.

What about sense 8 "improve; change for the better"? Example: slipcovers help old furniture (make furniture look better). "It helps them strike a friendly posture" isn't about improving condition of them, but enabling action. Not sense 8.

Sense 2 health improvement no.

Thus decision is between 1 and 3. Need be confident. Let's see if target surface form "helps" as third person singular present. In WordNet, sense 1 and 3 are both regular forms.

Let's search mental all-words WSD datasets. In Senseval-3/SEM-2007, "help" word often tag? I recall ambiguous mapping: In many tasks, examples of "help" with inanimate subject and infinitive are tagged as "help%2:42:00::" (be of use). E.g., "the act ... would help ..." tagged as sense 3. For animate subject helping animate object to do, sense 1. In this sentence: subject "it" refers to "this kind of libel" (a noun phrase; inanimate). Object "them" is animate. Infinitive "strike". That could be considered sense 1 because the object "them" is beneficiary, not the action; but the inanimate subject suggests sense 3.

Let's look in context: The antecedent of "it": "It is also the kind of libel politicians find useful". The pronoun "it" = "this kind of libel" / "the claim that teachers would educate children better if paid more". It is a rhetorical tool. "since it helps them strike a friendly posture on behalf of an important constituency." The thing helps the politicians perform a political act. Could be like "this evidence will help you win your case" - evidence is inanimate, beneficiary animate, action win. Which WN sense would that be? I would label as sense 1 (assist/aid) in common usage, but WordNet might label sense 3 (be of use). Let's check definitions: "Can you help me carry this table?" vs "This will help to prevent accidents." If you say "This evidence will help you win your case," it sounds like sense 1 because it's analogous to "Can you help me carry this table?". But the subject is inanimate. WordNet doesn't restrict.

Maybe we can derive from lexical file frames. Let's recall WordNet morphological/index data: help%2:42:00:: (sense 3) has lexical file verb.stative. Stative verbs typically don't have agent subjects. But can have cause/experience subject. "This tool helps me open jars" is stative? In FrameNet, there is "Assistance" frame. Words in "verb.social" include assist, help, aid. Words in "verb.stative" include help (be of use), facilitate? Hmm.

Let's look at examples for "be of use" synonyms: "facilitate" is in which lexical file? facilitate%2:41:00::? Actually I think "facilitate" is verb.social (41). Wait maybe not. If help sense 3 synonyms facilitate, but its own senses could be in stative? Let's recall: WordNet entry for facilitate v (1 sense): make easier; "you could facilitate the process by sharing your knowledge". Lexical file maybe verb.change? Not sure. But if sense 3 synonyms facilitate, the frame may include transitive process object.

Hmm, but the prompt's synonym for sense 3 is "facilitate". The example "This will help to prevent accidents" subject inanimate. Our sentence has person object, which "facilitate" can also take? "This will facilitate them to win"? Sounds off; you'd say "facilitate their victory". So sense 3 with person object is less natural. Thus sense 1.

Let's examine the phrase "strike a friendly posture". The libel doesn't literally provide help; it allows them to posture. Maybe meaning: it helps (facilitates) the act of striking posture. But the syntax "helps them strike" chooses sense 1.

However, the instruction says WordNet glosses are schematic; use context, examples, synonyms. They want choose best indexed sense. They explicitly mention "do not hedge". We should output JSON only. I need ensure final answer is just {"sense_index": 1} (or 3). No extra text.

Let's do a deeper semantic/constructional analysis.

The target "helps" with an animate object and an infinitive clause is a classic control/raising verb. The subject can be an inanimate entity that causes the event to be easier. This is generally the first sense in dictionaries: "make it easier for (someone) to do something by doing part of the work; assist." Actually the first sense in Merriam-Webster: "to give assistance or support to (someone) : to provide (someone) with something that is useful or necessary in achieving an end." Example: "Help me with this." That is sense 1. Sense "to be of use or benefit" (intransitive) is second or third. WordNet splits: sense 1 assist/aid, sense 3 be of use/facilitate. The transitive with person object is likely sense 1. The intransitive/infinitive with thing subject is sense 3. So answer 1.

But one more nuance: WN sense 1 examples do not include inanimate subject; but definition says "give help or assistance; be of service". Inanimate can "be of service". The second part "be of service" perhaps applies to all. So it's fine.

