Triple

T18382342
Position Surface form Disambiguated ID Type / Status
Subject Gustav Roch E446483 entity
Predicate notableConcept P201 FINISHED
Object Roch part of the Riemann–Roch theorem — NE NERFINISHED

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: Roch part of the Riemann–Roch theorem | Statement: [Gustav Roch, notableConcept, Roch part of the Riemann–Roch theorem]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Roch part of the Riemann–Roch theorem
Context triple: [Gustav Roch, notableConcept, Roch part of the Riemann–Roch theorem]
  • A. Riemann–Roch theorem chosen
    The Riemann–Roch theorem is a fundamental result in algebraic geometry and complex analysis that relates the dimension of spaces of meromorphic sections of a line bundle on a curve to topological data such as genus and degree.
  • B. 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.
  • C. Grothendieck–Riemann–Roch theorem
    The Grothendieck–Riemann–Roch theorem is a fundamental result in algebraic geometry that generalizes the classical Riemann–Roch theorem by relating pushforwards in K-theory to pushforwards in cohomology via characteristic classes.
  • D. Riemann–Hurwitz formula
    The Riemann–Hurwitz formula is a fundamental result in algebraic geometry and complex analysis that relates the genera of two Riemann surfaces connected by a branched covering map, accounting for the ramification data.
  • E. equivariant Riemann–Roch theorem
    The equivariant Riemann–Roch theorem is a generalization of the classical Riemann–Roch theorem that computes characteristic classes and indices in the presence of a group action, relating equivariant K-theory to equivariant cohomology.
  • F. None of above.
  • G. Unsure - the case is ambiguous/there is not enough information to decide.

Provenance (2 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_69d8b9f370b88190b1e5081c2c238e7f completed April 10, 2026, 8:50 a.m.
NER Named-entity recognition batch_69e5179c931c8190b1c7c8284f42f7b7 completed April 19, 2026, 5:57 p.m.
Created at: April 10, 2026, 10:45 a.m.