Triple

T14704228
Position Surface form Disambiguated ID Type / Status
Subject Émile Borel E345382 entity
Predicate notableWork P4 FINISHED
Object Borel’s normal number theorem E824093 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: Borel’s normal number theorem | Statement: [Émile Borel, notableWork, Borel’s normal number theorem]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Borel’s normal number theorem
Context triple: [Émile Borel, notableWork, Borel’s normal number theorem]
  • A. Khinchin's representation theorem
    Khinchin's representation theorem is a result in probability theory that characterizes stationary stochastic processes by representing them in terms of simpler, more fundamental random components.
  • B. Liouville numbers
    Liouville numbers are real numbers that can be approximated extremely closely by rationals, making them a classic example of transcendental numbers in number theory.
  • C. theory of uniform distribution modulo 1 chosen
    The theory of uniform distribution modulo 1 is a branch of number theory that studies how sequences of real numbers distribute their fractional parts evenly in the unit interval.
  • D. Khintchine theorem
    Khintchine theorem is a fundamental result in metric Diophantine approximation that characterizes, via a simple convergence–divergence criterion, when almost all real numbers admit infinitely many rational approximations of a prescribed quality.
  • E. Khinchin's law of the iterated logarithm
    Khinchin's law of the iterated logarithm is a fundamental result in probability theory that precisely characterizes the almost-sure fluctuations of partial sums of independent random variables on the scale of the square root of twice the product of their variance and the iterated logarithm of the sample size.
  • 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_69d822e4a8c08190a155df736bb7bc13 completed April 9, 2026, 10:06 p.m.
NER Named-entity recognition batch_69deb6071e5c8190bb5509c859135c2d completed April 14, 2026, 9:47 p.m.
NED1 Entity disambiguation (via context triple) batch_69fdf087ce8c819081a7186df67bcf1f completed May 8, 2026, 2:17 p.m.
Created at: April 10, 2026, 1:28 a.m.