Triple

T16150925
Position Surface form Disambiguated ID Type / Status
Subject Todd class E391905 entity
Predicate appearsAsFactorIn P90033 FINISHED
Object Grothendieck–Riemann–Roch integrand E254119 NE FINISHED

How this triple was built (3 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: Grothendieck–Riemann–Roch integrand | Statement: [Todd class, appearsAsFactorIn, Grothendieck–Riemann–Roch integrand]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Grothendieck–Riemann–Roch integrand
Context triple: [Todd class, appearsAsFactorIn, Grothendieck–Riemann–Roch integrand]
  • A. Grothendieck–Riemann–Roch theorem chosen
    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.
  • 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. 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.
  • D. Grothendieck–Lefschetz trace formula
    The Grothendieck–Lefschetz trace formula is a fundamental result in algebraic geometry that expresses the number of rational points of a variety over a finite field in terms of traces of Frobenius acting on its étale cohomology groups.
  • E. Bott residue formula
    The Bott residue formula is a fundamental result in differential and algebraic geometry that expresses global invariants, such as characteristic numbers, as sums of local contributions at the fixed points of a holomorphic vector field or group action.
  • F. None of above.
  • G. Unsure - the case is ambiguous/there is not enough information to decide.
PD Predicate disambiguation gpt-5-mini-2025-08-07
Target predicate: appearsAsFactorIn
Context triple: [Todd class, appearsAsFactorIn, Grothendieck–Riemann–Roch integrand]
  • A. factor chosen
    Indicates that one entity is a contributing cause, influence, or component affecting the state, outcome, or existence of another entity.
  • B. arisesIn
    Indicates that something originates, emerges, or comes into existence within a specified context, source, or location.
  • C. considersFactor
    Indicates that one entity takes another entity into account as a factor when forming a judgment, decision, or evaluation.
  • D. areUsedIn
    Indicates that certain entities serve as components, tools, or resources within a particular process, context, or application.
  • E. isUsedAs
    Indicates that one entity serves a particular function, role, or purpose as another entity.
  • F. None of above.

Provenance (4 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_69fff7a9ebf08190aa21cdff051f4ba2 completed May 10, 2026, 3:12 a.m.
PD Predicate disambiguation batch_69e1828abb608190a99d86bce1d77de2 completed April 17, 2026, 12:44 a.m.
Created at: April 10, 2026, 5:01 a.m.