Triple

T7678358
Position Surface form Disambiguated ID Type / Status
Subject Hodge Conjecture E173923 entity
Predicate concerns P1256 FINISHED
Object Hodge decomposition E553414 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: Hodge decomposition | Statement: [Hodge Conjecture, concerns, Hodge decomposition]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Hodge decomposition
Context triple: [Hodge Conjecture, concerns, Hodge decomposition]
  • A. Hodge decomposition chosen
    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.
  • B. Hodge theory
    Hodge theory is a branch of mathematics that studies the relationship between differential forms, cohomology, and complex geometry, particularly on complex manifolds.
  • C. Hodge Laplacian
    The Hodge Laplacian is a differential operator on differential forms of a Riemannian manifold that combines the exterior derivative and its adjoint to study harmonic forms and de Rham cohomology.
  • D. 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.
  • E. Hodge–Riemann bilinear relations
    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.
  • 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_69c6995703e0819081de77361b602e78 completed March 27, 2026, 2:51 p.m.
NER Named-entity recognition batch_69c701fd18d88190888144a7d0f228d9 completed March 27, 2026, 10:17 p.m.
NED1 Entity disambiguation (via context triple) batch_69c8a240057081908826a5371ef5215b completed March 29, 2026, 3:53 a.m.
Created at: March 27, 2026, 4:01 p.m.