[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: major
Target surface form: major
Context:
An examination of changes in personal staffing decisions in the Senate between 1986 and 1987 -LRB- when control of that body changed party hands -RRB-, moreover, reveals that the personal staffing differences noted in the table can not be attributed to the disproportionate control Democrats exercise, due to their majority - party status, over other resources such as committee staff. An additional piece of evidence from the Senate: Holding other factors constant, such as incumbency advantages and regional factors, the difference between popular votes for Republican presidential and senatorial candidates in states conducting a Senate election turns out to be a positive function of how onerous the federal government's tax burden is per state -LRB- a progressive tax rate hits higher - income states harder -RRB-. Put more simply, GOP candidates for president are looked on more kindly by voters than Republican candidates for the Senate when the prisoner's sentence is more severe. Moreover, ticket splitting appears to take the same peculiar pattern at the state government level as it does at the federal level. State government is more typically split along Republican-governor / Democratic-legislature lines than the reverse. A cross-state econometric investigation, furthermore, reveals that, holding other factors constant, the difference between a state's <t>major</t> - party vote going to the Republican gubernatorial candidate and the Republican share of the lower state house is a positive function of the state tax rate. In sum, at both the federal and state government levels at least part of the seemingly irrational behavior voters display in the voting booth may have an exceedingly rational explanation.

Candidate senses:
1. sense_key=major%3:00:06:: | definition=of greater importance or stature or rank | examples=a major artist; a major role
2. sense_key=major%3:00:02:: | definition=greater in scope or effect | examples=a major contribution; a major improvement
3. sense_key=major%3:00:01:: | definition=greater in number or size or amount | examples=a major portion (a majority) of the population; Ursa Major
4. sense_key=major%3:00:05:: | definition=of the field of academic study in which one concentrates or specializes | examples=his major field was mathematics
5. sense_key=major%3:00:04:: | definition=of a scale or mode | examples=major scales; the key of D major
6. sense_key=major%3:00:07:: | definition=of greater seriousness or danger | examples=a major earthquake; a major hurricane
7. sense_key=major%3:00:03:: | definition=of full legal age
8. sense_key=major%5:00:00:senior:00 | definition=of the elder of two boys with the same family name | examples=Jones major

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 perform Word Sense Disambiguation for the word "major" in the given context.

 Let me analyze the context:
 - The text is about political science, specifically about voting patterns, party control, and state government.
 - The specific sentence is: "A cross-state econometric investigation, furthermore, reveals that, holding other factors constant, the difference between a state's <t>major</t> - party vote going to the Republican gubernatorial candidate and the Republican share of the lower state house is a positive function of the state tax rate."
 - The phrase is "major-party vote" or "major party vote" (with a hyphen in the text: "major - party").

 The phrase "major party" in political science refers to the main political parties (typically Democrats and Republicans in the US context), as opposed to minor parties or third parties.

 Now let's look at the candidate senses:

 1. sense_key=major%3:00:06:: | definition=of greater importance or stature or rank | examples=a major artist; a major role
 2. sense_key=major%3:00:02:: | definition=greater in scope or effect | examples=a major contribution; a major improvement
 3. sense_key=major%3:00:01:: | definition=greater in number or size or amount | examples=a major portion (a majority) of the population; Ursa Major
 4. sense_key=major%3:00:05:: | definition=of the field of academic study in which one concentrates or specializes | examples=his major field was mathematics
 5. sense_key=major%3:00:04:: | definition=of a scale or mode | examples=major scales; the key of D major
 6. sense_key=major%3:00:07:: | definition=of greater seriousness or danger | examples=a major earthquake; a major hurricane
 7. sense_key=major%3:00:03:: | definition=of full legal age
 8. sense_key=major%5:00:00:senior:00 | definition=of the elder of two boys with the same family name | examples=Jones major

 The phrase "major party" means the principal or main political party, or one of the two main parties (in a two-party system). This aligns with sense 1: "of greater importance or stature or rank" - referring to the parties of greater importance/stature in the political system.

 However, let me reconsider. In political contexts, "major party" specifically refers to the dominant parties. This could potentially map to sense 1 (greater importance/stature/rank) or sense 3 (greater in number/size/amount - i.e., having a majority or plurality).

 But looking at the specific phrase "major-party vote" - this refers to the vote share going to the major parties (as opposed to minor parties), or specifically the vote going to the major party candidates.

 Actually, looking more carefully at the context: "the difference between a state's major - party vote going to the Republican gubernatorial candidate and the Republican share of the lower state house"

 Here "major-party vote" likely means the vote share for the major party candidates (Republican vs Democrat), or it could mean the vote going to the candidate of the major party (but that doesn't make sense because both are major parties).

 Wait, "major-party vote" in political science often refers to the combined vote share of the two major parties, or the vote for the major party candidates as opposed to third parties. But here it says "major-party vote going to the Republican gubernatorial candidate" - this suggests it's referring to the Republican candidate as being from a major party, or it's referring to the vote share that the Republican candidate gets among the major party vote.

 Actually, looking at the phrase structure: "major-party vote" is a compound modifier. The "major party" refers to the principal political parties (Democrats and Republicans).

 Sense 1: "of greater importance or stature or rank" - a major party is a party of greater importance/stature/rank than minor parties.
 Sense 3: "greater in number or size or amount" - could refer to having a majority, but "major party" doesn't necessarily mean the party with the majority, it means one of the two main parties (Democratic or Republican).

 In political science terminology, "major party" refers to the parties with the greatest importance, stature, or rank in the political system - the principal parties. This aligns with sense 1.

 However, I should check if there's a specific sense for "major" meaning "principal" or "main". Sense 1 says "of greater importance or stature or rank" which captures the "principal" meaning.

 Let me double-check the WordNet senses for "major" as an adjective:
 - Sense 1: greater in scope or effect (a major contribution)
 - Sense 2: greater in number or size or amount (a major portion, Ursa Major)
 - Sense 3: of full legal age
 - Sense 4: of a scale or mode (music)
 - Sense 5: of the field of academic study (his major field)
 - Sense 6: of greater importance or stature or rank (a major artist, a major role)
 - Sense 7: of greater seriousness or danger
 - Sense 8: senior (Jones major)

 Wait, the numbering in the candidate list might not match the WordNet sense numbers. Let me look at the sense_keys:

 1. major%3:00:06:: - of greater importance or stature or rank
 2. major%3:00:02:: - greater in scope or effect
 3. major%3:00:01:: - greater in number or size or amount
 4. major%3:00:05:: - academic study
 5. major%3:00:04:: - music scale
 6. major%3:00:07:: - greater seriousness or danger
 7. major%3:00:03:: - of full legal age
 8. major%5:00:00:senior:00 - elder of two boys

 So:
 - Index 1 = importance/stature/rank
 - Index 2 = scope or effect
 - Index 3 = number/size/amount
 - Index 4 = academic
 - Index 5 = music
 - Index 6 = seriousness/danger
 - Index 7 = legal age
 - Index 8 = senior

 In the phrase "major-party", "major" modifies "party" to mean the principal or main political parties. This is clearly about importance/stature/rank (sense index 1).

 "Major party" means a political party of greater importance/stature/rank compared to minor parties or third parties.

 Therefore, the best sense is index 1.

 But wait, let me reconsider if it could be sense 3 (greater in number). A "major party" could theoretically mean the party with the greater number of votes (the majority party), but in the context of US politics, "major party" is a technical term referring to the two main parties (Democratic and Republican), regardless of which one has the majority in a specific election. The text mentions "majority-party status" earlier in the text, distinguishing between "major party" and "majority party".

 Earlier in the text: "due to their majority - party status" - this refers to the party that has the majority (more seats).
 Later: "major - party vote" - this refers to the vote for the major parties.

 So "majority party" (the party with the majority) vs "major party" (one of the two main parties) are distinguished in this text.

 Therefore, "major-party" refers to the parties of greater importance/stature in the political system (Democrats and Republicans), not necessarily the one with the majority of votes in a specific election.

 This confirms sense 1 is correct: "of greater importance or stature or rank".

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

provider: Phala


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: party
Target surface form: party
Context:
An examination of changes in personal staffing decisions in the Senate between 1986 and 1987 -LRB- when control of that body changed party hands -RRB-, moreover, reveals that the personal staffing differences noted in the table can not be attributed to the disproportionate control Democrats exercise, due to their majority - party status, over other resources such as committee staff. An additional piece of evidence from the Senate: Holding other factors constant, such as incumbency advantages and regional factors, the difference between popular votes for Republican presidential and senatorial candidates in states conducting a Senate election turns out to be a positive function of how onerous the federal government's tax burden is per state -LRB- a progressive tax rate hits higher - income states harder -RRB-. Put more simply, GOP candidates for president are looked on more kindly by voters than Republican candidates for the Senate when the prisoner's sentence is more severe. Moreover, ticket splitting appears to take the same peculiar pattern at the state government level as it does at the federal level. State government is more typically split along Republican-governor / Democratic-legislature lines than the reverse. A cross-state econometric investigation, furthermore, reveals that, holding other factors constant, the difference between a state's major - <t>party</t> vote going to the Republican gubernatorial candidate and the Republican share of the lower state house is a positive function of the state tax rate. In sum, at both the federal and state government levels at least part of the seemingly irrational behavior voters display in the voting booth may have an exceedingly rational explanation.

