Triple

T13255923
Position Surface form Disambiguated ID Type / Status
Subject Paolo Ruffini E315656 entity
Predicate notableWork P4 FINISHED
Object Ruffini's rule for synthetic division E1030529 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: Ruffini's rule for synthetic division | Statement: [Paolo Ruffini, notableWork, Ruffini's rule for synthetic division]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Ruffini's rule for synthetic division
Context triple: [Paolo Ruffini, notableWork, Ruffini's rule for synthetic division]
  • A. Ruffini's rule for polynomial division chosen
    Ruffini's rule for polynomial division is a simplified algorithm for dividing polynomials by linear factors, often used as a shortcut form of synthetic division.
  • B. Euclidean algorithm for polynomials
    The Euclidean algorithm for polynomials is a procedure that repeatedly applies polynomial division to compute the greatest common divisor of two polynomials over a given field or ring.
  • C. Zassenhaus algorithm for factoring polynomials over the rationals
    The Zassenhaus algorithm for factoring polynomials over the rationals is a classical computational method that reduces rational polynomial factorization to modular factorization and then recombines the results using lifting techniques.
  • D. Berlekamp’s algorithm for factoring polynomials over finite fields
    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.
  • E. Cantor–Zassenhaus algorithm
    The Cantor–Zassenhaus algorithm is a probabilistic method used to factor polynomials over finite fields efficiently, widely employed in computational algebra and cryptography.
  • 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_69d806b1d9ac8190852c5571d5bd5f0f completed April 9, 2026, 8:06 p.m.
NER Named-entity recognition batch_69d98f7614fc8190a1cac076d706e9aa completed April 11, 2026, 12:01 a.m.
NED1 Entity disambiguation (via context triple) batch_69f716c90c5c8190a6de94b92db12210 completed May 3, 2026, 9:35 a.m.
Created at: April 9, 2026, 9:24 p.m.