Triple

T12596951
Position Surface form Disambiguated ID Type / Status
Subject Euler’s theorem E300757 entity
Predicate relatedTo P37 FINISHED
Object Chinese remainder theorem E530312 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: Chinese remainder theorem | Statement: [Euler’s theorem, relatedTo, Chinese remainder theorem]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Chinese remainder theorem
Context triple: [Euler’s theorem, relatedTo, Chinese remainder theorem]
  • A. Chinese remainder theorem chosen
    The Chinese remainder theorem is a fundamental result in number theory that provides conditions and a method for solving systems of simultaneous congruences with pairwise coprime moduli.
  • B. Fermat's little theorem
    Fermat's little theorem is a fundamental result in number theory that characterizes how prime numbers interact with integer powers modulo that prime, forming the basis for many modern cryptographic algorithms.
  • C. NTIC
    NTIC is the commonly used abbreviation for the National Telecommunications and Information Council, a governmental body focused on telecommunications and information policy.
  • D. Wilson's theorem
    Wilson's theorem is a result in number theory stating that a positive integer n > 1 is prime if and only if the factorial of (n − 1) is congruent to −1 modulo n.
  • E. quadratic reciprocity law
    The quadratic reciprocity law is a fundamental theorem in number theory that characterizes when a quadratic equation modulo one odd prime has solutions in terms of solvability modulo another, revealing a deep symmetry between primes.
  • 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_69d7bdea2ca881908f379526c13b1145 completed April 9, 2026, 2:55 p.m.
NER Named-entity recognition batch_69d954cf33b88190bff339fcd3142cc8 completed April 10, 2026, 7:51 p.m.
NED1 Entity disambiguation (via context triple) batch_69f65ec75fc08190aa13cbb0161eb35c completed May 2, 2026, 8:29 p.m.
Created at: April 9, 2026, 5:08 p.m.