Triple

T4927360
Position Surface form Disambiguated ID Type / Status
Subject Weierstrass substitution E110609 entity
Predicate alsoKnownAs P39 FINISHED
Object tangent half-angle substitution
Tangent half-angle substitution is a trigonometric technique that converts integrals involving sine and cosine into rational functions by substituting in terms of the tangent of half the angle.
E480875 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: tangent half-angle substitution | Statement: [Weierstrass substitution, alsoKnownAs, tangent half-angle substitution]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: tangent half-angle substitution
Context triple: [Weierstrass substitution, alsoKnownAs, tangent half-angle substitution]
  • A. Radau
    Radau is a river in Lower Saxony, Germany, known as a tributary of the Oker and for flowing through the Harz region.
  • B. Seča
    Seča is a small coastal settlement in southwestern Slovenia, situated near the town of Piran on the Adriatic Sea.
  • C. Tangen
    Tangen is a former settlement in Norway that was incorporated into the city of Drammen through a municipal merger.
  • D. Tangtse
    Tangtse is a village in the Leh district of Ladakh, India, situated along key routes between the Indus Valley and the Pangong Tso region in the Himalayas.
  • E. Trizina
    Trizina is a modern Greek settlement located near the ancient city of Troezen in the northeastern Peloponnese.
  • 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: tangent half-angle substitution
Triple: [Weierstrass substitution, alsoKnownAs, tangent half-angle substitution]
Generated description
Tangent half-angle substitution is a trigonometric technique that converts integrals involving sine and cosine into rational functions by substituting in terms of the tangent of half the angle.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: tangent half-angle substitution
Target entity description: Tangent half-angle substitution is a trigonometric technique that converts integrals involving sine and cosine into rational functions by substituting in terms of the tangent of half the angle.
  • A. Radau
    Radau is a river in Lower Saxony, Germany, known as a tributary of the Oker and for flowing through the Harz region.
  • B. Seča
    Seča is a small coastal settlement in southwestern Slovenia, situated near the town of Piran on the Adriatic Sea.
  • C. Tangen
    Tangen is a former settlement in Norway that was incorporated into the city of Drammen through a municipal merger.
  • D. Tangtse
    Tangtse is a village in the Leh district of Ladakh, India, situated along key routes between the Indus Valley and the Pangong Tso region in the Himalayas.
  • E. Trizina
    Trizina is a modern Greek settlement located near the ancient city of Troezen in the northeastern Peloponnese.
  • 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_69bd4415190c8190817bee7ec9f9f944 completed March 20, 2026, 12:56 p.m.
NER Named-entity recognition batch_69bd7036d8e88190bc4be2975160da23 completed March 20, 2026, 4:05 p.m.
NED1 Entity disambiguation (via context triple) batch_69be77ac88148190a51fa2e9085d6897 completed March 21, 2026, 10:49 a.m.
NEDg Description generation batch_69be7847a378819081687ec783a8b862 completed March 21, 2026, 10:51 a.m.
NED2 Entity disambiguation (via description) batch_69be7915a26c81909b21a128daebf5b3 completed March 21, 2026, 10:55 a.m.
Created at: March 20, 2026, 1:30 p.m.