Let's also consider the possibility of wordnet sense indexing in candidate list not same as actual WordNet sense ordering due to lexical IDs. They provided 1-8. The question: choose single best indexed sense. The output should be index. If we choose 1.

But I recall a past WSD exercise where this exact sentence appears and gold answer is sense 1? Not sure. Let's try to infer from broader context style: It strongly resembles a passage from an article by Thomas Sowell? "If he is competent and conscientious, he serves us well. Our teachers are not an important factor..." Could be from "Inside American Education" or similar. The author says politicians find the libel useful because it helps them strike a friendly posture. This is rhetoric. In all-words WSD, tags were assigned by humans. Given the object "them" is people, likely tag = help%2:41:00:: (sense 1). Let's check if any tag for "help" in this passage might be sense 6 because "contribute to furtherance of". But no.

Let's see if sense 3 could be tagged if the object were "to strike" not them. Sentence: "since it helps them strike a friendly posture" = "since it helps [them strike a friendly posture]"? The semantic object might be the whole clause. "Help" can take a sentential complement: "It helped that he arrived early" (stative sense 3). But here it's an object + bare infinitive: "helps them strike". That's definitely sense 1 frame.

Let's also examine the provided examples and synonyms for sense 6: "contribute to the furtherance of" examples: "This money will help the development of literacy" has object "development of literacy" = noun phrase. Not infinitive. So no.

Therefore final answer: {"sense_index": 1}.

Before final, check if any trick: The target lemma "help", surface "helps". Candidate sense 1 sense_key=help%2:41:00::. The index #1 likely corresponds. So final JSON exactly. Ensure no Markdown code fence? The instruction says "Return only a JSON object exactly like {"sense_index": 3}." So final should be just the JSON, no code block. We should output raw JSON. Good.

One more thought: The instruction explicitly says "Do not answer with a WordNet sense key." We won't. Output only index. Good.

Let's consider if sense 3 might be considered because "it" (the libel) being useful. Many lexicographers tag "help" with inanimate subject and infinitival as sense 3. But our sentence has animate object. Let's search memory from WordNet gloss matching: For sense 3, "be of use; 'This will help to prevent accidents'". If we add a person "This will help you to prevent accidents", it still means "be of use to you". Would WordNet list that under sense 3? Maybe not because the social sense 1 covers. But in WN, sense 3's synonym "facilitate" cannot be "facilitate you to prevent accidents". Thus sense 1 is the construction with person object. So 1.

Let's verify with actual WordNet relation: help v.1 frames:
- Somebody ----s
- Somebody ----s somebody
- Somebody ----s somebody with something
- Somebody ----s somebody PP
- Somebody ----s somebody INFINITIVE
- Somebody ----s PP

help v.3 frames:
- Something ----s
- Something ----s to INFINITIVE
- Somebody ----s somebody
- Somebody ----s PP
Actually not sure. But likely sense 1 has "help me carry".

Thus final answer: {"sense_index": 1}.

provider: Parasail


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: 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}.

finish_reason: stop

role: assistant

reasoning_content: We need answer to WSD. Need choose sense for "strike" in sentence: "since it helps them strike a friendly posture on behalf of an important constituency." Meaning to assume/adopt a friendly posture. Candidate 17: occupy or take on (synonyms assume, take, take up; examples He assumes the lotus position; She took her seat on the stage). That matches "strike a friendly posture" = assume/take on a friendly posture. Need return JSON {"sense_index":17}. Ensure only JSON.

format: unknown

native_finish_reason: stop

provider: AtlasCloud

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: 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 need answer with JSON only. We need decide best sense. Context: politicians strike a friendly posture on behalf of an important constituency. "friendly posture" here means a favorable, supportive posture toward constituency, not necessarily befitting a friend in personal sense. Sense 2 definition: inclined to help or support; not antagonistic or hostile; synonyms favorable, well-disposed; examples: a government friendly to our interests. That matches political posture favorable to constituency. Sense 1: characteristic of or befitting a friend; friendly advice/neighborhood. Not best. Sense 3: easy to understand/use. No. Sense 4: allied forces. No. So index 2.

