Triple

T10946694
Position Surface form Disambiguated ID Type / Status
Subject Atiyah–Bott fixed-point theorem E258614 entity
Predicate generalizes P2372 FINISHED
Object Holomorphic Lefschetz fixed-point formula 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: Holomorphic Lefschetz fixed-point formula | Statement: [Atiyah–Bott fixed-point theorem, generalizes, Holomorphic Lefschetz fixed-point formula]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Holomorphic Lefschetz fixed-point formula
Context triple: [Atiyah–Bott fixed-point theorem, generalizes, Holomorphic Lefschetz fixed-point formula]
  • A. 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.
  • B. 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.
  • C. 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.
  • D. 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.
  • 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_69d6aa8769b4819082bfe5e61b9017f0 completed April 8, 2026, 7:20 p.m.
NER Named-entity recognition batch_69d770eaaea08190b06e508600d8a305 completed April 9, 2026, 9:27 a.m.
NED1 Entity disambiguation (via context triple) batch_69e23c3c885081908edcece772b2e759 completed April 17, 2026, 1:57 p.m.
Created at: April 8, 2026, 9:23 p.m.