Triple

T22965007
Position Surface form Disambiguated ID Type / Status
Subject Bombieri–Pila determinant method E571014 entity
Predicate relatedTo P37 FINISHED
Object determinant method of Heath-Brown — NE NERFINISHED

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: determinant method of Heath-Brown | Statement: [Bombieri–Pila determinant method, relatedTo, determinant method of Heath-Brown]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: determinant method of Heath-Brown
Context triple: [Bombieri–Pila determinant method, relatedTo, determinant method of Heath-Brown]
  • A. Hurwitz determinants
    Hurwitz determinants are specific determinants constructed from a polynomial’s coefficients that are used to test whether all roots of the polynomial lie in the left half of the complex plane, thereby assessing system stability.
  • B. Hardy–Littlewood circle method
    The Hardy–Littlewood circle method is a powerful analytic number theory technique that uses complex analysis and Fourier series to study additive problems such as Waring’s problem and the Goldbach conjecture.
  • C. Bombieri–Pila determinant method chosen
    The Bombieri–Pila determinant method is a technique in analytic and Diophantine geometry used to obtain upper bounds on the number of rational or integral points of bounded height lying on algebraic curves or more general sets.
  • D. Sylvester determinant
    The Sylvester determinant is a mathematical construct introduced by James Joseph Sylvester, typically referring to a determinant associated with resultants and elimination theory in algebra.
  • E. van der Corput method for estimating exponential sums
    The van der Corput method for estimating exponential sums is a classical analytic number theory technique that provides bounds for oscillatory sums by exploiting differencing and smoothness properties of the phase function.
  • F. None of above.
  • G. Unsure - the case is ambiguous/there is not enough information to decide.

Provenance (2 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_69e245b212a88190b5259caf51606084 completed April 17, 2026, 2:37 p.m.
NER Named-entity recognition batch_69f181f763688190aab8f444a1a71577 completed April 29, 2026, 3:58 a.m.
Created at: April 17, 2026, 3:47 p.m.