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: 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 need do WSD for target "posture" in context "strike a friendly <t>posture</t> on behalf of an important constituency". Need choose among 4 senses. Let's analyze.

Senses:
1. posture%1:07:00:: arrangement of body and limbs; synonyms position, attitude; examples assumed an attitude of surrender. Physical bodily arrangement/attitude.
2. posture%1:07:01:: characteristic way of bearing one's body; synonyms carriage, bearing; examples stood with good posture. Physical demeanor.
3. posture%1:09:00:: a rationalized mental attitude; synonyms position, stance. Mental/abstract stance or attitude, often "strike a posture" meaning adopt a public position/stance.
4. posture%1:07:02:: capability in terms of personnel and materiel that affect capacity to fight war; synonyms military capability etc. Not relevant.

Context: politicians find useful, since it helps them strike a friendly posture on behalf of an important constituency. "Strike a friendly posture" means adopt a public/ideological position or stance, not physical body arrangement. Politicians libel about teacher salaries helps them appear friendly to teachers. This is a mental/attitudinal stance, a rationalized attitude. So sense 3 (posture%1:09:00::) best.

Need return JSON {"sense_index": 3} only. Ensure exactformat.

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: 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 need answer only JSON with sense_index 1 or 2. Need determine best sense for behalf in context "strike a friendly posture on behalf of an important constituency." Phrase "on behalf of" typical means as the agent of or on someone's part, or for someone's benefit. Here politicians find useful since it helps them strike a friendly posture on behalf of an important constituency. They posture as representing/acting for constituency (agent/on someone's part). Candidate 1 definition: as the agent of or on someone's part (usually expressed as rather than ) examples on behalf of; in behalf of. Candidate 2: for someone's benefit (usually expressed as `in behalf' rather than `on behalf' and usually with a possessive). In context, not necessarily benefit but representing constituency to appear friendly. "on behalf of" sense 1. So choose index 1. Must output JSON exactly {"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: 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:
 The user is performing Word Sense Disambiguation (WSD) for the target word "important" in a specific context. Let me analyze the context and candidate senses carefully.

Context analysis:
The sentence is: "It is also the kind of libel politicians find useful, since it helps them strike a friendly posture on behalf of an important constituency."
- A politician is striking a friendly posture on behalf of a constituency.
- The constituency is described as "important"
- In politics, a constituency is a group of voters. An "important constituency" typically means a significant voting bloc or a group that has influence or power to affect election outcomes.
- Calling a group an "important constituency" suggests that the group is influential, has weight, is sizable enough to matter politically.

Candidate sense analysis:

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
   - This is the general sense of "important". Could apply to an important constituency.
   - "Important people" in examples suggests people of significance; a constituency of significance.

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
   - This is more about effect/meaning, not typically used for groups of people.

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
   - "Crucial" seems too strong here. The politician pandering to a constituency doesn't imply crisis resolution.

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
   - This sense is about having authority or influence. An "important official" has sway. Could an "important constituency" mean an influential one? Yes, in politics, a constituency is important because it has voting power/influence.

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
   - This is about self-importance. Doesn't apply to describing a constituency.

Now I need to distinguish between sense 1 (general "of great significance or value") and sense 4 (influential/authoritative).

In WordNet, "important" has several senses. Let me think about how WordNet distinguishes them.

Sense 1: important%3:00:00:: - "of great significance or value" - this is the core, general adjective
Sense 4: important%5:00:00:influential:00 - "having authority or ascendancy or influence" - this is a specific subtype

The famous WSD example for "important official" typically maps to sense 4 because an official is important by virtue of their authority/influence.

For "important constituency", is this more like:
(a) a constituency that is significant/valuable in general (sense 1)
(b) a constituency that has influence/authority (sense 4)

Political constituencies are important because they can vote and thus influence elections. The phrase "important constituency" in political discourse usually means influential/powerful in the political process. Politicians care about such constituencies because they have power to affect outcomes.

However, we need to be careful. WordNet sense 4 is defined as "having authority or ascendancy or influence" with synonyms "authoritative". The example is "an important official". Can a constituency be "authoritative" or "influential"? Yes - constituencies are influential groups.

But is there a distinction? Sense 1 "of great significance or value" has examples "important people; the important questions of the day". This could also subsume "important constituency".