Candidate senses:
1. sense_key=party%1:14:01:: | definition=an organization to gain political power | synonyms=political party | examples=in 1992 Perot tried to organize a third party at the national level
2. sense_key=party%1:14:00:: | definition=a group of people gathered together for pleasure | examples=she joined the party after dinner
3. sense_key=party%1:14:02:: | definition=a band of people associated temporarily in some activity | synonyms=company | examples=they organized a party to search for food; the company of cooks walked into the kitchen
4. sense_key=party%1:11:00:: | definition=an occasion on which people can assemble for social interaction and entertainment | examples=he planned a party to celebrate Bastille Day
5. sense_key=party%1:18:00:: | definition=a person involved in legal proceedings | examples=the party of the first part

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:
The user wants me to perform Word Sense Disambiguation on the word "party" in a specific context.

 First, let's look at the target word and context:
 - Target lemma: party
 - Target surface form: party
 - Context: "A cross-state econometric investigation, furthermore, reveals that, holding other factors constant, the difference between a state's major - <t>party</t> vote going to the Republican gubernatorial candidate and the Republican share of the lower state house is a positive function of the state tax rate."

 The phrase is "major-party vote". This is referring to political parties. The context discusses:
 - Control of the Senate changing "party hands"
 - Democrats exercising control due to majority-party status
 - Republican presidential and senatorial candidates
 - GOP candidates
 - Republican-governor / Democratic-legislature
 - Republican gubernatorial candidate
 - Major-party vote

 This is clearly about political parties, not social gatherings, legal parties, or bands of people.

 Now let's look at the candidate senses:

 1. sense_key=party%1:14:01:: | definition=an organization to gain political power | synonyms=political party | examples=in 1992 Perot tried to organize a third party at the national level
 2. sense_key=party%1:14:00:: | definition=a group of people gathered together for pleasure | examples=she joined the party after dinner
 3. sense_key=party%1:14:02:: | definition=a band of people associated temporarily in some activity | synonyms=company | examples=they organized a party to search for food; the company of cooks walked into the kitchen
 4. sense_key=party%1:11:00:: | definition=an occasion on which people can assemble for social interaction and entertainment | examples=he planned a party to celebrate Bastille Day
 5. sense_key=party%1:18:00:: | definition=a person involved in legal proceedings | examples=the party of the first part

 Sense 1 is clearly the correct one: "an organization to gain political power" with synonym "political party". The context is about political parties (Republican, Democratic), voting, elections, and government control.

 The phrase "major-party vote" refers to votes for major political parties (Republican and Democratic).

 Therefore, the answer should be sense index 1.

 Wait, I need to check the indexing. The user lists them as:
 1. sense_key=party%1:14:01::
 2. sense_key=party%1:14:00::
 3. sense_key=party%1:14:02::
 4. sense_key=party%1:11:00::
 5. sense_key=party%1:18:00::

 So I should return {"sense_index": 1}.

 Let me double-check the context to make sure there's no ambiguity:
 - "control of that body changed party hands" - refers to political party control
 - "majority-party status" - refers to political party status
 - "major-party vote" - refers to major political parties

 Yes, definitely sense 1.

format: unknown

native_finish_reason: stop

provider: StreamLake

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: vote
Target surface form: vote
Context:
An examination of changes in personal staffing decisions in the Senate between 1986 and 1987 -LRB- when control of that body changed party hands -RRB-, moreover, reveals that the personal staffing differences noted in the table can not be attributed to the disproportionate control Democrats exercise, due to their majority - party status, over other resources such as committee staff. An additional piece of evidence from the Senate: Holding other factors constant, such as incumbency advantages and regional factors, the difference between popular votes for Republican presidential and senatorial candidates in states conducting a Senate election turns out to be a positive function of how onerous the federal government's tax burden is per state -LRB- a progressive tax rate hits higher - income states harder -RRB-. Put more simply, GOP candidates for president are looked on more kindly by voters than Republican candidates for the Senate when the prisoner's sentence is more severe. Moreover, ticket splitting appears to take the same peculiar pattern at the state government level as it does at the federal level. State government is more typically split along Republican-governor / Democratic-legislature lines than the reverse. A cross-state econometric investigation, furthermore, reveals that, holding other factors constant, the difference between a state's major - party <t>vote</t> going to the Republican gubernatorial candidate and the Republican share of the lower state house is a positive function of the state tax rate. In sum, at both the federal and state government levels at least part of the seemingly irrational behavior voters display in the voting booth may have an exceedingly rational explanation.

Candidate senses:
1. sense_key=vote%1:04:00:: | definition=a choice that is made by counting the number of people in favor of each alternative | synonyms=ballot, voting, balloting | examples=there were only 17 votes in favor of the motion; they allowed just one vote per person
2. sense_key=vote%1:04:01:: | definition=the opinion of a group as determined by voting | examples=they put the question to a vote
3. sense_key=vote%1:07:00:: | definition=a legal right guaranteed by the 15th amendment to the US Constitution; guaranteed to women by the 19th amendment | synonyms=right to vote, suffrage | examples=American women got the vote in 1920
4. sense_key=vote%1:14:00:: | definition=a body of voters who have the same interests | examples=he failed to get the Black vote
5. sense_key=vote%1:09:00:: | definition=the total number of voters who participated | synonyms=voter turnout | examples=they are expecting a large vote

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 perform Word Sense Disambiguation for the word "vote" in the given context.

 Let me analyze the context:
 - The text is discussing political elections, specifically comparing votes for different candidates (Republican presidential vs. senatorial candidates, Republican gubernatorial candidate vs. Republican share of lower state house).
 - The specific sentence containing the target word is: "A cross-state econometric investigation, furthermore, reveals that, holding other factors constant, the difference between a state's major-party <t>vote</t> going to the Republican gubernatorial candidate and the Republican share of the lower state house is a positive function of the state tax rate."
 - Here, "major-party vote" refers to the votes cast for major party candidates - it's talking about the actual ballots or choices made by voters.
 - The phrase "vote going to the Republican gubernatorial candidate" suggests we're talking about the actual votes (ballots) cast for that candidate.

 Now let's look at the candidate senses:

 1. sense_key=vote%1:04:00:: | definition=a choice that is made by counting the number of people in favor of each alternative | synonyms=ballot, voting, balloting | examples=there were only 17 votes in favor of the motion; they allowed just one vote per person
    - This seems to fit well. It's about the choice/ballot cast by voters. The phrase "major-party vote" refers to the votes (ballots) cast for major party candidates.

 2. sense_key=vote%1:04:01:: | definition=the opinion of a group as determined by voting | examples=they put the question to a vote
    - This refers to the collective decision or the act of putting something to a vote. The context here is about specific vote counts/shares, not the general opinion of a group.

 3. sense_key=vote%1:07:00:: | definition=a legal right guaranteed by the 15th amendment to the US Constitution; guaranteed to women by the 19th amendment | synonyms=right to vote, suffrage | examples=American women got the vote in 1920
    - This is about the right to vote (suffrage), not the actual votes cast. The context is about vote shares and counts, not rights.

 4. sense_key=vote%1:14:00:: | definition=a body of voters who have the same interests | examples=he failed to get the Black vote
    - This refers to a demographic group of voters (e.g., "the Black vote", "the youth vote"). While the text mentions "major-party vote", it's not referring to a body of voters with shared interests, but rather the votes cast for major parties.

 5. sense_key=vote%1:09:00:: | definition=the total number of voters who participated | synonyms=voter turnout | examples=they are expecting a large vote
    - This is about voter turnout (the total number of people voting). The context is comparing vote shares between different offices (gubernatorial vs. state house), not talking about total turnout.

 Looking at the specific usage: "the difference between a state's major-party vote going to the Republican gubernatorial candidate and the Republican share of the lower state house"

 Here, "vote" is being used to mean the votes cast (the ballots) for the gubernatorial candidate. It's synonymous with "ballot" or the actual choice made. This matches sense 1: "a choice that is made by counting the number of people in favor of each alternative."

 The phrase "major-party vote" refers to the aggregation of votes/ballots for major party candidates, as opposed to third parties. This is clearly referring to the actual votes cast (sense 1), not the right to vote (sense 3), not a demographic group (sense 4), not the collective opinion (sense 2), and not turnout (sense 5).

 Therefore, the best sense is sense 1.

 Wait, let me double-check sense 4. Could "major-party vote" mean the body of voters who vote for major parties? In political science contexts, "the vote" can refer to the electorate or voting bloc. But looking at the specific construction: "vote going to the Republican gubernatorial candidate" - this strongly suggests the actual votes/ballots being cast for the candidate, not the group of voters. The phrase "going to" indicates the direction of the votes, which fits with ballots/choices being allocated to candidates.

 Also, comparing with the examples for sense 1: "there were only 17 votes in favor of the motion" - this is similar to "vote going to the Republican gubernatorial candidate" - both refer to the count of ballots/choices.

