Triple

T10855521
Position Surface form Disambiguated ID Type / Status
Subject Serre spectral sequence E256258 entity
Predicate alternativeName P39 FINISHED
Object Leray–Serre spectral sequence E256258 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: Leray–Serre spectral sequence | Statement: [Serre spectral sequence, alternativeName, Leray–Serre spectral sequence]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Leray–Serre spectral sequence
Context triple: [Serre spectral sequence, alternativeName, Leray–Serre spectral sequence]
  • A. Serre spectral sequence chosen
    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.
  • 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. 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.
  • 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. Mayer–Vietoris sequence in de Rham cohomology
    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.
  • 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_69d6aa83d1448190a66d93c32394d21f completed April 8, 2026, 7:20 p.m.
NER Named-entity recognition batch_69d75135df24819090ce43afa3ea9b38 completed April 9, 2026, 7:11 a.m.
NED1 Entity disambiguation (via context triple) batch_69dff7d0403c8190bc0b92197a25d3ee completed April 15, 2026, 8:40 p.m.
Created at: April 8, 2026, 9:20 p.m.