Triple

T10991955
Position Surface form Disambiguated ID Type / Status
Subject Hirzebruch–Riemann–Roch theorem E259772 entity
Predicate generalizes P2372 FINISHED
Object Riemann–Roch theorem for curves E47350 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: Riemann–Roch theorem for curves | Statement: [Hirzebruch–Riemann–Roch theorem, generalizes, Riemann–Roch theorem for curves]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Riemann–Roch theorem for curves
Context triple: [Hirzebruch–Riemann–Roch theorem, generalizes, Riemann–Roch theorem for curves]
  • 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. 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. Théorie des intersections et théorème de Riemann–Roch
    "Théorie des intersections et théorème de Riemann–Roch" is a volume of the Séminaire de Géométrie Algébrique (SGA 6) that develops the foundations of intersection theory in algebraic geometry and establishes a general form of the Riemann–Roch theorem.
  • D. 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.
  • E. Hurwitz bound on automorphism groups of curves
    The Hurwitz bound on automorphism groups of curves is a classical result in algebraic geometry stating that a compact Riemann surface of genus at least 2 has at most 84(g − 1) automorphisms.
  • 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_69d6aa8a6a548190a750f944ccdc8064 completed April 8, 2026, 7:20 p.m.
NER Named-entity recognition batch_69d795d1e918819090c71f5a077fa15a completed April 9, 2026, 12:04 p.m.
NED1 Entity disambiguation (via context triple) batch_69e374639f1481908ea372b81a834f6f completed April 18, 2026, 12:09 p.m.
Created at: April 8, 2026, 9:24 p.m.