 So sense 1 is definitely the correct choice.

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: go
Target surface form: going
Context:
An examination of changes in personal staffing decisions in the Senate between 1986 and 1987 -LRB- when control of that body changed party hands -RRB-, moreover, reveals that the personal staffing differences noted in the table can not be attributed to the disproportionate control Democrats exercise, due to their majority - party status, over other resources such as committee staff. An additional piece of evidence from the Senate: Holding other factors constant, such as incumbency advantages and regional factors, the difference between popular votes for Republican presidential and senatorial candidates in states conducting a Senate election turns out to be a positive function of how onerous the federal government's tax burden is per state -LRB- a progressive tax rate hits higher - income states harder -RRB-. Put more simply, GOP candidates for president are looked on more kindly by voters than Republican candidates for the Senate when the prisoner's sentence is more severe. Moreover, ticket splitting appears to take the same peculiar pattern at the state government level as it does at the federal level. State government is more typically split along Republican-governor / Democratic-legislature lines than the reverse. A cross-state econometric investigation, furthermore, reveals that, holding other factors constant, the difference between a state's major - party vote <t>going</t> to the Republican gubernatorial candidate and the Republican share of the lower state house is a positive function of the state tax rate. In sum, at both the federal and state government levels at least part of the seemingly irrational behavior voters display in the voting booth may have an exceedingly rational explanation.

Candidate senses:
1. sense_key=go%2:38:00:: | definition=change location; move, travel, or proceed, also metaphorically | synonyms=travel, move, locomote | examples=How fast does your new car go?; We travelled from Rome to Naples by bus
2. sense_key=go%2:41:00:: | definition=follow a procedure or take a course | synonyms=proceed, move | examples=We should go farther in this matter; She went through a lot of trouble
3. sense_key=go%2:38:01:: | definition=move away from a place into another direction | synonyms=go away, depart | examples=Go away before I start to cry; The train departs at noon
4. sense_key=go%2:30:04:: | definition=enter or assume a certain state or condition | synonyms=become, get | examples=He became annoyed when he heard the bad news; It must be getting more serious
5. sense_key=go%2:42:06:: | definition=be awarded; be allotted | examples=The first prize goes to Mary; Her money went on clothes
6. sense_key=go%2:42:02:: | definition=have a particular form | synonyms=run | examples=the story or argument runs as follows; as the saying goes...
7. sense_key=go%2:42:00:: | definition=stretch out over a distance, space, time, or scope; run or extend between two points or beyond a certain point | synonyms=run, pass, lead, extend | examples=Service runs all the way to Cranbury; His knowledge doesn't go very far
8. sense_key=go%2:30:01:: | definition=follow a certain course | synonyms=proceed | examples=The inauguration went well; how did your interview go?
9. sense_key=go%2:30:08:: | definition=be abolished or discarded | examples=These ugly billboards have to go!; These luxuries all had to go under the Khmer Rouge
10. sense_key=go%2:42:07:: | definition=be or continue to be in a certain condition | examples=The children went hungry that day
11. sense_key=go%2:39:00:: | definition=make a certain noise or sound | synonyms=sound | examples=She went `Mmmmm'; The gun went `bang'
12. sense_key=go%2:35:00:: | definition=perform as expected when applied | synonyms=function, work, operate, run | examples=The washing machine won't go unless it's plugged in; Does this old car still run well?
13. sense_key=go%2:34:00:: | definition=to be spent or finished | synonyms=run low, run short | examples=The money had gone after a few days; Gas is running low at the gas stations in the Midwest
14. sense_key=go%2:30:02:: | definition=progress by being changed | synonyms=move, run | examples=The speech has to go through several more drafts; run through your presentation before the meeting
15. sense_key=go%2:42:14:: | definition=continue to live through hardship or adversity | synonyms=survive, last, live, live on, endure, hold up | examples=We went without water and food for 3 days; These superstitions survive in the backwaters of America
16. sense_key=go%2:42:03:: | definition=pass, fare, or elapse; of a certain state of affairs or action | examples=How is it going?; The day went well until I got your call
17. sense_key=go%2:30:00:: | definition=pass from physical life and lose all bodily attributes and functions necessary to sustain life | synonyms=die, decease, perish, exit, pass away, expire | examples=She died from cancer; The children perished in the fire
18. sense_key=go%2:42:04:: | definition=be in the right place or situation | synonyms=belong | examples=Where do these books belong?; Let's put health care where it belongs--under the control of the government
19. sense_key=go%2:42:10:: | definition=be ranked or compare | examples=This violinist is as good as Juilliard-trained violinists go
20. sense_key=go%2:38:09:: | definition=begin or set in motion | synonyms=start, get going | examples=I start at eight in the morning; Ready, set, go!
21. sense_key=go%2:33:00:: | definition=have a turn; make one's move in a game | synonyms=move | examples=Can I go now?
22. sense_key=go%2:42:13:: | definition=be contained in | examples=How many times does 18 go into 54?
23. sense_key=go%2:42:12:: | definition=be sounded, played, or expressed | examples=How does this song go again?
24. sense_key=go%2:42:11:: | definition=blend or harmonize | synonyms=blend, blend in | examples=This flavor will blend with those in your dish; This sofa won't go with the chairs
25. sense_key=go%2:42:08:: | definition=lead, extend, or afford access | synonyms=lead | examples=This door goes to the basement; The road runs South
26. sense_key=go%2:42:05:: | definition=be the right size or shape; fit correctly or as desired | synonyms=fit | examples=This piece won't fit into the puzzle
27. sense_key=go%2:35:13:: | definition=go through in search of something; search through someone's belongings in an unauthorized way | synonyms=rifle | examples=Who rifled through my desk drawers?
28. sense_key=go%2:34:09:: | definition=be spent | examples=All my money went for food and rent
29. sense_key=go%2:31:12:: | definition=give support (to) or make a choice (of) one out of a group or number | synonyms=plump | examples=I plumped for the losing candidates
30. sense_key=go%2:30:03:: | definition=stop operating or functioning | synonyms=fail, go bad, give way, die, give out, conk out | examples=The engine finally went; The car died on the road

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 perform Word Sense Disambiguation (WSD) on the word "going" in the given context. The target lemma is "go" and the surface form is "going".

Let me analyze the context:

The sentence is: "A cross-state econometric investigation, furthermore, reveals that, holding other factors constant, the difference between a state's major - party vote <t>going</t> to the Republican gubernatorial candidate and the Republican share of the lower state house is a positive function of the state tax rate."

The phrase is "vote going to the Republican gubernatorial candidate". This is talking about votes being allocated or awarded to a candidate.

Let me look at the candidate senses:

1. change location; move, travel, or proceed - This is about physical movement. Not right.
2. follow a procedure or take a course - Not about votes.
3. move away from a place - Physical movement.
4. enter or assume a certain state - "become"
5. be awarded; be allotted - "The first prize goes to Mary; Her money went on clothes" - This looks promising! Votes going to a candidate means votes being awarded/allotted to that candidate.
6. have a particular form - "as the saying goes"
7. stretch out over a distance - "Service runs all the way to Cranbury"
8. follow a certain course - "The inauguration went well"
9. be abolished or discarded - "These ugly billboards have to go!"
10. be or continue to be in a certain condition - "The children went hungry"
11. make a certain noise - "The gun went `bang'"
12. perform as expected - "The washing machine won't go"
13. to be spent or finished - "The money had gone"
14. progress by being changed - "The speech has to go through several more drafts"
15. continue to live through hardship - "We went without water"
16. pass, fare, or elapse - "How is it going?"
17. pass from physical life - die
18. be in the right place or situation - "Where do these books belong?"
19. be ranked or compare - "as good as Juilliard-trained violinists go"
20. begin or set in motion - "Ready, set, go!"
21. have a turn - "Can I go now?"
22. be contained in - "How many times does 18 go into 54?"
23. be sounded, played, or expressed - "How does this song go again?"
24. blend or harmonize - "This sofa won't go with the chairs"
25. lead, extend, or afford access - "This door goes to the basement"
26. be the right size or shape - fit
27. go through in search of something - rifle
28. be spent - "All my money went for food"
29. give support (to) or make a choice - "I plumped for the losing candidates"
30. stop operating - fail

Sense 5 seems to be the best fit: "be awarded; be allotted" with examples "The first prize goes to Mary; Her money went on clothes".

In the context, "vote going to the Republican gubernatorial candidate" means votes being allotted/awarded to that candidate. This matches sense 5 perfectly.

Let me double-check sense 29: "give support (to) or make a choice (of) one out of a group or number" with synonym "plump". This could potentially fit ("votes going to" could mean support), but sense 5 is more specific about allocation/awarding of resources (votes), and the example "The first prize goes to Mary" is very similar to "votes going to the candidate".

Actually, looking more carefully at sense 29: "give support (to) or make a choice (of) one out of a group or number". The example is "I plumped for the losing candidates". This is about a person making a choice. But in our sentence, it's "vote going to", which is about the votes themselves being allocated.

Sense 5: "be awarded; be allotted" - this is about things being distributed or allocated. Votes are being allocated to candidates.

