Triple

T1389382
Position Surface form Disambiguated ID Type / Status
Subject Gauss–Bonnet theorem (early form) E29918 entity
Predicate hasGeneralization P2372 FINISHED
Object higher-dimensional Gauss–Bonnet formulas E159880 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: higher-dimensional Gauss–Bonnet formulas | Statement: [Gauss–Bonnet theorem (early form), hasGeneralization, higher-dimensional Gauss–Bonnet formulas]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: higher-dimensional Gauss–Bonnet formulas
Context triple: [Gauss–Bonnet theorem (early form), hasGeneralization, higher-dimensional Gauss–Bonnet formulas]
  • A. Gauss–Bonnet theorem (early form)
    The Gauss–Bonnet theorem (early form) is an early version of the fundamental result in differential geometry that links the total curvature of a surface to its topological characteristics, originally developed by Carl Friedrich Gauss.
  • B. Chern–Weil theory chosen
    Chern–Weil theory is a framework in differential geometry that constructs characteristic classes of vector bundles from curvature forms, linking topology and geometry through invariant polynomials.
  • C. 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.
  • D. Theorema Egregium
    Theorema Egregium is Gauss’s celebrated theorem in differential geometry showing that the Gaussian curvature of a surface is an intrinsic property independent of how the surface is embedded in space.
  • E. 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.
  • 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_69a498dc92f8819094a1108f8ac90f43 completed March 1, 2026, 7:51 p.m.
NER Named-entity recognition batch_69a4c35ce48c81909aaad7dfa2df63fa completed March 1, 2026, 10:53 p.m.
NED1 Entity disambiguation (via context triple) batch_69ad08ac24948190b85c8e38b34509c9 completed March 8, 2026, 5:27 a.m.
Created at: March 1, 2026, 7:59 p.m.