Triple

T11085989
Position Surface form Disambiguated ID Type / Status
Subject Lefschetz fixed-point theorem E262120 entity
Predicate hasExtension P455 FINISHED
Object Lefschetz fixed-point theorem in sheaf cohomology E262120 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: Lefschetz fixed-point theorem in sheaf cohomology | Statement: [Lefschetz fixed-point theorem, hasExtension, Lefschetz fixed-point theorem in sheaf cohomology]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Lefschetz fixed-point theorem in sheaf cohomology
Context triple: [Lefschetz fixed-point theorem, hasExtension, Lefschetz fixed-point theorem in sheaf cohomology]
  • A. 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.
  • B. 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.
  • C. Grothendieck–Lefschetz trace formula
    The Grothendieck–Lefschetz trace formula is a fundamental result in algebraic geometry that expresses the number of rational points of a variety over a finite field in terms of traces of Frobenius acting on its étale cohomology groups.
  • D. Serre’s cohomological methods in algebraic geometry
    Serre’s cohomological methods in algebraic geometry are foundational techniques that use sheaf cohomology to relate and study algebraic and analytic geometry, profoundly influencing modern algebraic geometry and complex geometry.
  • E. Lefschetz hyperplane theorem
    The Lefschetz hyperplane theorem is a fundamental result in algebraic geometry and topology that relates the topology (especially homology and homotopy groups) of a smooth projective variety to that of its hyperplane sections.
  • 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_69d6aa9983c08190b0ef61603b69feac completed April 8, 2026, 7:20 p.m.
NER Named-entity recognition batch_69d799c3ed9c8190a3f5cdf1fe0e74a2 completed April 9, 2026, 12:21 p.m.
NED1 Entity disambiguation (via context triple) batch_69e42d66ded88190877a20a10f012d6b completed April 19, 2026, 1:18 a.m.
Created at: April 8, 2026, 9:27 p.m.