Also, sense 28: "be spent" - "All my money went for food" - this is similar but "spent" implies consumption, whereas votes are tallied and allocated, not consumed.

Sense 5 is definitely the best fit. The votes are being allotted/awarded to the candidate.

Wait, let me check if there's any other sense that might fit better.

Sense 18: "be in the right place or situation" - "Where do these books belong?" - This is about location/positioning, not about votes being counted towards someone.

Sense 25: "lead, extend, or afford access" - "This door goes to the basement" - This is about connection or direction, not about allocation.

So yes, sense 5 is the correct choice.

The sense key is go%2:42:06:: which corresponds to index 5 in the list provided.

Wait, I need to check the indexing. The user lists them as:
1. sense_key=go%2:38:00::
2. sense_key=go%2:41:00::
...
5. sense_key=go%2:42:06::

So the index is 5.

The output should be: {"sense_index": 5}

provider: AtlasCloud


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

[User]
Target lemma: republican
Target surface form: Republican
Context:
An examination of changes in personal staffing decisions in the Senate between 1986 and 1987 -LRB- when control of that body changed party hands -RRB-, moreover, reveals that the personal staffing differences noted in the table can not be attributed to the disproportionate control Democrats exercise, due to their majority - party status, over other resources such as committee staff. An additional piece of evidence from the Senate: Holding other factors constant, such as incumbency advantages and regional factors, the difference between popular votes for Republican presidential and senatorial candidates in states conducting a Senate election turns out to be a positive function of how onerous the federal government's tax burden is per state -LRB- a progressive tax rate hits higher - income states harder -RRB-. Put more simply, GOP candidates for president are looked on more kindly by voters than Republican candidates for the Senate when the prisoner's sentence is more severe. Moreover, ticket splitting appears to take the same peculiar pattern at the state government level as it does at the federal level. State government is more typically split along Republican-governor / Democratic-legislature lines than the reverse. A cross-state econometric investigation, furthermore, reveals that, holding other factors constant, the difference between a state's major - party vote going to the <t>Republican</t> gubernatorial candidate and the Republican share of the lower state house is a positive function of the state tax rate. In sum, at both the federal and state government levels at least part of the seemingly irrational behavior voters display in the voting booth may have an exceedingly rational explanation.

Candidate senses:
1. sense_key=republican%3:01:01:: | definition=relating to or belonging to the Republican Party | examples=a Republican senator; Republican party politics
2. sense_key=republican%5:00:00:democratic:00 | definition=having the supreme power lying in the body of citizens entitled to vote for officers and representatives responsible to them or characteristic of such government; - United States Constitution; ; - Philip Marsh; -Nathaniel Hawthorne | examples=the United States shall guarantee to every state in this union a republican form of government; a very republican notion

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 perform Word Sense Disambiguation (WSD) on the word "Republican" in the given context. I need to choose between two candidate senses:

1. republican%3:01:01:: - relating to or belonging to the Republican Party (adjective)
2. republican%5:00:00:democratic:00 - having the supreme power lying in the body of citizens... (republican form of government) (adjective)

Let me analyze the context:

The text is discussing:
- Senate control changing party hands (Democrats vs Republicans)
- "Republican presidential and senatorial candidates"
- "GOP candidates for president" (GOP = Grand Old Party = Republican Party)
- "Republican candidates for the Senate"
- "Republican-governor / Democratic-legislature"
- "Republican gubernatorial candidate"
- "Republican share of the lower state house"

The target word "Republican" appears in the phrase: "the difference between a state's major-party vote going to the <t>Republican</t> gubernatorial candidate"

This is clearly referring to the Republican Party candidate for governor, not the general concept of a republican form of government.

Sense 1 is explicitly about the Republican Party: "relating to or belonging to the Republican Party" with examples like "a Republican senator; Republican party politics".

Sense 2 is about the form of government (republican vs monarchical): "having the supreme power lying in the body of citizens entitled to vote..." with examples about "republican form of government".

In the context, "Republican gubernatorial candidate" clearly means a candidate from the Republican Party, not a candidate who supports a republican form of government (as opposed to a monarchy). The context is about party politics, voting patterns, Democrats vs Republicans, ticket splitting, etc.

Therefore, Sense 1 is the correct choice.

The user wants me to return a JSON object exactly like {"sense_index": 1}.

Wait, looking at the candidate senses:
1. sense_key=republican%3:01:01::
2. sense_key=republican%5:00:00:democratic:00

So sense_index should be 1.

The instructions say: "Do not answer with a WordNet sense key." and "Return only a JSON object exactly like {"sense_index": 3}."

So I should return {"sense_index": 1}.

provider: DigitalOcean


[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: candidate
Target surface form: candidate
Context:
An examination of changes in personal staffing decisions in the Senate between 1986 and 1987 -LRB- when control of that body changed party hands -RRB-, moreover, reveals that the personal staffing differences noted in the table can not be attributed to the disproportionate control Democrats exercise, due to their majority - party status, over other resources such as committee staff. An additional piece of evidence from the Senate: Holding other factors constant, such as incumbency advantages and regional factors, the difference between popular votes for Republican presidential and senatorial candidates in states conducting a Senate election turns out to be a positive function of how onerous the federal government's tax burden is per state -LRB- a progressive tax rate hits higher - income states harder -RRB-. Put more simply, GOP candidates for president are looked on more kindly by voters than Republican candidates for the Senate when the prisoner's sentence is more severe. Moreover, ticket splitting appears to take the same peculiar pattern at the state government level as it does at the federal level. State government is more typically split along Republican-governor / Democratic-legislature lines than the reverse. A cross-state econometric investigation, furthermore, reveals that, holding other factors constant, the difference between a state's major - party vote going to the Republican gubernatorial <t>candidate</t> and the Republican share of the lower state house is a positive function of the state tax rate. In sum, at both the federal and state government levels at least part of the seemingly irrational behavior voters display in the voting booth may have an exceedingly rational explanation.

Candidate senses:
1. sense_key=candidate%1:18:01:: | definition=a politician who is running for public office | synonyms=campaigner, nominee
2. sense_key=candidate%1:18:00:: | definition=someone who is considered for something (for an office or prize or honor etc.) | synonyms=prospect

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 perform Word Sense Disambiguation on the word "candidate" in the given context. I need to choose between two senses:

1. candidate%1:18:01:: - a politician who is running for public office (synonyms: campaigner, nominee)
2. candidate%1:18:00:: - someone who is considered for something (for an office or prize or honor etc.) (synonyms: prospect)

Let me analyze the context:

The text discusses:
- "senatorial candidates" (Republican candidates for the Senate)
- "GOP candidates for president"
- "Republican candidates for the Senate"
- "Republican gubernatorial candidate"

All of these refer to people running for political office (Senate, President, Governor).

Sense 1 specifically mentions "a politician who is running for public office" which matches perfectly with senatorial candidates, presidential candidates, and gubernatorial candidates.

Sense 2 is broader: "someone who is considered for something (for an office or prize or honor etc.)" - while technically politicians running for office could fit this broader definition, Sense 1 is more specific and accurate for this political context.

The examples in the text are all about electoral politics:
- "senatorial candidates"
- "GOP candidates for president"
- "Republican candidates for the Senate"
- "gubernatorial candidate"

These are all politicians running for public office, which aligns exactly with sense 1.

Sense 2 would be more appropriate for contexts like "a candidate for the award" or "a candidate for the position" in a non-political or general sense, or when someone is being considered but not necessarily actively campaigning in an election.

Given the specific context of electoral politics (Senate elections, presidential elections, gubernatorial elections), sense 1 is the best fit.

The target surface form appears in: "Republican gubernatorial <t>candidate</t>" - referring to someone running for governor (public office).

Therefore, the answer should be 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: republican
Target surface form: Republican
Context:
An examination of changes in personal staffing decisions in the Senate between 1986 and 1987 -LRB- when control of that body changed party hands -RRB-, moreover, reveals that the personal staffing differences noted in the table can not be attributed to the disproportionate control Democrats exercise, due to their majority - party status, over other resources such as committee staff. An additional piece of evidence from the Senate: Holding other factors constant, such as incumbency advantages and regional factors, the difference between popular votes for Republican presidential and senatorial candidates in states conducting a Senate election turns out to be a positive function of how onerous the federal government's tax burden is per state -LRB- a progressive tax rate hits higher - income states harder -RRB-. Put more simply, GOP candidates for president are looked on more kindly by voters than Republican candidates for the Senate when the prisoner's sentence is more severe. Moreover, ticket splitting appears to take the same peculiar pattern at the state government level as it does at the federal level. State government is more typically split along Republican-governor / Democratic-legislature lines than the reverse. A cross-state econometric investigation, furthermore, reveals that, holding other factors constant, the difference between a state's major - party vote going to the Republican gubernatorial candidate and the <t>Republican</t> share of the lower state house is a positive function of the state tax rate. In sum, at both the federal and state government levels at least part of the seemingly irrational behavior voters display in the voting booth may have an exceedingly rational explanation.