Looking at WordNet structure:
- important%3:00:00:: is the base adjective (all-important would be related)
- important%5:00:00:influential:00 is a satellite adjective with relation to influential

Actually, in WordNet 3.0/3.1:
- "important (a)" has senses:
  - of great significance or value (3:00:00)
  - important in effect or meaning (3:00:04)
  - of extreme importance; vital to the resolution of a crisis (3:00:02)
  - having authority or ascendancy or influence (5:00:00:influential:00)
  - having or suggesting a consciousness of high position (5:00:00:immodest:02)

The WordNet sense key format indicates:
- 3:00:00 is adjective (non-satellite)
- 5:00:00 is adjective satellite (derivative)

"Having authority or ascendancy or influence" is a satellite of influential. So when we say "an important official" we mean an official with influence.

For "important constituency", I think this could go either way but the most natural reading in political context is "influential constituency" - a constituency with power/voting strength.

Let me think about typical WSD annotations:

"important official" -> sense 4 (has authority/influence)
"important people" -> sense 1 (of great significance)
"important question" -> sense 1
"important decision" -> sense 1 or sense 3 depending on context

For "important constituency":
A constituency is a group of people. The adjective could simply modify the group as being of significance (sense 1). But in the context of politicians pandering to a group, the group is important because of its political influence (sense 4).

Wait, but constituency itself is a political term. A "constituency" by definition has political influence through voting. So saying it's "important" might emphasize that it's significant in size or sway.

Let me reconsider. In the sentence: "politicians find useful, since it helps them strike a friendly posture on behalf of an important constituency."

The phrase "on behalf of an important constituency" means politicians are trying to appeal to voters who matter. The constituency matters because it has political clout.

I think sense 4 (influential) is the best fit here. The constituency isn't just generically important; it's specifically influential/authoritative in the political arena.

Actually, let me reconsider once more. Dictionary definitions of "important":

Sense 1: "of great significance or value" - This is very broad. "Important constituency" = a constituency of significance.

Sense 4: "having authority or ascendancy or influence" - This specifically attributes influence.

In many WSD systems, "important constituency" might be annotated as sense 1 because it's the most common/general sense and constituency is just being described as significant.

However, the political context strongly suggests "influential" because:
1. Politicians pander to constituencies that can influence elections
2. The context is about political strategy (unions, politicians, salary debates)
3. A voting bloc is important precisely because of its influence

But I want to think about whether WordNet disambiguation data would favor sense 1 or 4.

In the original sentence corpus (perhaps SemCor), "important" may have been annotated. Let me reason from the examples:
- "important people" -> sense 1
- "important official" -> sense 4
- "important questions" -> sense 1
- "important air" -> sense 5

A constituency is people, but it's also a political entity with influence. The phrase "important constituency" is closer semantically to "important official" than to "important people" because both denote entities with institutional/political power. However, "constituency" can also just mean a group of people.

Hmm, actually I think this is a close call. Let me weight the evidence:

For sense 1:
- The phrase "important X" where X is a group of people commonly uses sense 1
- "important people" is explicitly listed as sense 1
- Constituency consists of people

For sense 4:
- Political context emphasizes influence
- A constituency's importance to politicians derives from its voting power
- "Important official" is sense 4, and constituencies are political actors

Given your instruction to "choose the single best indexed sense" and not hedge, I need to make a definitive choice.

I think the best answer is sense 4. Here's why:
The context is explicitly political. The phrase "politicians strike a friendly posture on behalf of an important constituency" clearly means the politicians are courting a politically powerful or influential group. The constituency's importance is defined by its ability to influence politics/elections, which matches "having authority or ascendancy or influence" (sense 4).

Wait, I'm second-guessing. Let me think about this differently. If I replace "important" with synonyms from each sense:

Sense 1 synonym: "of import" - "an of import constituency" (awkward but "a constituency of import")
Sense 2 synonym: "significant" - "a significant constituency"
Sense 3 synonym: "crucial" - "a crucial constituency" (too strong)
Sense 4 synonym: "authoritative" - "an authoritative constituency" (a bit odd for a group)
Sense 5: doesn't apply

"Significant constituency" works well - a sizable voting bloc. But sense 2 is defined as "important in effect or meaning" with examples about changes and tax laws. Does that fit a group of people? Not really.

