Triple

T7871957
Position Surface form Disambiguated ID Type / Status
Subject Jacobi’s four-square theorem E182757 entity
Predicate refines P6555 FINISHED
Object Lagrange’s four-square theorem E156185 NE FINISHED

How this triple was built (2 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: Lagrange’s four-square theorem | Statement: [Jacobi’s four-square theorem, refines, Lagrange’s four-square theorem]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Lagrange’s four-square theorem
Context triple: [Jacobi’s four-square theorem, refines, Lagrange’s four-square theorem]
  • A. Lagrange's four-square theorem chosen
    Lagrange's four-square theorem is a fundamental result in number theory stating that every natural number can be expressed as the sum of four integer squares.
  • B. Jacobi’s four-square theorem
    Jacobi’s four-square theorem is a fundamental result in number theory that gives a precise formula for the number of ways an integer can be expressed as a sum of four squares.
  • C. 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.
  • D. 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.
  • E. 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.
  • F. None of above.
  • G. Unsure - the case is ambiguous/there is not enough information to decide.

Provenance (3 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_69ca82894d9081908a832bfce71a4714 completed March 30, 2026, 2:02 p.m.
NER Named-entity recognition batch_69cb39a5950481908399211c5dfe2569 completed March 31, 2026, 3:04 a.m.
NED1 Entity disambiguation (via context triple) batch_69cb5b6bc7248190adbf4377c52e16a9 completed March 31, 2026, 5:28 a.m.
Created at: March 30, 2026, 4:56 p.m.