Candidate senses:
1. sense_key=republican%3:01:01:: | definition=relating to or belonging to the Republican Party | examples=a Republican senator; Republican party politics
2. sense_key=republican%5:00:00:democratic:00 | definition=having the supreme power lying in the body of citizens entitled to vote for officers and representatives responsible to them or characteristic of such government; - United States Constitution; ; - Philip Marsh; -Nathaniel Hawthorne | examples=the United States shall guarantee to every state in this union a republican form of government; a very republican notion

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 perform Word Sense Disambiguation for the target word "Republican" (capitalized) in the given context.

Let me analyze the context:
- The text discusses Senate control changing party hands, Democrats, GOP candidates, Republican presidential and senatorial candidates, Republican-governor/Democratic-legislature, Republican gubernatorial candidate, and "the Republican share of the lower state house".
- The target is "Republican" in the phrase "the Republican share of the lower state house".
- This is clearly referring to the Republican Party, not the general concept of a republican form of government.

Candidate senses:
1. republican%3:01:01:: - relating to or belonging to the Republican Party (adjective). Examples: "a Republican senator; Republican party politics"
2. republican%5:00:00:democratic:00 - having supreme power lying in the body of citizens... characteristic of such government. Examples: "republican form of government", "very republican notion".

In the context, "Republican share of the lower state house" refers to the share of seats or votes belonging to the Republican Party. This matches sense 1.

The text is full of political party references: "Republican presidential and senatorial candidates", "GOP candidates", "Republican-governor", "Republican gubernatorial candidate", "Republican share". All of these refer to the Republican Party.

Sense 2 is about the political philosophy/system of government (republicanism), which is not what's meant here.

Therefore, the best sense is sense 1.

The user wants only a JSON object like {"sense_index": 1}.

provider: SiliconFlow


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

[User]
Target lemma: share
Target surface form: share
Context:
An examination of changes in personal staffing decisions in the Senate between 1986 and 1987 -LRB- when control of that body changed party hands -RRB-, moreover, reveals that the personal staffing differences noted in the table can not be attributed to the disproportionate control Democrats exercise, due to their majority - party status, over other resources such as committee staff. An additional piece of evidence from the Senate: Holding other factors constant, such as incumbency advantages and regional factors, the difference between popular votes for Republican presidential and senatorial candidates in states conducting a Senate election turns out to be a positive function of how onerous the federal government's tax burden is per state -LRB- a progressive tax rate hits higher - income states harder -RRB-. Put more simply, GOP candidates for president are looked on more kindly by voters than Republican candidates for the Senate when the prisoner's sentence is more severe. Moreover, ticket splitting appears to take the same peculiar pattern at the state government level as it does at the federal level. State government is more typically split along Republican-governor / Democratic-legislature lines than the reverse. A cross-state econometric investigation, furthermore, reveals that, holding other factors constant, the difference between a state's major - party vote going to the Republican gubernatorial candidate and the Republican <t>share</t> of the lower state house is a positive function of the state tax rate. In sum, at both the federal and state government levels at least part of the seemingly irrational behavior voters display in the voting booth may have an exceedingly rational explanation.

Candidate senses:
1. sense_key=share%1:21:00:: | definition=assets belonging to or due to or contributed by an individual person or group | synonyms=portion, part, percentage | examples=he wanted his share in cash
2. sense_key=share%1:21:01:: | definition=any of the equal portions into which the capital stock of a corporation is divided and ownership of which is evidenced by a stock certificate | examples=he bought 100 shares of IBM at the market price
3. sense_key=share%1:04:00:: | definition=the allotment of some amount by dividing something | synonyms=parcel, portion | examples=death gets more than its share of attention from theologians
4. sense_key=share%1:04:01:: | definition=the part played by a person in bringing about a result | synonyms=contribution, part | examples=I am proud of my contribution in advancing the project; they all did their share of the work
5. sense_key=share%1:06:00:: | definition=a sharp steel wedge that cuts loose the top layer of soil | synonyms=plowshare, ploughshare

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 perform Word Sense Disambiguation for the word "share" in the given context.

Let me analyze the context carefully:

The sentence is: "A cross-state econometric investigation, furthermore, reveals that, holding other factors constant, the difference between a state's major - party vote going to the Republican gubernatorial candidate and the Republican <t>share</t> of the lower state house is a positive function of the state tax rate."

Here, "share" refers to the Republican portion/proportion of the lower state house. It's talking about the proportion or percentage of seats or votes that Republicans have in the lower state house.

Now let's look at the candidate senses:

1. sense_key=share%1:21:00:: | definition=assets belonging to or due to or contributed by an individual person or group | synonyms=portion, part, percentage | examples=he wanted his share in cash
   - This seems to be about assets, money, or tangible things belonging to someone. The example mentions "cash". This doesn't fit the political context of vote proportions.

2. sense_key=share%1:21:01:: | definition=any of the equal portions into which the capital stock of a corporation is divided and ownership of which is evidenced by a stock certificate | examples=he bought 100 shares of IBM at the market price
   - This is clearly about stock shares. Not relevant here.

3. sense_key=share%1:04:00:: | definition=the allotment of some amount by dividing something | synonyms=parcel, portion | examples=death gets more than its share of attention from theologians
   - This is about an allotment or portion resulting from division. The example "death gets more than its share of attention" suggests a metaphorical portion. But the definition says "allotment of some amount by dividing something."

4. sense_key=share%1:04:01:: | definition=the part played by a person in bringing about a result | synonyms=contribution, part | examples=I am proud of my contribution in advancing the project; they all did their share of the work
   - This is about a person's contribution or role in an activity. "They all did their share of the work." Not quite right for a proportion of votes.

5. sense_key=share%1:06:00:: | definition=a sharp steel wedge that cuts loose the top layer of soil | synonyms=plowshare, ploughshare
   - Completely irrelevant.

Wait, let me reconsider sense 1 vs sense 3.

Sense 1: "assets belonging to or due to or contributed by an individual person or group" - synonyms: portion, part, percentage. This is a noun referring to a part of something, but specifically in the context of assets? Let me think about WordNet hierarchies.

Actually, looking at the sense keys:
- share%1:21:00:: - This is under noun.possession (21)
- share%1:04:00:: - This is under noun.act (04)? No, wait. Let me check WordNet lexicographer file names.
  - 21 = noun.possession
  - 04 = noun.act? Actually:
    - 00 = adj.all
    - 01 = noun.Tops
    - 03 = noun.animal
    - 04 = noun.artifact? No, let me recall:
    Actually, the second number in the sense key is the lexicographer file number.
    - 1:04 = noun.act? No, 04 might be noun.act... wait.
    Let me think... WordNet lex file numbers:
    - 00 = adj.all
    - 01 = noun.Tops
    - 02 = noun.group
    - 03 = noun.person
    - 04 = noun.artifact? No...
    Actually, I should rely on the definitions given rather than the hierarchy numbers.

Wait, the context is: "Republican share of the lower state house". This means the proportion/percentage of seats or representation that Republicans have.

Sense 1 has synonyms: portion, part, percentage. The definition says "assets belonging to or due to or contributed by an individual person or group". But "assets" might be interpreted broadly? However, in the context of voting, a "share" of the vote is often expressed as a percentage.

Sense 3: "the allotment of some amount by dividing something" - synonyms=parcel, portion. Example: "death gets more than its share of attention".

Actually, looking at standard WordNet senses for "share":
- Sense 1: any of the equal portions into which the capital stock of a corporation is divided (stock share)
- Sense 2: assets belonging to or due to or contributed by an individual person or group (portion, part, percentage)
- Sense 3: the allotment of some amount by dividing something
- Sense 4: the part played by a person in bringing about a result
- Sense 5: plowshare

Wait, the numbering in the candidate senses might not match the standard WordNet order. Let me look at the sense keys:
1. share%1:21:00:: - This is the "assets/possession" sense (portion, part, percentage)
2. share%1:21:01:: - This is the stock sense
3. share%1:04:00:: - This is "allotment of some amount by dividing something"
4. share%1:04:01:: - This is "part played by a person"
5. share%1:06:00:: - This is plowshare

In the context: "Republican share of the lower state house" - this refers to the proportion or percentage of seats/votes.

Which sense is best?

Sense 1 (share%1:21:00::): "assets belonging to or due to or contributed by an individual person or group" - synonyms: portion, part, percentage. While the definition mentions "assets", WordNet glosses are schematic. The example given is "he wanted his share in cash". But the synonyms include "percentage". In political science contexts, "vote share" is extremely common and means the percentage of votes.

Sense 3 (share%1:04:00::): "the allotment of some amount by dividing something" - synonyms: parcel, portion. Example: "death gets more than its share of attention".

Hmm. "Republican share of the lower state house" - is this an allotment? Or is it a portion/percentage?

Actually, in many WSD datasets, "share" when referring to "market share" or "vote share" is often tagged as sense 1 (portion, part, percentage) or sense 3. Let me think about the distinction.

Sense 1 is in noun.possession (lexfile 21). It relates to what someone has or owns - their portion of something divisible. The example "he wanted his share in cash" suggests something that is owed or belongs to someone.

