Triple

T16876440
Position Surface form Disambiguated ID Type / Status
Subject Finite Operator Calculus E421310 entity
Predicate hasKeyResult P70725 FINISHED
Object classification of polynomial sequences of binomial type via delta operators E421310 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: classification of polynomial sequences of binomial type via delta operators | Statement: [Finite Operator Calculus, hasKeyResult, classification of polynomial sequences of binomial type via delta operators]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: classification of polynomial sequences of binomial type via delta operators
Context triple: [Finite Operator Calculus, hasKeyResult, classification of polynomial sequences of binomial type via delta operators]
  • A. Bernoulli polynomials
    Bernoulli polynomials are a sequence of polynomials deeply connected to number theory and analysis, appearing in the study of special functions, series expansions, and the evaluation of sums of powers of integers.
  • B. Jack polynomials
    Jack polynomials are a family of symmetric polynomials depending on a continuous parameter that generalize several classical symmetric functions and play a key role in algebraic combinatorics, representation theory, and mathematical physics.
  • C. Askey scheme of hypergeometric orthogonal polynomials
    The Askey scheme of hypergeometric orthogonal polynomials is a hierarchical classification of families of (basic) hypergeometric orthogonal polynomials, organized by limit relations between them.
  • D. Bernstein polynomials
    Bernstein polynomials are a family of polynomials used in approximation theory that provide a constructive proof of the Weierstrass approximation theorem by uniformly approximating continuous functions on a closed interval.
  • E. Finite Operator Calculus chosen
    Finite Operator Calculus is a mathematical framework, developed and popularized by Gian-Carlo Rota, that systematically studies sequences of polynomials and discrete analogues of differential operators using algebraic and combinatorial methods.
  • 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_69d889d470fc8190b4aec199636c0c56 completed April 10, 2026, 5:25 a.m.
NER Named-entity recognition batch_69e3b7f704a081909921d00b3c470472 completed April 18, 2026, 4:57 p.m.
NED1 Entity disambiguation (via context triple) batch_6a00c2b4abd08190841c5bb0b0eaa177 completed May 10, 2026, 5:39 p.m.
Created at: April 10, 2026, 5:29 a.m.