"Authoritative constituency" is odd because constituencies aren't typically described as "authoritative" (which connotes expertise or official power).

"Important constituency" = a constituency that matters because of its political weight. This seems most like sense 1 (of great significance or value) because a constituency can be significant in size, voting power, etc.

Actually, looking at the synonyms more carefully:
- Sense 1: "of import" - formal/literary equivalent
- Sense 4: "authoritative" - the actual synonym provided

If "authoritative" is the given synonym for sense 4, and we wouldn't say "an authoritative constituency," then sense 4 might not be the best fit.

But WordNet satellites often have multiple near-synonyms. The definition is "having authority or ascendancy or influence." A constituency can have ascendancy or influence (via votes), even if "authoritative" sounds odd.

Hmm. This is genuinely ambiguous. Let me look at the broader discourse context:

The passage argues that teacher salaries are not an educational problem but a political/equity problem. It says the idea that more pay would improve teaching is "silly libel" that teachers' unions spread "for their own narrow purposes" and that politicians find useful because it helps them "strike a friendly posture on behalf of an important constituency."

So "important constituency" refers to teachers as a voting bloc or interest group. Politicians want to appeal to this group because it's politically valuable. This is about political significance/influence.

I think sense 4 is the better answer because:
1. The passage explicitly describes political maneuvering (politicians, posture, constituency)
2. A constituency is politically definitionally influential
3. The "importance" is tied to political power, which aligns with "having authority or ascendancy or influence"

But I'm still uncertain because sense 1 is the default broad sense and constituencies are groups of people.

Let me consider: Would a WSD system or human annotator likely choose sense 1 or 4?

I recall that in WordNet, the satellite senses (5:00:00) are typically used for more specific meanings. The fact that "important official" is sense 4 and not sense 1 suggests that when importance derives from position/authority/influence, annotators choose sense 4.

A political constituency derives its importance from its organized political power. So it should be sense 4.

OK, I'm going to go with sense 4, but I want to acknowledge this was a close decision between 1 and 4.

Actually, wait. Let me reconsider the original text one more time. It says "an important constituency." It's indefinite, suggesting just "a significant group of voters" rather than "an influential/powerful bloc." The indefinite article weakens the case for sense 4 (influential) somewhat.

But on balance, I still think sense 4 is best because:
- The context is political strategy
- Constituencies matter because of their voting influence
- The parallel structure with "teachers' unions" (organized political actors) reinforces the political-influence reading

Final decision: sense 4.

Wait, I just realized I should also consider that "constituency" might be used metaphorically here. A constituency is a group of voters or supporters. In this case, teachers. The phrase "important constituency" in political science commonly means a group with significance to electoral outcomes, i.e., influential.

Yes, sense 4.

Actually, one more consideration: WordNet sense 4 includes "influential" as its core related word. In the sentence, the constituency is "important" because politicians care about it. That's exactly being influential in the political process. So sense 4.

Final answer: {"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 need choose sense index for 'shred' in context. The phrase "not one shred of evidence" is common idiom meaning not the smallest amount, a tiny amount. This is sense 1: a tiny or scarcely detectable amount. The other sense is physical small piece. So 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: 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:
 The user is asking me to perform Word Sense Disambiguation for the word "evidence" in the given context. I need to choose the best sense from the three candidates and return a JSON object with the sense index.

Let me analyze the context:

"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."

The sentence is discussing whether there is proof/basis for belief that salary differentials cause educational differentials. The author is saying there's no basis to believe that teacher salary differences lead to educational outcome differences.

Now let's look at the senses:

1. evidence%1:09:00:: - "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. evidence%1:10:01:: - "an indication that makes something evident" - examples: "his trembling was evidence of his fear"

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"

Sense 1 seems to fit best. The context is about belief/disbelief - whether salary differentials result in educational differentials. It's about knowledge on which to base belief. The phrase "not one shred of evidence that..." is a common construction with sense 1.

Sense 2 is more about indication/sign - "his trembling was evidence of his fear." While you could theoretically use it, the context is about empirical support for a claim, not an indication.

Sense 3 is specifically legal, which doesn't apply here.

So the answer should be sense_index: 1.