Sense 3 is in noun.act? Wait, lexfile 04... let me verify. Actually, looking at WordNet 3.0:
- share, portion, part, percentage (noun.possession) - lexfile 21
- share (noun.act) - lexfile 04? No, "the allotment of some amount by dividing something" - this might be noun.act or noun.cognition?
Actually, "allotment" sounds like noun.act.

But "Republican share of the lower state house" - Republicans don't "possess" the share as an asset, but they have a proportion of the seats.

Wait, looking at the example for sense 3: "death gets more than its share of attention from theologians". This is very similar to "Republican share of the lower state house". Death's share of attention = the amount of attention death receives. Republican share of the lower state house = the amount/proportion of the lower state house that Republicans have.

But sense 1 has synonyms "percentage" and the example is about cash. However, "vote share" is a percentage.

Let me reconsider the WordNet senses more carefully.

In WordNet 3.0:
- share, portion, part, percentage (noun possession) - "assets belonging to or due to or contributed by an individual person or group"
  This is sense 1 in the list above.
- share (noun artifact? No, noun possession?) - "any of the equal portions into which the capital stock of a corporation is divided..." - sense 2 above.
- share, portion, part (noun act?) - "the allotment of some amount by dividing something" - sense 3 above.
- contribution, part, share (noun act?) - "the part played by a person in bringing about a result" - sense 4 above.
- plowshare (noun artifact) - sense 5 above.

Wait, I think I need to be more careful. The context is: "Republican share of the lower state house". This is clearly referring to the proportion of seats or votes.

Between sense 1 and sense 3:
- Sense 1: portion, part, percentage. Definition mentions "assets" but glosses are schematic. The key is that it's something belonging to or due to a person/group. The Republican share belongs to the Republican party.
- Sense 3: allotment by dividing something. Example: "death gets more than its share of attention". This is also a strong candidate.

However, in the context of elections and voting, "share" almost always means "percentage" or "proportion" of the total. The synonym "percentage" is explicitly listed in sense 1. The phrase "vote share" or "share of the vote" is standard political terminology meaning percentage.

Also, looking at the example for sense 3: "death gets more than its share of attention" - this is about an abstract amount of attention. "Republican share of the lower state house" is about the proportion of legislative seats.

But wait - is there a sense that specifically means "proportion/percentage"? Sense 1 includes "percentage" as a synonym. The definition says "assets belonging to or due to or contributed by..." but in schematic glosses, this is the "portion" sense. The example "he wanted his share in cash" is one instantiation.

Actually, I recall that in WordNet, "share" as in "market share" or "vote share" maps to sense 1 (share, portion, part, percentage). The key is that it's a quantity belonging to a group.

Let me check if sense 3 could be better. Sense 3: "the allotment of some amount by dividing something". This focuses on the act of allotting or the result of dividing. But "Republican share" is not an allotment (something given out), it's a proportion of votes received.

Also, the text says "Republican share of the lower state house" - this parallels "death's share of attention". But death doesn't possess attention as an asset. However, Republicans do possess seats in the house.

Actually, looking at standard WSD for "share":
- "market share" -> usually sense 1 (portion, part, percentage)
- "share of the vote" -> usually sense 1
- "do one's share" -> sense 4
- "share of stock" -> sense 2
- "plowshare" -> sense 5

The example "death gets more than its share of attention" in sense 3 is interesting because it's similar to "share of attention/lower state house". But I think the distinction in WordNet is:
- Sense 1: a quantity of something that is allocated to or owned by someone (possession)
- Sense 3: the result of dividing something (allotment)

In political science academic writing, "vote share" is standard terminology. The word "percentage" is a synonym in sense 1. The context mentions "major-party vote" and "Republican gubernatorial candidate" and "Republican share" - this is clearly about the percentage/proportion of votes or seats.

I think sense 1 is the best fit because:
1. It has "percentage" as a synonym
2. It refers to a part belonging to a group (Republicans)
3. "Vote share" is a standard compound meaning percentage of votes
4. While the gloss mentions "assets", WordNet glosses are schematic and this is the general "portion" sense

Wait, but let me reconsider sense 3. The definition is "the allotment of some amount by dividing something". The Republican share of the lower state house is indeed the result of dividing the house into Republican and Democratic portions. But the word "allotment" implies an active distribution, whereas election results are not allotted but won.

Actually, looking at the WordNet hierarchy again:
- share%1:21:00:: (noun.possession) - This is the "portion/part/percentage" sense.
- share%1:04:00:: - What is lexfile 04? Let me think... In WordNet, lexicographer files:
  - noun.Tops (01)
  - noun.act (04)? Actually no, I think noun.act might be 04. Let me verify from the sense key format: word%ss_type:lex_filenum:lex_id:head_word:head_id.
  - ss_type 1 = noun
  - lex_filenum 04 = noun.act? Or noun.animal? No, noun.animal is 05? Let me recall:
    - 00 = adj.all
    - 01 = noun.Tops
    - 02 = noun.group
    - 03 = noun.person
    - 04 = noun.artifact? No...
    Actually, I found a reference: WordNet lexicographer file numbers:
    - 00 - adj.all
    - 01 - noun.Tops
    - 02 - noun.group
    - 03 - noun.person
    - 04 - noun.artifact? No, 04 is noun.act? Wait.
    Let me think of words in noun.act: "act", "action", "activity".
    Actually, looking at "share%1:04:00::" with definition "the allotment of some amount by dividing something" - "allotment" is an act, so this is likely noun.act.
    And "share%1:04:01::" with definition "the part played by a person in bringing about a result" - also noun.act (contribution).

But regardless of the lexfile, the question is which sense applies.

Let me look at the context again: "the Republican share of the lower state house". This is parallel to "the Republican percentage of the lower state house" or "the Republican portion of the lower state house".

Sense 1 synonyms: portion, part, percentage.
Sense 3 synonyms: parcel, portion.

Both have "portion". But sense 1 has "percentage" which is exactly what is meant in voting contexts.

Also, the example for sense 1: "he wanted his share in cash" - this is about a specific quantity owed to someone. The Republican share is the specific quantity of seats/votes won by Republicans.

The example for sense 3: "death gets more than its share of attention" - this is more idiomatic/metaphorical.

In academic political science text, "share" meaning proportion of votes is very literal and quantitative. Sense 1 with "percentage" as a synonym is the best fit.

I should choose sense 1.

Wait, I want to double-check. Is there any chance it's sense 3? Let me think about "market share". If a company has a 30% market share, is that sense 1 or 3? I believe in WordNet it's sense 1 (portion, part, percentage) because it's a possession or quantity belonging to the company. Similarly, vote share is a quantity belonging to the party.

Also, the text mentions "the difference between a state's major-party vote going to the Republican gubernatorial candidate and the Republican share of the lower state house". This is comparing vote percentages. "Share" here is clearly synonymous with "percentage" or "proportion".

Therefore, sense 1 is the best choice.

One more check: The user says "Do not hedge. Choose the single best indexed sense." and "Return only a JSON object exactly like {"sense_index": 3}."

So I will return {"sense_index": 1}.

Actually, wait. Let me reconsider one more time. Is it possible that sense 3 is better because the context is about dividing something?

Definition of sense 3: "the allotment of some amount by dividing something"
Definition of sense 1: "assets belonging to or due to or contributed by an individual person or group"

The text is talking about the lower state house being divided between parties. The Republican share is what Republicans get when the house is divided. But actually, the house isn't divided - it's elected. But metaphorically, the seats are divided among parties.

However, "assets belonging to..." - are seats in a legislature "assets"? In a schematic sense, they are resources or positions controlled by the party. The gloss says "assets belonging to or due to or contributed by" - in political science, seats are indeed political assets.

But I think the strongest argument is the synonym "percentage" in sense 1. In this context, "share" = "percentage" of the vote/seats. This is a perfect match.

I'll go with sense 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: house
Target surface form: house
Context:
An examination of changes in personal staffing decisions in the Senate between 1986 and 1987 -LRB- when control of that body changed party hands -RRB-, moreover, reveals that the personal staffing differences noted in the table can not be attributed to the disproportionate control Democrats exercise, due to their majority - party status, over other resources such as committee staff. An additional piece of evidence from the Senate: Holding other factors constant, such as incumbency advantages and regional factors, the difference between popular votes for Republican presidential and senatorial candidates in states conducting a Senate election turns out to be a positive function of how onerous the federal government's tax burden is per state -LRB- a progressive tax rate hits higher - income states harder -RRB-. Put more simply, GOP candidates for president are looked on more kindly by voters than Republican candidates for the Senate when the prisoner's sentence is more severe. Moreover, ticket splitting appears to take the same peculiar pattern at the state government level as it does at the federal level. State government is more typically split along Republican-governor / Democratic-legislature lines than the reverse. A cross-state econometric investigation, furthermore, reveals that, holding other factors constant, the difference between a state's major - party vote going to the Republican gubernatorial candidate and the Republican share of the lower state <t>house</t> is a positive function of the state tax rate. In sum, at both the federal and state government levels at least part of the seemingly irrational behavior voters display in the voting booth may have an exceedingly rational explanation.

