Triple

T4996541
Position Surface form Disambiguated ID Type / Status
Subject Weierstrass preparation theorem E112259 entity
Predicate hasVariant P455 FINISHED
Object Weierstrass preparation over complete local rings E112259 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: Weierstrass preparation over complete local rings | Statement: [Weierstrass preparation theorem, hasVariant, Weierstrass preparation over complete local rings]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Weierstrass preparation over complete local rings
Context triple: [Weierstrass preparation theorem, hasVariant, Weierstrass preparation over complete local rings]
  • A. Weierstrass preparation theorem chosen
    The Weierstrass preparation theorem is a fundamental result in complex analysis and analytic geometry that locally expresses analytic functions near a zero as a product of a polynomial and a unit, enabling a power-series analogue of factorization.
  • B. Singular Points of Complex Hypersurfaces
    "Singular Points of Complex Hypersurfaces" is a foundational monograph in singularity theory that systematically studies the local and topological properties of singularities arising in complex algebraic and analytic hypersurfaces.
  • 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. Hilbert’s fourteenth problem
    Hilbert’s fourteenth problem is one of David Hilbert’s famous list of 23 problems, concerning the finite generation of certain algebras of invariants in algebraic geometry and invariant theory.
  • E. Hasse–Arf theorem
    The Hasse–Arf theorem is a fundamental result in algebraic number theory that precisely characterizes the jumps in the ramification filtration of abelian extensions of local fields, showing they occur at integer values.
  • 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_69bd4432b32c81909f3b3c6bd10f0653 completed March 20, 2026, 12:57 p.m.
NER Named-entity recognition batch_69bd72a130708190b9bc1393ba78bfb1 completed March 20, 2026, 4:15 p.m.
NED1 Entity disambiguation (via context triple) batch_69be8a3489f08190a338de8d8be09813 completed March 21, 2026, 12:08 p.m.
Created at: March 20, 2026, 1:34 p.m.