Triple

T3780962
Position Surface form Disambiguated ID Type / Status
Subject Ulam problem in set theory E85414 entity
Predicate relatedTo P37 FINISHED
Object Ulam stability E85413 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: Ulam stability | Statement: [Ulam problem in set theory, relatedTo, Ulam stability]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Ulam stability
Context triple: [Ulam problem in set theory, relatedTo, Ulam stability]
  • A. Ulam stability chosen
    Ulam stability is a concept in the theory of functional equations that studies when approximate solutions imply the existence of exact solutions nearby, forming the basis of what is now called Hyers–Ulam stability.
  • B. Lyapunov stability theory
    Lyapunov stability theory is a fundamental framework in dynamical systems and control theory that uses energy-like functions to assess the stability of equilibrium points without explicitly solving differential equations.
  • C. Lyapunov inequality
    The Lyapunov inequality is a fundamental result in stability theory and analysis that provides bounds relating norms or moments of functions or solutions to differential equations, widely used in studying the stability of dynamical systems.
  • D. Ulam sequence
    The Ulam sequence is an integer sequence starting with 1 and 2 in which each subsequent term is the smallest integer that can be written uniquely as the sum of two distinct earlier terms.
  • E. Routh–Hurwitz stability criterion
    The Routh–Hurwitz stability criterion is a mathematical test in control theory that determines whether all roots of a system’s characteristic polynomial lie in the left half of the complex plane, ensuring system stability without explicitly computing the roots.
  • 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_69aed937fa8881908208ef3801060826 completed March 9, 2026, 2:29 p.m.
NER Named-entity recognition batch_69aee3d98b38819094df9569b549124f completed March 9, 2026, 3:14 p.m.
NED1 Entity disambiguation (via context triple) batch_69b4fb19229c8190a6f0ee4ae7f52dab completed March 14, 2026, 6:07 a.m.
Created at: March 9, 2026, 3:12 p.m.