Triple

T5633996
Position Surface form Disambiguated ID Type / Status
Subject Fermat polygonal number theorem E147900 entity
Predicate specialCase P7025 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: [Fermat polygonal number theorem, specialCase, 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: [Fermat polygonal number theorem, specialCase, 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. 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. 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.
  • E. Waring's problem
    Waring's problem is a famous conjecture in number theory that concerns representing natural numbers as sums of fixed powers of integers and determining how many such powers are needed.
  • 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_69c00907bc8881909ed760d3ed73ef35 completed March 22, 2026, 3:21 p.m.
NER Named-entity recognition batch_69c0226118548190877793dadf6cacba completed March 22, 2026, 5:09 p.m.
NED1 Entity disambiguation (via context triple) batch_69c04d6d2dfc8190a2eabb8beda04ee5 completed March 22, 2026, 8:13 p.m.
Created at: March 22, 2026, 3:41 p.m.