Candidate senses:
1. sense_key=house%1:06:00:: | definition=a dwelling that serves as living quarters for one or more families | examples=he has a house on Cape Cod; she felt she had to get out of the house
2. sense_key=house%1:14:01:: | definition=the members of a business organization that owns or operates one or more establishments | synonyms=firm, business firm | examples=he worked for a brokerage house
3. sense_key=house%1:14:04:: | definition=the members of a religious community living together
4. sense_key=house%1:14:03:: | definition=the audience gathered together in a theatre or cinema | examples=the house applauded; he counted the house
5. sense_key=house%1:14:02:: | definition=an official assembly having legislative powers | examples=a bicameral legislature has two houses
6. sense_key=house%1:14:00:: | definition=aristocratic family line | examples=the House of York
7. sense_key=house%1:04:00:: | definition=play in which children take the roles of father or mother or children and pretend to interact like adults | examples=the children were playing house
8. sense_key=house%1:15:00:: | definition=(astrology) one of 12 equal areas into which the zodiac is divided | synonyms=sign of the zodiac, star sign, sign, mansion, planetary house
9. sense_key=house%1:14:06:: | definition=the management of a gambling house or casino | examples=the house gets a percentage of every bet
10. sense_key=house%1:14:05:: | definition=a social unit living together | synonyms=family, household, home, menage | examples=he moved his family to Virginia; It was a good Christian household
11. sense_key=house%1:06:02:: | definition=a building where theatrical performances or motion-picture shows can be presented | synonyms=theater, theatre | examples=the house was full
12. sense_key=house%1:06:01:: | definition=a building in which something is sheltered or located | examples=they had a large carriage house

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 perform Word Sense Disambiguation for the word "house" in the given context.

 Let me analyze the context:
 - The text is discussing political science/economics, specifically about voting patterns in the US Senate and state legislatures.
 - The specific sentence containing "house" is: "A cross-state econometric investigation, furthermore, reveals that, holding other factors constant, the difference between a state's major - party vote going to the Republican gubernatorial candidate and the Republican share of the lower state <t>house</t> is a positive function of the state tax rate."
 - Earlier in the text, it mentions: "An examination of changes in personal staffing decisions in the Senate between 1986 and 1987..."
 - It also mentions: "State government is more typically split along Republican-governor / Democratic-legislature lines than the reverse."
 - The phrase "lower state house" clearly refers to the lower chamber of a state legislature (as opposed to the state senate, which is typically the upper chamber).

 Now let's look at the candidate senses:
 1. house%1:06:00:: - a dwelling (physical building) - not relevant here
 2. house%1:14:01:: - business organization - not relevant
 3. house%1:14:04:: - religious community - not relevant
 4. house%1:14:03:: - theatre audience - not relevant
 5. house%1:14:02:: - an official assembly having legislative powers; examples mention "a bicameral legislature has two houses" - This fits perfectly! "Lower state house" refers to the lower legislative chamber.
 6. house%1:14:00:: - aristocratic family line - not relevant
 7. house%1:04:00:: - children's play - not relevant
 8. house%1:15:00:: - astrology - not relevant
 9. house%1:14:06:: - gambling management - not relevant
 10. house%1:14:05:: - social unit/family - not relevant
 11. house%1:06:02:: - theatre building - not relevant
 12. house%1:06:01:: - building for shelter - not relevant

 The context clearly refers to the legislative body - specifically the "lower state house" which is the lower chamber of a state legislature (like the House of Representatives at the state level, as opposed to the State Senate).

 Sense 5 (house%1:14:02::) is defined as "an official assembly having legislative powers" with the example "a bicameral legislature has two houses". This matches the context perfectly where "lower state house" refers to the lower legislative chamber.

 The answer should be sense index 5.

 Wait, let me double-check the indexing. The user lists:
 1. sense_key=house%1:06:00::
 2. sense_key=house%1:14:01::
 3. sense_key=house%1:14:04::
 4. sense_key=house%1:14:03::
 5. sense_key=house%1:14:02::
 6. sense_key=house%1:14:00::
 7. sense_key=house%1:04:00::
 8. sense_key=house%1:15:00::
 9. sense_key=house%1:14:06::
 10. sense_key=house%1:14:05::
 11. sense_key=house%1:06:02::
 12. sense_key=house%1:06:01::

 So sense 5 is indeed house%1:14:02:: which is the legislative assembly sense.

 The context mentions "lower state house" in contrast to "Republican gubernatorial candidate" and discusses state government being split between governor and legislature. This confirms it's referring to the legislative chamber.

 Therefore, the correct answer is sense_index: 5.


[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: positive
Target surface form: positive
Context:
An examination of changes in personal staffing decisions in the Senate between 1986 and 1987 -LRB- when control of that body changed party hands -RRB-, moreover, reveals that the personal staffing differences noted in the table can not be attributed to the disproportionate control Democrats exercise, due to their majority - party status, over other resources such as committee staff. An additional piece of evidence from the Senate: Holding other factors constant, such as incumbency advantages and regional factors, the difference between popular votes for Republican presidential and senatorial candidates in states conducting a Senate election turns out to be a positive function of how onerous the federal government's tax burden is per state -LRB- a progressive tax rate hits higher - income states harder -RRB-. Put more simply, GOP candidates for president are looked on more kindly by voters than Republican candidates for the Senate when the prisoner's sentence is more severe. Moreover, ticket splitting appears to take the same peculiar pattern at the state government level as it does at the federal level. State government is more typically split along Republican-governor / Democratic-legislature lines than the reverse. A cross-state econometric investigation, furthermore, reveals that, holding other factors constant, the difference between a state's major - party vote going to the Republican gubernatorial candidate and the Republican share of the lower state house is a <t>positive</t> function of the state tax rate. In sum, at both the federal and state government levels at least part of the seemingly irrational behavior voters display in the voting booth may have an exceedingly rational explanation.

Candidate senses:
1. sense_key=positive%3:00:01:: | definition=characterized by or displaying affirmation or acceptance or certainty etc. | examples=a positive attitude; the reviews were all positive
2. sense_key=positive%5:00:00:certain:02 | definition=persuaded of; very sure | synonyms=convinced, confident | examples=were convinced that it would be to their advantage to join; I am positive he is lying
3. sense_key=positive%5:00:00:advantageous:00 | definition=involving advantage or good | synonyms=plus | examples=a plus (or positive) factor
4. sense_key=positive%3:00:04:: | definition=indicating existence or presence of a suspected condition or pathogen | synonyms=confirming | examples=a positive pregnancy test
5. sense_key=positive%5:00:00:formal:01 | definition=formally laid down or imposed | synonyms=prescribed | examples=positive laws
6. sense_key=positive%5:00:00:undeniable:00 | definition=impossible to deny or disprove | synonyms=incontrovertible, irrefutable | examples=incontrovertible proof of the defendant's innocence; proof positive
7. sense_key=positive%3:01:00:: | definition=of or relating to positivism | synonyms=positivist, positivistic | examples=positivist thinkers; positivist doctrine
8. sense_key=positive%3:00:05:: | definition=reckoned, situated or tending in the direction which naturally or arbitrarily is taken to indicate increase or progress or onward motion | examples=positive increase in graduating students
9. sense_key=positive%5:00:00:plus:00 | definition=greater than zero | examples=positive numbers
10. sense_key=positive%5:00:00:charged:00 | definition=having a positive charge | synonyms=electropositive, positively charged | examples=protons are positive
11. sense_key=positive%5:00:00:confident:00 | definition=marked by excessive confidence | synonyms=cocksure, overconfident | examples=an arrogant and cocksure materialist; so overconfident and impudent as to speak to the queen

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 perform Word Sense Disambiguation (WSD) for the word "positive" in the given context.

 First, let me look at the context sentence containing the target word:
 "A cross-state econometric investigation, furthermore, reveals that, holding other factors constant, the difference between a state's major - party vote going to the Republican gubernatorial candidate and the Republican share of the lower state house is a <t>positive</t> function of the state tax rate."

 The phrase is "positive function". This is a mathematical/statistical term. In mathematics and economics, a "positive function" typically means that as one variable increases, the other variable also increases (positive correlation/direct relationship), or it could mean the function values are greater than zero, but in this context it's about the relationship between variables.

 Let me look at the candidate senses:

 1. characterized by or displaying affirmation or acceptance or certainty etc. - This is about attitude or reviews. Not applicable here.
 2. persuaded of; very sure - This is about being convinced. Not applicable.
 3. involving advantage or good - This is about being beneficial. While tax rate might be seen as good or bad, "positive function" in econometrics doesn't mean "advantageous function".
 4. indicating existence or presence of a suspected condition or pathogen - Medical context. Not applicable.
 5. formally laid down or imposed - Legal context. Not applicable.
 6. impossible to deny or disprove - About proof. Not applicable.
 7. of or relating to positivism - Philosophical context. Not applicable.
 8. reckoned, situated or tending in the direction which naturally or arbitrarily is taken to indicate increase or progress or onward motion - This mentions "increase" and direction indicating increase. The example is "positive increase in graduating students". This seems related to the mathematical sense where positive indicates increase.
 9. greater than zero - Mathematical sense. Example: "positive numbers". In the context of a "function", this could mean the function values are > 0, but in econometrics, "positive function of" usually means that Y increases as X increases (positive relationship).
 10. having a positive charge - Physics/chemistry. Not applicable.
 11. marked by excessive confidence - Personality trait. Not applicable.

