Triple

T9296983
Position Surface form Disambiguated ID Type / Status
Subject Diophantine geometry E223662 entity
Predicate fieldOfStudy P3 FINISHED
Object Diophantine equations E629500 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: Diophantine equations | Statement: [Diophantine geometry, fieldOfStudy, Diophantine equations]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Diophantine equations
Context triple: [Diophantine geometry, fieldOfStudy, Diophantine equations]
  • A. Diophantine equations chosen
    Diophantine equations are polynomial equations for which only integer or rational solutions are sought, forming a central and often notoriously difficult area of number theory.
  • B. Diophantine geometry
    Diophantine geometry is the branch of number theory that studies solutions to polynomial equations with integer or rational coefficients using geometric methods, particularly those from algebraic geometry.
  • C. Ramanujan–Nagell equation
    The Ramanujan–Nagell equation is a famous Diophantine equation in number theory that has only finitely many integer solutions and is closely associated with the work of Srinivasa Ramanujan.
  • D. Diophantine approximation
    Diophantine approximation is a branch of number theory that studies how closely real numbers can be approximated by rational numbers, often with quantitative bounds on the quality of approximation.
  • E. Erdős–Moser equation
    The Erdős–Moser equation is a famous unsolved Diophantine equation in number theory that asks whether 1^k + 2^k + ... + (m−1)^k = m^k has any integer solutions beyond the trivial case (k, m) = (1, 2).
  • 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_69ca8423edb08190bc0c91287a484768 completed March 30, 2026, 2:09 p.m.
NER Named-entity recognition batch_69cd089c9c588190967404c9eb938dfb completed April 1, 2026, 11:59 a.m.
NED1 Entity disambiguation (via context triple) batch_69d0b251c4148190a94fafdc23a601d6 completed April 4, 2026, 6:40 a.m.
Created at: March 30, 2026, 7:36 p.m.