Triple

T10829400
Position Surface form Disambiguated ID Type / Status
Subject Atiyah–Hirzebruch spectral sequence E255575 entity
Predicate relatedConcept P37 FINISHED
Object Künneth theorem in generalized cohomology E860097 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: Künneth theorem in generalized cohomology | Statement: [Atiyah–Hirzebruch spectral sequence, relatedConcept, Künneth theorem in generalized cohomology]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Künneth theorem in generalized cohomology
Context triple: [Atiyah–Hirzebruch spectral sequence, relatedConcept, Künneth theorem in generalized cohomology]
  • A. 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.
  • B. Künneth formula chosen
    The Künneth formula is a fundamental result in algebraic topology and homological algebra that expresses the (co)homology of a product space or object in terms of the (co)homology of its factors.
  • C. Thom cobordism theory
    Thom cobordism theory is a foundational branch of algebraic topology developed by René Thom that classifies manifolds up to cobordism using homotopy-theoretic and characteristic class methods.
  • D. Eilenberg–MacLane spaces
    Eilenberg–MacLane spaces are topological spaces characterized by having a single nontrivial homotopy group, serving as fundamental building blocks in homotopy theory and the definition of cohomology.
  • 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 (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_69d6aa8081448190a9324184f2bd1c26 completed April 8, 2026, 7:20 p.m.
NER Named-entity recognition batch_69d74420fa188190b5b3c59e1a9f551d completed April 9, 2026, 6:16 a.m.
NED1 Entity disambiguation (via context triple) batch_69de85a068b08190948c3ca32cdda147 completed April 14, 2026, 6:21 p.m.
Created at: April 8, 2026, 9:19 p.m.