Triple

T16151043
Position Surface form Disambiguated ID Type / Status
Subject equivariant index theorem E391908 entity
Predicate hasVersion P455 FINISHED
Object 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: Lefschetz fixed point formula | Statement: [equivariant index theorem, hasVersion, Lefschetz fixed point formula]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Lefschetz fixed point formula
Context triple: [equivariant index theorem, hasVersion, Lefschetz fixed point formula]
  • 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. Lefschetz number
    The Lefschetz number is a topological invariant, computed from the traces of induced maps on homology, that predicts the existence and number of fixed points of a continuous self-map on a topological space.
  • D. 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.
  • E. 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.
  • 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_69d87f1c65e48190aa2b4c472e9bafc4 completed April 10, 2026, 4:39 a.m.
NER Named-entity recognition batch_69e21d981950819087fdacc7879dca97 completed April 17, 2026, 11:46 a.m.
NED1 Entity disambiguation (via context triple) batch_69fff7a9ebf08190aa21cdff051f4ba2 completed May 10, 2026, 3:12 a.m.
Created at: April 10, 2026, 5:01 a.m.