Triple

T16150904
Position Surface form Disambiguated ID Type / Status
Subject Todd class E391905 entity
Predicate appearsIn P795 FINISHED
Object Riemann–Roch formulas 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 formulas | Statement: [Todd class, appearsIn, Riemann–Roch formulas]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Riemann–Roch formulas
Context triple: [Todd class, appearsIn, Riemann–Roch formulas]
  • 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. 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.
  • D. 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.
  • E. 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.
  • 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_69e21d9724808190a8332987583a345a completed April 17, 2026, 11:46 a.m.
NED1 Entity disambiguation (via context triple) batch_69fffef2f49081909841a1f9bfbd622b completed May 10, 2026, 3:43 a.m.
Created at: April 10, 2026, 5:01 a.m.