Triple

T1451912
Position Surface form Disambiguated ID Type / Status
Subject Elwyn R. Berlekamp E31309 entity
Predicate knownFor P22 FINISHED
Object Berlekamp’s algorithm for factoring polynomials over finite fields E165811 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: Berlekamp’s algorithm for factoring polynomials over finite fields | Statement: [Elwyn R. Berlekamp, knownFor, Berlekamp’s algorithm for factoring polynomials over finite fields]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Berlekamp’s algorithm for factoring polynomials over finite fields
Context triple: [Elwyn R. Berlekamp, knownFor, Berlekamp’s algorithm for factoring polynomials over finite fields]
  • A. Berlekamp’s algorithm for factoring polynomials over finite fields chosen
    Berlekamp’s algorithm for factoring polynomials over finite fields is a foundational deterministic method in computational algebra that efficiently decomposes polynomials into irreducible factors over finite fields and underpins many modern algorithms in coding theory and cryptography.
  • B. Gauss’s lemma in number theory
    Gauss’s lemma in number theory is a result that relates the Legendre symbol to the number of sign changes in a certain sequence of multiples, providing a practical criterion for determining quadratic residues modulo an odd prime.
  • C. Blum–Blum–Shub pseudorandom number generator
    The Blum–Blum–Shub pseudorandom number generator is a cryptographically secure generator based on the hardness of factoring large composite numbers, widely studied in theoretical computer science and cryptography.
  • D. Hilbert’s irreducibility theorem
    Hilbert’s irreducibility theorem is a fundamental result in number theory and algebraic geometry that ensures many polynomial equations with parameterized coefficients retain irreducibility for infinitely many specializations of those parameters.
  • E. Hilbert’s Nullstellensatz
    Hilbert’s Nullstellensatz is a foundational theorem in algebraic geometry that establishes a deep correspondence between ideals in polynomial rings and algebraic sets, linking algebra and geometry.
  • 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_69a499171a28819085b993a3ac78e363 completed March 1, 2026, 7:52 p.m.
NER Named-entity recognition batch_69a4c57d34cc8190801b769d9d9b2e2e completed March 1, 2026, 11:02 p.m.
NED1 Entity disambiguation (via context triple) batch_69ad0e71ffd481909dfd0f77201dc17c completed March 8, 2026, 5:51 a.m.
Created at: March 1, 2026, 8 p.m.