Triple

T7648190
Position Surface form Disambiguated ID Type / Status
Subject Alexandrov–Čech cohomology E173178 entity
Predicate hasFeature P182 FINISHED
Object Mayer–Vietoris sequence E620669 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: Mayer–Vietoris sequence | Statement: [Alexandrov–Čech cohomology, hasFeature, Mayer–Vietoris sequence]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Mayer–Vietoris sequence
Context triple: [Alexandrov–Čech cohomology, hasFeature, Mayer–Vietoris sequence]
  • A. Mayer–Vietoris sequence in de Rham cohomology chosen
    The Mayer–Vietoris sequence in de Rham cohomology is a long exact sequence that computes the de Rham cohomology of a manifold by relating it to the cohomology of an open cover and their intersection.
  • B. Grothendieck spectral sequence
    The Grothendieck spectral sequence is a fundamental tool in homological algebra that relates the derived functors of a composite functor to the derived functors of its components, enabling efficient computation of cohomology.
  • C. Serre spectral sequence
    The Serre spectral sequence is a fundamental tool in algebraic topology that relates the homology or cohomology of a fibration to that of its base and fiber, enabling complex computations in a systematic way.
  • D. Atiyah–Hirzebruch spectral sequence
    The Atiyah–Hirzebruch spectral sequence is a fundamental computational tool in algebraic topology that relates generalized cohomology theories, such as K-theory, to ordinary cohomology, enabling the step-by-step calculation of these invariants from simpler data.
  • E. Eilenberg–Steenrod axioms
    The Eilenberg–Steenrod axioms are a foundational set of conditions that formally characterize homology theories in algebraic topology.
  • 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_69c6995473348190a4f41d110d619a18 completed March 27, 2026, 2:51 p.m.
NER Named-entity recognition batch_69c6faf6328c8190bce0a3f8a17ef890 completed March 27, 2026, 9:47 p.m.
NED1 Entity disambiguation (via context triple) batch_69c89ada2a54819098672d45ab56f784 completed March 29, 2026, 3:22 a.m.
Created at: March 27, 2026, 3:58 p.m.