Triple

T2663840
Position Surface form Disambiguated ID Type / Status
Subject Euler’s polyhedron formula E54784 entity
Predicate hasConcept P531 FINISHED
Object Euler characteristic E54784 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: Euler characteristic | Statement: [Euler’s polyhedron formula, hasConcept, Euler characteristic]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Euler characteristic
Context triple: [Euler’s polyhedron formula, hasConcept, Euler characteristic]
  • A. Poincaré–Hopf theorem
    The Poincaré–Hopf theorem is a fundamental result in differential topology that relates the sum of the indices of a vector field’s isolated zeros on a compact manifold to the manifold’s Euler characteristic.
  • B. Euler’s polyhedron formula chosen
    Euler’s polyhedron formula is a fundamental result in topology and geometry that relates the numbers of vertices, edges, and faces of a convex polyhedron through the equation V − E + F = 2.
  • C. Poincaré duality
    Poincaré duality is a fundamental theorem in algebraic topology that relates the homology and cohomology groups of an oriented closed manifold in complementary dimensions.
  • 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. Milnor number
    The Milnor number is an invariant in singularity theory that measures the complexity of an isolated critical point of a complex hypersurface or function.
  • 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_69ab49e028948190b97e01d73548b1d9 completed March 6, 2026, 9:40 p.m.
NER Named-entity recognition batch_69abd96dba44819085c3e651afba7806 completed March 7, 2026, 7:53 a.m.
NED1 Entity disambiguation (via context triple) batch_69afa056f478819091f6751edfee0132 completed March 10, 2026, 4:38 a.m.
Created at: March 6, 2026, 9:54 p.m.