Triple

T10389201
Position Surface form Disambiguated ID Type / Status
Subject Weil cohomology E244845 entity
Predicate hasAxiom P12252 FINISHED
Object Lefschetz trace formula E262120 NE FINISHED

Named-entity recognition

Before disambiguation, gpt-5-mini classified whether the object phrase is a named entity — the step behind the object's NE type shown above.

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: Lefschetz trace formula | Statement: [Weil cohomology, hasAxiom, Lefschetz trace formula]

Disambiguation candidates (1 decision)

The exact options the model was shown at each disambiguation step, with the option it chose highlighted — the evidence behind this triple's disambiguated ids.

NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Lefschetz trace formula
Context triple: [Weil cohomology, hasAxiom, Lefschetz trace formula]
  • A. Grothendieck–Ogg–Shafarevich formula
    The Grothendieck–Ogg–Shafarevich formula is a result in arithmetic geometry that relates the Euler characteristic of an ℓ-adic sheaf on a curve over a finite field to local invariants such as conductors and ramification data.
  • B. Lefschetz fixed-point theorem chosen
    The Lefschetz fixed-point theorem is a fundamental result in algebraic topology that relates the number of fixed points of a continuous map on a topological space to traces of the induced maps on its homology groups.
  • C. Weil conjectures
    The Weil conjectures are a set of deep statements about the zeta functions of algebraic varieties over finite fields that guided the development of modern algebraic geometry and were ultimately proved using étale cohomology.
  • 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. Atiyah–Bott fixed-point theorem
    The Atiyah–Bott fixed-point theorem is a fundamental result in equivariant cohomology that expresses global invariants, such as indices of elliptic operators, in terms of local data at the fixed points of a group action.
  • F. None of above.
  • G. Unsure - the case is ambiguous/there is not enough information to decide.

Provenance (3 batches)

Stage Batch ID Job type Status
creating batch_69d381b5116081908d85227bab6d3c0c elicitation completed
NER batch_69d4e9b40dd8819080ac839487020a44 ner completed
NED1 batch_69d7fbae9a9c81908178fca68eb142b6 ned_source_triple completed
Created at: April 6, 2026, 12:05 p.m.