 Now, between sense 8 and 9:
 - Sense 9: "greater than zero" - If it were "positive number" or "positive value", this would fit. But "positive function of" is different.
 - Sense 8: "reckoned, situated or tending in the direction which naturally or arbitrarily is taken to indicate increase or progress or onward motion" - The key phrase here is "indicate increase". In mathematics/economics, when we say Y is a positive function of X, we mean that as X increases, Y increases (positive correlation/slope).

 Actually, looking closely at sense 8's definition: "reckoned, situated or tending in the direction which naturally or arbitrarily is taken to indicate increase or progress or onward motion". This seems to be describing the directional sense - like positive direction, positive trend.

 But wait, let me reconsider the exact phrase in the text: "is a positive function of"

 In econometrics/statistics, this is standard terminology meaning that there is a positive relationship (as one goes up, the other goes up). This aligns with sense 8 which mentions "indicate increase".

 However, sense 9 "greater than zero" is also mathematical. But "positive function of" is not saying the function is greater than zero, it's saying the relationship is positive (direct).

 Let me look at the examples for sense 8: "positive increase in graduating students" - this is redundant but emphasizes the direction of change.

 Actually, looking at WordNet structure, sense 9 (greater than zero) is often used for numbers. Sense 8 seems to be about direction/increase.

 But there's another interpretation: In mathematics, a function can be "positive" meaning it takes positive values. But the phrase "function of" suggests the relationship meaning.

 Let me look at the surrounding context again: "the difference... is a positive function of the state tax rate". This means as tax rate increases, the difference increases. This is a positive correlation/relationship.

 Sense 8: "reckoned, situated or tending in the direction which naturally or arbitrarily is taken to indicate increase or progress or onward motion"
 - This captures the idea of "increasing" or "upward" direction.

 Sense 3: "involving advantage or good" - could this fit? "A positive function" could mean a good/beneficial function? But in academic econometric writing, "positive function" is technical terminology, not evaluative.

 Sense 9 is about being > 0. If the text meant the function values are positive, it might fit, but the standard interpretation of "Y is a positive function of X" is the directional one (monotonic increasing).

 Wait, I should check if there's a specific sense for mathematical functions. Looking at the list, sense 8 and 9 are the mathematical ones.

 Sense 8 example: "positive increase in graduating students" - this is about increase.
 Sense 9 example: "positive numbers" - this is about > 0.

 The phrase "positive function of" is ambiguous without context, but given this is an econometric investigation discussing relationships between variables (tax rate and vote difference), it's describing a relationship where the dependent variable increases as the independent variable increases.

 Therefore, sense 8 seems best: it relates to increase, progress, onward motion.

 But let me double-check sense 3: "involving advantage or good" with synonym "plus". Could "positive function" mean a plus/good function? In the context of "ticket splitting" and voting behavior, they are describing a pattern. "Positive function" here is technical.

 Actually, looking at the gloss for sense 8 again: "reckoned, situated or tending in the direction which naturally or arbitrarily is taken to indicate increase or progress or onward motion". This is somewhat awkwardly phrased but refers to the directional sense of positive (as opposed to negative).

 In calculus/economics, a positive function usually means f(x) > 0 for all x. A monotonic function or increasing function is different. But the phrase "positive function of" specifically (with "of") strongly suggests the relationship meaning: Y = f(X) where f is increasing, or specifically, the correlation is positive.

 However, looking at standard WordNet senses for "positive":
 - Sense 8 (positive%3:00:05::) is typically the one for "positive direction", "positive trend", etc.
 - Sense 9 (positive%5:00:00:plus:00) is "greater than zero".

 The example for sense 8 mentions "positive increase", which is exactly the kind of collocation we have here (positive function implying increasing relationship).

 Also, note the previous sentence in the context: "the difference... turns out to be a positive function of how onerous the federal government's tax burden is". This parallels the target sentence. Both describe how a difference increases with tax burden/rate.

 Therefore, sense 8 is the correct choice.

 Wait, I should verify the index. The user lists:
 1. sense_key=positive%3:00:01::
 2. sense_key=positive%5:00:00:certain:02
 3. sense_key=positive%5:00:00:advantageous:00
 4. sense_key=positive%3:00:04::
 5. sense_key=positive%5:00:00:formal:01
 6. sense_key=positive%5:00:00:undeniable:00
 7. sense_key=positive%3:01:00::
 8. sense_key=positive%3:00:05::
 9. sense_key=positive%5:00:00:plus:00
 10. sense_key=positive%5:00:00:charged:00
 11. sense_key=positive%5:00:00:confident:00

 So sense 8 is positive%3:00:05:: with definition "reckoned, situated or tending in the direction which naturally or arbitrarily is taken to indicate increase or progress or onward motion".

 This fits best because the context describes a relationship where one variable increases as another increases (positive correlation/monotonic relationship), which is about the direction of change/increase.

 Sense 9 (greater than zero) would imply the function values are > 0, which is possible but less likely the meaning here compared to the relational/directional meaning.

 Also, sense 3 (advantageous) is tempting because "positive" often means good, but in this academic context, it's clearly a technical term about the mathematical relationship.

 Therefore, the answer is sense_index: 8.


[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: function
Target surface form: function
Context:
An examination of changes in personal staffing decisions in the Senate between 1986 and 1987 -LRB- when control of that body changed party hands -RRB-, moreover, reveals that the personal staffing differences noted in the table can not be attributed to the disproportionate control Democrats exercise, due to their majority - party status, over other resources such as committee staff. An additional piece of evidence from the Senate: Holding other factors constant, such as incumbency advantages and regional factors, the difference between popular votes for Republican presidential and senatorial candidates in states conducting a Senate election turns out to be a positive function of how onerous the federal government's tax burden is per state -LRB- a progressive tax rate hits higher - income states harder -RRB-. Put more simply, GOP candidates for president are looked on more kindly by voters than Republican candidates for the Senate when the prisoner's sentence is more severe. Moreover, ticket splitting appears to take the same peculiar pattern at the state government level as it does at the federal level. State government is more typically split along Republican-governor / Democratic-legislature lines than the reverse. A cross-state econometric investigation, furthermore, reveals that, holding other factors constant, the difference between a state's major - party vote going to the Republican gubernatorial candidate and the Republican share of the lower state house is a positive <t>function</t> of the state tax rate. In sum, at both the federal and state government levels at least part of the seemingly irrational behavior voters display in the voting booth may have an exceedingly rational explanation.

Candidate senses:
1. sense_key=function%1:24:00:: | definition=(mathematics) a mathematical relation such that each element of a given set (the domain of the function) is associated with an element of another set (the range of the function) | synonyms=mathematical function, single-valued function, map, mapping
2. sense_key=function%1:07:00:: | definition=what something is used for | synonyms=purpose, role, use | examples=the function of an auger is to bore holes; ballet is beautiful but what use is it?
3. sense_key=function%1:04:00:: | definition=the actions and activities assigned to or required or expected of a person or group | synonyms=office, part, role | examples=the function of a teacher; the government must do its part
4. sense_key=function%1:24:01:: | definition=a relation such that one thing is dependent on another | examples=height is a function of age; price is a function of supply and demand
5. sense_key=function%1:14:00:: | definition=a formal or official social gathering or ceremony | examples=it was a black-tie function
6. sense_key=function%1:11:00:: | definition=a vaguely specified social event | synonyms=affair, occasion, social occasion, social function | examples=the party was quite an affair; an occasion arranged to honor the president
7. sense_key=function%1:10:00:: | definition=a set sequence of steps, part of larger computer program | synonyms=routine, subroutine, subprogram, procedure

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 perform Word Sense Disambiguation on the word "function" in a specific context.

Let me analyze the context:
The sentence is: "A cross-state econometric investigation, furthermore, reveals that, holding other factors constant, the difference between a state's major - party vote going to the Republican gubernatorial candidate and the Republican share of the lower state house is a positive <t>function</t> of the state tax rate."

This is talking about a mathematical/statistical relationship where one variable (the difference in votes) depends on or is determined by another variable (the state tax rate).

Looking at the candidate senses:
1. Mathematical function (strict mathematical definition with domain/range) - this is more about the mathematical concept itself
2. Purpose/use - "what something is used for" - doesn't fit here
3. Role/office - "actions and activities assigned to..." - doesn't fit
4. "a relation such that one thing is dependent on another" - examples: "height is a function of age; price is a function of supply and demand" - This fits perfectly! The text is saying the vote difference is a function of (depends on) the tax rate.
5. Social gathering - no
6. Social event - no
7. Computer programming routine - no

The phrase "is a positive function of" is a statistical/econometric term meaning that as one variable increases, the other increases (positive correlation/dependency). This matches sense 4: "a relation such that one thing is dependent on another" with examples like "price is a function of supply and demand."

Sense 1 is too specific to pure mathematics (domain/range mapping), while sense 4 captures the dependency relationship meant in econometric contexts.

Sense index 4 is the correct choice.