Triple

T2111241
Position Surface form Disambiguated ID Type / Status
Subject Hilbert’s Nullstellensatz E42506 entity
Predicate concerns P1256 FINISHED
Object Zariski topology E159881 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: Zariski topology | Statement: [Hilbert’s Nullstellensatz, concerns, Zariski topology]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Zariski topology
Context triple: [Hilbert’s Nullstellensatz, concerns, Zariski topology]
  • A. Zariski topology chosen
    The Zariski topology is a fundamental topology in algebraic geometry, defined on the spectrum of a ring or an algebraic variety, whose closed sets correspond to solution sets of polynomial equations.
  • B. Noetherian space
    A Noetherian space is a topological space in which every descending chain of closed subsets stabilizes, mirroring the finiteness conditions of Noetherian rings in algebra.
  • C. 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.
  • D. Krull dimension
    Krull dimension is a fundamental invariant in commutative algebra that measures the "size" of a ring by the maximum length of chains of its prime ideals.
  • E. Noetherian rings
    Noetherian rings are a fundamental class of rings in commutative algebra characterized by the property that every ascending chain of ideals stabilizes, ensuring that all ideals are finitely generated.
  • 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_69a8871040f08190aac2e2d0ab6b47ad completed March 4, 2026, 7:25 p.m.
NER Named-entity recognition batch_69abbb024ce88190a30e1320e53b82bc completed March 7, 2026, 5:43 a.m.
NED1 Entity disambiguation (via context triple) batch_69ae30721e1c8190869d577f58015141 completed March 9, 2026, 2:29 a.m.
Created at: March 4, 2026, 7:43 p.m.