Triple

T11085977
Position Surface form Disambiguated ID Type / Status
Subject Lefschetz fixed-point theorem E262120 entity
Predicate relatedTo P37 FINISHED
Object Atiyah–Bott fixed-point theorem E258614 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: Atiyah–Bott fixed-point theorem | Statement: [Lefschetz fixed-point theorem, relatedTo, Atiyah–Bott fixed-point theorem]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Atiyah–Bott fixed-point theorem
Context triple: [Lefschetz fixed-point theorem, relatedTo, Atiyah–Bott fixed-point theorem]
  • A. Atiyah–Bott fixed-point theorem chosen
    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.
  • B. Atiyah–Singer index theorem
    The Atiyah–Singer index theorem is a fundamental result in mathematics that links the analytical properties of elliptic differential operators to topological invariants of manifolds, unifying analysis, topology, and geometry.
  • C. Hirzebruch signature theorem
    The Hirzebruch signature theorem is a fundamental result in differential topology that expresses the signature of a smooth, compact, oriented 4k-dimensional manifold as a polynomial in its Pontryagin classes.
  • D. Lefschetz fixed-point theorem
    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.
  • E. Hirzebruch–Riemann–Roch theorem
    The Hirzebruch–Riemann–Roch theorem is a fundamental result in algebraic geometry and topology that expresses the holomorphic Euler characteristic of a complex manifold in terms of characteristic classes, unifying and extending classical Riemann–Roch type formulas.
  • 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_69e3e7a6dfa8819096f822294eb64dd1 completed April 18, 2026, 8:20 p.m.
Created at: April 8, 2026, 9:27 p.m.