Triple

T9297104
Position Surface form Disambiguated ID Type / Status
Subject Castelnuovo–Mumford regularity E223664 entity
Predicate relatedTo P37 FINISHED
Object Mumford’s theorem on regularity E223664 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: Mumford’s theorem on regularity | Statement: [Castelnuovo–Mumford regularity, relatedTo, Mumford’s theorem on regularity]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Mumford’s theorem on regularity
Context triple: [Castelnuovo–Mumford regularity, relatedTo, Mumford’s theorem on regularity]
  • A. Castelnuovo–Mumford regularity chosen
    Castelnuovo–Mumford regularity is an invariant in commutative algebra and algebraic geometry that measures the complexity of the minimal graded free resolution of a module or sheaf, often used to control vanishing of cohomology and bounds on generators.
  • B. Chevalley’s theorem in algebraic geometry
    Chevalley’s theorem in algebraic geometry is a fundamental result stating that the image of a morphism of finite type between schemes (or varieties) is a constructible set, playing a key role in understanding how geometric properties behave under mappings.
  • C. Hilbert’s syzygy theorem
    Hilbert’s syzygy theorem is a fundamental result in commutative algebra that describes the finite length and structure of free resolutions of modules over polynomial rings.
  • D. 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.
  • E. 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.
  • 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_69ca8423edb08190bc0c91287a484768 completed March 30, 2026, 2:09 p.m.
NER Named-entity recognition batch_69cd089e3ae88190aa4181cdd85a67b8 completed April 1, 2026, 11:59 a.m.
NED1 Entity disambiguation (via context triple) batch_69d0b251c4148190a94fafdc23a601d6 completed April 4, 2026, 6:40 a.m.
Created at: March 30, 2026, 7:36 p.m.