Triple

T8143144
Position Surface form Disambiguated ID Type / Status
Subject Speusippus E190143 entity
Predicate notableWork P4 FINISHED
Object On Pythagorean Numbers
On Pythagorean Numbers is a lost philosophical work by the ancient Greek philosopher Speusippus that explored numerical doctrines associated with Pythagorean thought.
E712305 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: On Pythagorean Numbers | Statement: [Speusippus, notableWork, On Pythagorean Numbers]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: On Pythagorean Numbers
Context triple: [Speusippus, notableWork, On Pythagorean Numbers]
  • A. Fermat polygonal number theorem
    The Fermat polygonal number theorem is a result in number theory stating that every positive integer can be expressed as a sum of a fixed number of polygonal numbers of a given order.
  • B. Three Pearls of Number Theory
    Three Pearls of Number Theory is a classic mathematical text that presents three elegant and accessible problems in number theory, illustrating deep ideas through simple, beautifully explained examples.
  • C. Fermat's theorem on sums of two squares
    Fermat's theorem on sums of two squares is a result in number theory stating exactly which prime numbers (and, more generally, which integers) can be expressed as the sum of two perfect squares.
  • D. Legendre's three-square theorem
    Legendre's three-square theorem is a result in number theory that characterizes exactly which positive integers can be expressed as the sum of three squares of integers.
  • E. Pythagorean triples
    Pythagorean triples are sets of three positive integers that satisfy the Pythagorean theorem, representing the side lengths of right-angled triangles.
  • 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: On Pythagorean Numbers
Triple: [Speusippus, notableWork, On Pythagorean Numbers]
Generated description
On Pythagorean Numbers is a lost philosophical work by the ancient Greek philosopher Speusippus that explored numerical doctrines associated with Pythagorean thought.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: On Pythagorean Numbers
Target entity description: On Pythagorean Numbers is a lost philosophical work by the ancient Greek philosopher Speusippus that explored numerical doctrines associated with Pythagorean thought.
  • A. Fermat polygonal number theorem
    The Fermat polygonal number theorem is a result in number theory stating that every positive integer can be expressed as a sum of a fixed number of polygonal numbers of a given order.
  • B. Three Pearls of Number Theory
    Three Pearls of Number Theory is a classic mathematical text that presents three elegant and accessible problems in number theory, illustrating deep ideas through simple, beautifully explained examples.
  • C. Fermat's theorem on sums of two squares
    Fermat's theorem on sums of two squares is a result in number theory stating exactly which prime numbers (and, more generally, which integers) can be expressed as the sum of two perfect squares.
  • D. Legendre's three-square theorem
    Legendre's three-square theorem is a result in number theory that characterizes exactly which positive integers can be expressed as the sum of three squares of integers.
  • E. Pythagorean triples
    Pythagorean triples are sets of three positive integers that satisfy the Pythagorean theorem, representing the side lengths of right-angled triangles.
  • 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_69ca82bd9900819099477cdc2eb4244f completed March 30, 2026, 2:03 p.m.
NER Named-entity recognition batch_69cb4444bb248190beaaa2ce4b8f3eaa completed March 31, 2026, 3:49 a.m.
NED1 Entity disambiguation (via context triple) batch_69cc94a9ecd08190a029a8d76d9f3bb1 completed April 1, 2026, 3:44 a.m.
NEDg Description generation batch_69cc95c228c08190a603c1dff44ff299 completed April 1, 2026, 3:49 a.m.
NED2 Entity disambiguation (via description) batch_69cc96b02d38819085eb51c1943b3045 completed April 1, 2026, 3:53 a.m.
Created at: March 30, 2026, 5:36 p.m.