Triple

T5425553
Position Surface form Disambiguated ID Type / Status
Subject Pythagorean theorem E121353 entity
Predicate generalizedBy P2372 FINISHED
Object Pythagorean identity in trigonometry
The Pythagorean identity in trigonometry is a fundamental relation among sine and cosine functions, stating that for any angle θ, sin²θ + cos²θ = 1.
E518471 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: Pythagorean identity in trigonometry | Statement: [Pythagorean theorem, generalizedBy, Pythagorean identity in trigonometry]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Pythagorean identity in trigonometry
Context triple: [Pythagorean theorem, generalizedBy, Pythagorean identity in trigonometry]
  • A. Pythagorean theorem
    The Pythagorean theorem is a fundamental principle of geometry stating that in a right-angled triangle, the square of the hypotenuse equals the sum of the squares of the other two sides.
  • B. Sine
    Sine was a precolonial Serer kingdom in what is now Senegal, known for its rich Serer culture, religious traditions, and resistance to Islamic and later French expansion.
  • C. Trigonometry and Double Algebra
    "Trigonometry and Double Algebra" is a 19th-century mathematical treatise by Augustus De Morgan that develops trigonometric theory alongside an early systematic treatment of complex numbers and symbolic algebra.
  • D. Trigon
    Trigon is a powerful demonic supervillain in the Teen Titans universe, best known as Raven’s tyrannical father and a major cosmic threat.
  • E. Thales’ theorem
    Thales’ theorem is a fundamental result in Euclidean geometry stating that any angle inscribed in a semicircle is a right angle.
  • 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: Pythagorean identity in trigonometry
Triple: [Pythagorean theorem, generalizedBy, Pythagorean identity in trigonometry]
Generated description
The Pythagorean identity in trigonometry is a fundamental relation among sine and cosine functions, stating that for any angle θ, sin²θ + cos²θ = 1.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Pythagorean identity in trigonometry
Target entity description: The Pythagorean identity in trigonometry is a fundamental relation among sine and cosine functions, stating that for any angle θ, sin²θ + cos²θ = 1.
  • A. Pythagorean theorem
    The Pythagorean theorem is a fundamental principle of geometry stating that in a right-angled triangle, the square of the hypotenuse equals the sum of the squares of the other two sides.
  • B. Sine
    Sine was a precolonial Serer kingdom in what is now Senegal, known for its rich Serer culture, religious traditions, and resistance to Islamic and later French expansion.
  • C. Trigonometry and Double Algebra
    "Trigonometry and Double Algebra" is a 19th-century mathematical treatise by Augustus De Morgan that develops trigonometric theory alongside an early systematic treatment of complex numbers and symbolic algebra.
  • D. Trigon
    Trigon is a powerful demonic supervillain in the Teen Titans universe, best known as Raven’s tyrannical father and a major cosmic threat.
  • E. Thales’ theorem
    Thales’ theorem is a fundamental result in Euclidean geometry stating that any angle inscribed in a semicircle is a right angle.
  • 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_69bd463b58d88190b258261573de9e91 completed March 20, 2026, 1:06 p.m.
NER Named-entity recognition batch_69bd881598448190a9bb456dee36004b completed March 20, 2026, 5:47 p.m.
NED1 Entity disambiguation (via context triple) batch_69bf3abfc7e88190b8f0a31b61c33973 completed March 22, 2026, 12:41 a.m.
NEDg Description generation batch_69bf3b592a08819090e2873bcf4e797f completed March 22, 2026, 12:44 a.m.
NED2 Entity disambiguation (via description) batch_69bf3c0b9e5481909101eccbd55f24b2 completed March 22, 2026, 12:47 a.m.
Created at: March 20, 2026, 2:06 p.m.