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.