Triple

T10389198
Position Surface form Disambiguated ID Type / Status
Subject Weil cohomology E244845 entity
Predicate hasAxiom P12252 FINISHED
Object Künneth formula 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 formula | Statement: [Weil cohomology, hasAxiom, Künneth formula]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Künneth formula
Context triple: [Weil cohomology, hasAxiom, Künneth formula]
  • A. 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.
  • B. Lefschetz duality
    Lefschetz duality is a generalization of Poincaré duality that relates the homology of a compact manifold with boundary to the cohomology of the manifold relative to its boundary.
  • 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. Grothendieck–Riemann–Roch theorem
    The Grothendieck–Riemann–Roch theorem is a fundamental result in algebraic geometry that generalizes the classical Riemann–Roch theorem by relating pushforwards in K-theory to pushforwards in cohomology via characteristic classes.
  • E. 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.
  • 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_69d381b5116081908d85227bab6d3c0c completed April 6, 2026, 9:49 a.m.
NER Named-entity recognition batch_69d4e9b40dd8819080ac839487020a44 completed April 7, 2026, 11:25 a.m.
NED1 Entity disambiguation (via context triple) batch_69d7fbae9a9c81908178fca68eb142b6 completed April 9, 2026, 7:19 p.m.
Created at: April 6, 2026, 12:05 p.m.