Triple

T22329102
Position Surface form Disambiguated ID Type / Status
Subject de Rham cohomology E551975 entity
Predicate relatedConcept P37 FINISHED
Object Mayer–Vietoris sequence NE NERFINISHED

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: [de Rham cohomology, relatedConcept, Mayer–Vietoris sequence]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Mayer–Vietoris sequence
Context triple: [de Rham cohomology, relatedConcept, 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. Cartan–Eilenberg spectral sequence
    The Cartan–Eilenberg spectral sequence is a fundamental tool in homological algebra that computes derived functors (such as Ext and Tor) of composite functors via a double complex construction.
  • E. Alexander–Spanier cohomology
    Alexander–Spanier cohomology is a cohomology theory in algebraic topology defined using cochains on all finite subsets of a space, notable for its generality and close relationship to Čech and singular cohomology.
  • F. None of above.
  • G. Unsure - the case is ambiguous/there is not enough information to decide.

Provenance (2 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_69e11e482f788190b78d1588fc26d606 completed April 16, 2026, 5:37 p.m.
NER Named-entity recognition batch_69f1576ab52c819087563cd778d6bc5e completed April 29, 2026, 12:57 a.m.
Created at: April 16, 2026, 8:43 p.m.