Let me double-check. The example for sense 1: "the evidence that smoking causes lung cancer is very compelling" - this parallels our sentence: "evidence that salary differentials result in educational differentials." The structure "evidence that [clause]" with a causal claim strongly matches sense 1.

Yes, sense 1 is correct.

provider: Ambient


[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:
The user wants me to choose the best WordNet sense for the word "other" in the given context. The target phrase is "other things being equal". Let me analyze.

The context is: "But there is not one shred of evidence that, other things being equal, salary differentials result in educational differentials."

The idiom "other things being equal" means "all other factors being the same" or "if everything else remains unchanged." This is a very common use of "other" meaning "not the same one or ones already mentioned or implied" or simply "additional" / "different."

Looking at 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

This seems to fit best. "Other things" refers to things/factors not being discussed (other than salary differentials), so "not the same one or ones already mentioned or implied."

2. sense_key=other%5:00:00:past:00 | definition=recently past | examples=the other evening
Doesn't fit - "other things" isn't temporal here.

3. sense_key=other%5:00:02:past:00 | definition=belonging to the distant past | synonyms=early, former
Doesn't fit - not referring to past time.

4. sense_key=other%5:00:00:strange:00 | definition=very unusual; different in character or quality from the normal or expected
Doesn't fit - "other things being equal" is not about strangeness.

So the best answer is sense 1.

I need to return only a JSON object exactly like {"sense_index": 3}. In this case, it should be {"sense_index": 1}.

provider: Moonshot AI


[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 need answer JSON only. Need choose best sense for "things" in phrase "other things being equal". Context: "other things being equal, salary differentials result in educational differentials." This is idiomatic phrase "other things being equal" = ceteris paribus. Here "things" refers to other factors/circumstances/conditions. Which WordNet sense? Candidate senses: 1 special situation; 2 action; 3 special abstraction; 4 artifact; 5 event; 6 vaguely specified concern (matter, affair); 7 statement; 8 entity not named specifically; 9 attribute/quality; 10 special objective; 11 feeling; 12 separate and self-contained entity.

"Other things being equal" uses "things" as a general, vaguely specified concerns/factors. Sense 6: a vaguely specified concern; synonyms matter, affair; examples several matters to attend to; it is none of your affair. That seems close: "things" = matters/factors. Sense 12 separate and self-contained entity is too concrete; things here are abstract conditions. Sense 8 entity not named specifically could also fit, but phrase "other things" refers to unspecified factors/conditions, not physical entities. Sense 6 is best. Need output JSON {"sense_index": 6}. Ensure no extra text.

provider: Cloudflare


[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 need choose best indexed sense for target word equal. Surface 'equal' in phrase 'other things being equal', economic/logical phrase. The first sense equal%3:00:00:: having same quantity value or measure as another. Examples include on equal terms; all men are equal. The phrase 'other things being equal' means other factors being the same/constant/unvaried. It matches core sense 1 (same quantity/value/measure). Sense 2 'adequate' doesn't fit. So answer 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: 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 need answer single best indexed sense. Need not use WordNet sense key. Return JSON.

We need choose among 3 senses: 1: mathematical derivative, 7: a quality that differentiates; 6: differential gear. Context: "salary differentials result in educational differentials" in education/pay differences. "salary differentials" = salary differences? WordNet sense 2 (1:07:00) is "a quality that differentiates between similar things" - that's not exactly difference in amount, but could be "differential" meaning a difference? In WordNet maybe only 3 senses. There is no separate financial/economic sense. The best sense is not gear, not mathematical derivative. It is a quality that differentiates. So index 2. Need return JSON.


[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 need answer as JSON {"sense_index": X}. Need choose lemma result, surface result. Context: "salary differentials result in educational differentials." That's a transitive-ish usage: A results in B. Candidate senses:
1 result%2:42:00:: definition issue or terminate (in specified way, state, etc.); end; synonyms ensue; examples result in tragedy. Hmm "result in tragedy" is transitive with result in. But definition issue or terminate? Seems maybe intransitive but takes PP "result in".
2 result%2:42:02:: definition have as a result or residue; synonyms leave, lead; examples water left mark. This seems causative: X leaves Y? But "result" with direct object? "result in"? WordNet maybe maps "result in" to sense 2? Let's inspect.
3 result%2:30:00:: definition come about or follow as a consequence; examples nothing will result from this meeting. Intransitive with from.

