Triple

T11086023
Position Surface form Disambiguated ID Type / Status
Subject Grothendieck–Ogg–Shafarevich formula E262121 entity
Predicate isRelatedTo P37 FINISHED
Object Riemann–Hurwitz formula E47610 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–Hurwitz formula | Statement: [Grothendieck–Ogg–Shafarevich formula, isRelatedTo, Riemann–Hurwitz formula]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Riemann–Hurwitz formula
Context triple: [Grothendieck–Ogg–Shafarevich formula, isRelatedTo, Riemann–Hurwitz formula]
  • A. Riemann–Hurwitz formula chosen
    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.
  • B. Riemann–Roch theorem
    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.
  • C. 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.
  • D. Noether’s formula
    Noether’s formula is a fundamental result in algebraic geometry that relates the holomorphic Euler characteristic of a smooth projective surface to its Chern numbers, serving as a special case of the Hirzebruch–Riemann–Roch theorem.
  • 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_69d6aa9983c08190b0ef61603b69feac completed April 8, 2026, 7:20 p.m.
NER Named-entity recognition batch_69d799c3ed9c8190a3f5cdf1fe0e74a2 completed April 9, 2026, 12:21 p.m.
NED1 Entity disambiguation (via context triple) batch_69e441b1b4dc8190a572d4d6269540cd completed April 19, 2026, 2:45 a.m.
Created at: April 8, 2026, 9:27 p.m.