Triple

T21494640
Position Surface form Disambiguated ID Type / Status
Subject Fermat surface E530319 entity
Predicate studiedIn P770 FINISHED
Object Hodge theory — 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: Hodge theory | Statement: [Fermat surface, studiedIn, Hodge theory]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Hodge theory
Context triple: [Fermat surface, studiedIn, Hodge theory]
  • A. Hodge theory chosen
    Hodge theory is a branch of mathematics that studies the relationship between differential forms, cohomology, and complex geometry, particularly on complex manifolds.
  • B. mixed Hodge structures
    Mixed Hodge structures are algebraic structures on cohomology groups that generalize pure Hodge structures by incorporating a weight filtration, allowing the study of varieties with singularities or non-compactness.
  • C. Hodge decomposition
    Hodge decomposition is a fundamental result in differential geometry and Hodge theory that expresses differential forms on a Riemannian manifold uniquely as sums of exact, co-exact, and harmonic components.
  • D. “Hodge Theory and Complex Algebraic Geometry, Volume 1”
    “Hodge Theory and Complex Algebraic Geometry, Volume 1” is a foundational graduate-level textbook that develops the interplay between Hodge theory and the geometry of complex algebraic varieties.
  • E. “Hodge Theory and Complex Algebraic Geometry, Volume 2”
    “Hodge Theory and Complex Algebraic Geometry, Volume 2” is a graduate-level mathematics text by Claire Voisin that develops advanced aspects of Hodge theory and its deep connections with the geometry of complex algebraic varieties.
  • 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_69e0c45bd15481909fba5910765cdda2 completed April 16, 2026, 11:13 a.m.
NER Named-entity recognition batch_69e9ea567244819091863350fedae3ae completed April 23, 2026, 9:45 a.m.
Created at: April 16, 2026, 6:23 p.m.