Need choose best. Context "salary differentials result in educational differentials." means cause. Synonyms leave, lead maybe "lead to" but given "result in". Examples sense1 includes "result in tragedy", definition "issue or terminate (in a specified way, state, etc.); end". In WordNet, "result in" likely sense 1? Let's reason from existing WordNet mapping. result verb frames:
- result (v.) 1: issue or terminate (in a specified way, state, etc.); end; "result in tragedy" (Sense 1). It usually is "result in something" meaning issue/end with. This is intransitive but with preposition in? Actually frame maybe "Something ----s something"? Let's recall WordNet result verb synsets:
result%2:42:00:: "issue or terminate (in a specified way, state, etc.); end; 'result in tragedy'"
result%2:42:02:: "have as a result or residue; "The water left a mark on the silk dress"; "Her blood left a stain on the napkin"" synonyms: leave, result, lead. It seems result here means "lead"? The example maybe not including result. Gloss "have as a result or residue" maps to leave/lead. Perhaps it is a different syntactic subcategorization: "result in" not listed. But sense 1 includes "result in tragedy". So for "salary differentials result in educational differentials", the phrase "result in" is exactly sense 1's example. However semantic nuance: "result in tragedy" could be tragic result or lead to tragedy.
Sense 2 is tied to "leave" patterns: have as a result or residue. Example with result? Maybe "His confusion resulted from ..." no. Synonyms leave, lead: lead to. But the gloss "have as a result or residue" doesn't fit "salary differentials result in educational differentials" well: salary differentials do not have educational differentials as a result/residue. Actually they lead to educational differentials. So sense 1/2 distinction depends on WordNet.
Sense 1 definition: issue or terminate (in a specified way, state, etc.); end. This focuses on ending in a state. "result in educational differentials" => salary differentials end/terminate in educational differentials? It means produce as an outcome. Sense 2: "have as a result or residue" more like "leave". Hmm "result" with direct object? "Water left a mark" not "water resulted a mark". So sense 2 likely "result" used as "lead to" not direct object. But phrase "result in educational differentials" uses "in", so sense 1 example.

We need fine-grained WSD. Use context. "other things being equal, salary differentials result in educational differentials." Means cause. Which indexed sense is best? Need choose one. Let's examine possible WordNet examples for each:
1 result%2:42:00:: examples: "result in tragedy".
2 result%2:42:02:: synonyms: leave, lead; examples: "The water left a mark..." (synonym leave). Perhaps the frame for result in this sense is "result in" meaning lead to? Because lead can be "lead to". The definition "have as a result or residue" might be "to leave" something and by extension "to result in". But no examples with result.
3 result%2:30:00:: examples: "nothing will result from this meeting." clearly intransitive "result from".

The target is followed by "in", so not sense 3. Between 1 and 2. Could be sense 2 because semantic synonyms include lead, and "salary differentials lead to educational differentials". However the definition "have as a result or residue" might be used for "lead" as in "The election led to social unrest"? Actually WordNet often glosses "leave" sense: "The accident left a scar." This is not cause lead. But includes lead, which can be causative. So perhaps sense 2 captures "lead to"/"result in". Sense 1 captures "result in" as in "issue/terminate in a state" (intransitive with preposition). Which is more appropriate? Let's think about WordNet mapping: If "result in" example belongs to sense 1, that should be the sense for "salary differentials result in educational differentials." Unless sense 2 is a causative use where result takes direct object (rare). Actually check WordNet data: result has 3 verb senses. Synset 2: verb.change? 2:42:02 "have as a result or residue" ; hypernym? Words: leave, result, lead. It's the same as "leave" sense: "act or be so as to become in a specified state"; "The inflation left them penniless"; "The president's remarks left us speechless"? Wait that's a different synset for leave. Let's recall exact WordNet synsets for result verb:
From WordNet 3.0:
result (v.):
1. issue or terminate (in a specified way, state, etc.); end; "result in tragedy"
2. have as a result or residue; "The water left a mark on the silk dress"; "Her blood left a stain on the napkin"
3. come about or follow as a consequence; "nothing will result from this meeting"

So indeed sense 1 has example "result in tragedy". Sense 2's examples use "leave", not "result". It might be grouped by semantic relation to leave, but result in that sense not common. The target phrase "result in educational differentials" matches "result in tragedy" almost exactly. So sense 1 is best.

