Triple

T15918518
Position Surface form Disambiguated ID Type / Status
Subject Erdős–Szekeres theorem E386031 entity
Predicate alsoKnownAs P39 FINISHED
Object happy ending theorem
The happy ending theorem is a result in combinatorial geometry stating that any sufficiently large set of points in general position in the plane contains a subset that forms the vertices of a convex polygon.
 E1182409 NE FINISHED

How this triple was built (4 steps)

Every LLM step that produced this triple, in pipeline order — named-entity classification, the disambiguation choices (the exact options shown, with the pick highlighted), and the generated description. The batch + timestamp of each is in the Provenance table below.

NER Named-entity recognition gpt-5-mini
Instruction
Given a phrase, classify it is english named entity (e.g., persons, organizations, works of art) in Latin script, or not (e.g., literals, dates, URLs, verbose phrases). For disambiguation, the statement where the phrase occurs as object is also given. Please return a JSON object with `phrase` (string, the phrase being analyzed) and `is_ne` (boolean, indicating whether the phrase is a Named Entity).
Input
Phrase: happy ending theorem | Statement: [Erdős–Szekeres theorem, alsoKnownAs, happy ending theorem]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: happy ending theorem
Context triple: [Erdős–Szekeres theorem, alsoKnownAs, happy ending theorem]
  • A. "Happy Ending"
    "Happy Ending" is a pop song by British singer-songwriter Mika, known for its emotive lyrics and soaring, melodic chorus.
  • B. A Happy End
    A Happy End is a stage play by Israeli playwright Iddo Netanyahu that portrays a Jewish couple in 1930s Berlin grappling with the rising threat of Nazism and the agonizing decision of whether to leave Germany.
  • C. The Happy Ending
    The Happy Ending is a 1969 American drama film written and directed by Richard Brooks, starring Jean Simmons as a disillusioned housewife who abruptly leaves her comfortable suburban life in search of independence and self-discovery.
  • D. Happy End
    Happy End is a 1929 satirical musical play with songs by Kurt Weill and lyrics by Bertolt Brecht, known for its blend of political commentary and cabaret-style music.
  • E. Happy Endings
    Happy Endings is an American ensemble sitcom that follows a close-knit group of friends navigating relationships and adulthood in Chicago with fast-paced, joke-heavy humor.
  • F. None of above. chosen
  • G. Unsure - the case is ambiguous/there is not enough information to decide.
NEDg Description generation gpt-5.1
Instruction
Generate a one-sentence description of the target entity. 
You are given a context triple in the form (subject, predicate, object), where the object is the target entity. 
# Instructions
Use the triple to infer relevant information about the entity. Describe the entity based on what is most defining, well-known. 
Avoid repeating the information from the triple, unless really essential.
# Response Format
Return only the sentence: "Description: [one-sentence description of the target entity]"
Input
Entity: happy ending theorem
Triple: [Erdős–Szekeres theorem, alsoKnownAs, happy ending theorem]
Generated description
The happy ending theorem is a result in combinatorial geometry stating that any sufficiently large set of points in general position in the plane contains a subset that forms the vertices of a convex polygon.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07 
Target entity: happy ending theorem
Target entity description: The happy ending theorem is a result in combinatorial geometry stating that any sufficiently large set of points in general position in the plane contains a subset that forms the vertices of a convex polygon.
  • A. "Happy Ending"
    "Happy Ending" is a pop song by British singer-songwriter Mika, known for its emotive lyrics and soaring, melodic chorus.
  • B. A Happy End
    A Happy End is a stage play by Israeli playwright Iddo Netanyahu that portrays a Jewish couple in 1930s Berlin grappling with the rising threat of Nazism and the agonizing decision of whether to leave Germany.
  • C. The Happy Ending
    The Happy Ending is a 1969 American drama film written and directed by Richard Brooks, starring Jean Simmons as a disillusioned housewife who abruptly leaves her comfortable suburban life in search of independence and self-discovery.
  • D. Happy End
    Happy End is a 1929 satirical musical play with songs by Kurt Weill and lyrics by Bertolt Brecht, known for its blend of political commentary and cabaret-style music.
  • E. Happy Endings
    Happy Endings is an American ensemble sitcom that follows a close-knit group of friends navigating relationships and adulthood in Chicago with fast-paced, joke-heavy humor.
  • F. None of above. chosen

Provenance (5 batches)

The batch behind each pipeline step, in order, with when it ran. Timestamps are batch-level — stages were processed in waves, so the object chain (NER → NED1 → NEDg → NED2) reads in order, but predicate / elicitation batches can sit in a different wave.

Step Stage Batch ID Status When
creating Elicitation batch_69d86da686e4819097cbf3b1fc2d881d completed April 10, 2026, 3:25 a.m.
NER Named-entity recognition batch_69e1567ff9e48190b73cb101fc3f7b2b completed April 16, 2026, 9:37 p.m.
NED1 Entity disambiguation (via context triple) batch_69ffb05d1fb481909b42bea774a15c70 completed May 9, 2026, 10:08 p.m.
NEDg Description generation batch_69ffb0cfac808190b32bb25659603fb4 completed May 9, 2026, 10:10 p.m.
NED2 Entity disambiguation (via description) batch_69ffb15b987c8190ae9c96f15fc55b27 completed May 9, 2026, 10:12 p.m.
Created at: April 10, 2026, 4:52 a.m.