Triple

T13444152
Position Surface form Disambiguated ID Type / Status
Subject Kolmogorov continuity theorem E320436 entity
Predicate alsoKnownAs P39 FINISHED
Object Kolmogorov–Chentsov continuity theorem E320436 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: Kolmogorov–Chentsov continuity theorem | Statement: [Kolmogorov continuity theorem, alsoKnownAs, Kolmogorov–Chentsov continuity theorem]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Kolmogorov–Chentsov continuity theorem
Context triple: [Kolmogorov continuity theorem, alsoKnownAs, Kolmogorov–Chentsov continuity theorem]
  • A. Kolmogorov continuity theorem chosen
    The Kolmogorov continuity theorem is a fundamental result in probability theory that provides conditions under which a stochastic process admits a modification with continuous (or Hölder-continuous) sample paths.
  • B. Cameron–Martin theorem
    The Cameron–Martin theorem is a fundamental result in probability theory and functional analysis that characterizes how Gaussian measures on infinite-dimensional spaces change under shifts by elements of a special Hilbert subspace (the Cameron–Martin space).
  • C. Lyons' rough path theory
    Lyons' rough path theory is a mathematical framework that extends classical calculus to analyze and solve differential equations driven by highly irregular signals, such as paths with low regularity or stochastic processes like Brownian motion.
  • D. Kolmogorov extension theorem
    The Kolmogorov extension theorem is a fundamental result in probability theory that guarantees the existence of a stochastic process with given consistent finite-dimensional distributions.
  • E. Lévy’s continuity theorem
    Lévy’s continuity theorem is a fundamental result in probability theory that characterizes convergence in distribution of random variables via pointwise convergence of their characteristic functions.
  • 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_69d80761e6cc8190a90c844589998ecc completed April 9, 2026, 8:09 p.m.
NER Named-entity recognition batch_69dbaee881888190811ddf01bc699864 completed April 12, 2026, 2:40 p.m.
NED1 Entity disambiguation (via context triple) batch_69f7547b484c8190881e869b3a722e89 completed May 3, 2026, 1:58 p.m.
Created at: April 9, 2026, 9:40 p.m.