Need output only JSON object exactly like {"sense_index": 3}. They say do not answer with sense key. Only JSON. So {"sense_index": 1}. Ensure no code fences perhaps to match exact only. Let's return plain.

provider: AkashML


[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 need answer which sense index. Need understand context: target 'educational' occurs in sentence: "But there is not one shred of evidence that, other things being equal, salary differentials result in <t>educational</t> differentials." The phrase 'educational differentials' – differentials in education / relating to education process? It means differences in educational outcomes/achievement. Sense 1: relating to the process of education; examples educational psychology. Sense 2: providing knowledge; examples an educational film. Here 'educational differentials' is attributive adjective modifying differentials, meaning differentials concerning/in education (process/system). Not 'providing knowledge'. So sense 1. Must output JSON {"sense_index": 1}. Ensure exact.

provider: DeepInfra


[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:
 Let me finish the reasoning. The target word is "differentials" in the sentence "salary differentials result in educational differentials." Here, "differential" is being used in the sense of a difference, particularly in wages or outcomes. Looking at the candidate senses:

1. Mathematical derivative - doesn't fit, the context is about education and salaries, not math.
2. "a quality that differentiates between similar things" - this is the closest to meaning "difference" between things. Salary differentials = differences in salary; educational differentials = differences in educational outcomes.
3. Bevel gear in automobiles - doesn't fit.

So the best sense is sense 2 (differential%1:07:00::).

The user wants only a JSON object like {"sense_index": 3}. Since sense 2 is the best, the answer should be {"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: 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:
 The user is performing word sense disambiguation (WSD) for the word "evidence" in the given context. I need to choose among three candidate senses:

1. evidence%1:09:00:: - basis for belief/disbelief; knowledge on which to base belief; synonym: grounds
2. evidence%1:10:01:: - an indication that makes something evident
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

Context: "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."

This is about factual proof/basis for belief regarding a claim - "salary differentials result in educational differentials." The phrase "not one shred of evidence" suggests basis for belief or disbelief; knowledge/data to support a proposition. This is not legal evidence (no judicial trial context).

Between sense 1 (basis for belief/disbelief, grounds) and sense 2 (indication that makes something evident):
- Sense 1 is more about proof/support for a belief/proposition (epistemic)
- Sense 2 is more about an indication or sign making something evident (e.g., trembling as evidence of fear)

The context here involves evidence for a causal proposition: "that salary differentials result in educational differentials." This is clearly "basis for belief or disbelief; knowledge on which to base belief." So sense 1.

I need to return only a JSON object: {"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: 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 need perform WSD for 'sure' in given context. Target surface 'sure', sentence: "If there were such evidence, you can be sure you would have heard of it."
Need choose among listed senses. Let's analyze.

The construction "you can be sure (that) you would have heard of it" means confident/certain. Expression "you can be sure" roughly "you may be certain/confident", i.e., having no doubt. This matches sense 1: having or feeling no doubt or uncertainty; confident and assured. "be sure" here? Hmm senses:

1. sure%3:00:00:: adj? definition having or feeling no doubt or uncertainty; confident and assured; examples "was sure (or certain) she had seen it". This is probably the sense in "I am sure". "you can be sure you would have heard of it" = you can be certain/confident. This is sense 1.

Sense 2: careful: "be sure to lock the doors" admonishing to take care. Not this context.

Sense 3: certain to occur; "he was certain to fail". Not this.

Sense 4 physically secure. No.

5 reliable in operation. No.

6 trustworthy of persons. No.

7 infallible true sign. No.

8 certain not to fail. No.

9 impossible to doubt/dispute proof. The phrase "you can be sure" relates to lack of doubt. So sense 1 likely.

Check indices by definition. The candidate list:
1. sense_key=sure%3:00:00::
2. sure%5:00:00:careful:00
3. sure%3:00:04::
4. sure%5:00:00:secure:02
...

WordNet index? The senses likely mapped. But we choose index 1. Return JSON only {"sense_index": 1}. Ensure no extratext.