Triple

T7997814
Position Surface form Disambiguated ID Type / Status
Subject Noether’s AF+BG theorem E186169 entity
Predicate relatedTo P37 FINISHED
Object Noether’s normalization lemma E29377 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: Noether’s normalization lemma | Statement: [Noether’s AF+BG theorem, relatedTo, Noether’s normalization lemma]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Noether’s normalization lemma
Context triple: [Noether’s AF+BG theorem, relatedTo, Noether’s normalization lemma]
  • A. Noether normalization lemma chosen
    The Noether normalization lemma is a fundamental result in commutative algebra and algebraic geometry that shows any finitely generated algebra over a field can be made integral over a polynomial subring, providing a way to relate complicated varieties to affine space.
  • B. 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.
  • C. Lasker–Noether theorem on primary decomposition
    The Lasker–Noether theorem on primary decomposition is a fundamental result in commutative algebra stating that every ideal in a Noetherian ring can be expressed as a finite intersection of primary ideals, generalizing the factorization of integers into prime powers.
  • D. Hilbert basis theorem
    The Hilbert basis theorem is a fundamental result in commutative algebra stating that if a ring is Noetherian then any polynomial ring over it is also Noetherian, ensuring that ideals in such rings are finitely generated.
  • E. 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.
  • 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_69ca829c6c308190ab05b43d234c52b2 completed March 30, 2026, 2:03 p.m.
NER Named-entity recognition batch_69cb3c98e39081908904d36a31bd6768 completed March 31, 2026, 3:16 a.m.
NED1 Entity disambiguation (via context triple) batch_69cbe10d5eb081909f257390094de442 completed March 31, 2026, 2:58 p.m.
Created at: March 30, 2026, 5:17 p.m.