Triple

T22328810
Position Surface form Disambiguated ID Type / Status
Subject Hard Lefschetz theorem E551969 entity
Predicate isRelatedTo P37 FINISHED
Object Hodge–Riemann bilinear relations — 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–Riemann bilinear relations | Statement: [Hard Lefschetz theorem, isRelatedTo, Hodge–Riemann bilinear relations]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Hodge–Riemann bilinear relations
Context triple: [Hard Lefschetz theorem, isRelatedTo, Hodge–Riemann bilinear relations]
  • A. Hodge–Riemann bilinear relations chosen
    The Hodge–Riemann bilinear relations are fundamental positivity and orthogonality conditions on the intersection form in Hodge theory that underpin results such as the hard Lefschetz theorem and the Hodge index theorem.
  • B. Standard Conjectures on Algebraic Cycles
    The Standard Conjectures on Algebraic Cycles are a set of deep, still unproven hypotheses in algebraic geometry that aim to provide a foundational theory of algebraic cycles and their cohomological properties, underpinning much of the modern theory of motives.
  • C. Hodge filtration
    The Hodge filtration is a decreasing sequence of complex subspaces on the cohomology of a complex algebraic variety that encodes its Hodge decomposition and mixed Hodge structure.
  • D. Lazarsfeld’s Positivity in Algebraic Geometry
    Lazarsfeld’s *Positivity in Algebraic Geometry* is a two-volume monograph that serves as a standard modern reference on the theory of positivity for line bundles and divisors in algebraic geometry, integrating techniques from cohomology, vanishing theorems, and birational geometry.
  • E. Hodge theory
    Hodge theory is a branch of mathematics that studies the relationship between differential forms, cohomology, and complex geometry, particularly on complex manifolds.
  • 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_69e11e482f788190b78d1588fc26d606 completed April 16, 2026, 5:37 p.m.
NER Named-entity recognition batch_69f1576ab52c819087563cd778d6bc5e completed April 29, 2026, 12:57 a.m.
Created at: April 16, 2026, 8:43 p.m.