Triple

T22328963
Position Surface form Disambiguated ID Type / Status
Subject Hodge filtration E551972 entity
Predicate relatedConcept P37 FINISHED
Object Griffiths transversality
Griffiths transversality is a fundamental condition in Hodge theory stating that the Gauss–Manin connection shifts the Hodge filtration by at most one step, governing how Hodge structures vary in families.
E1531321 NE FINISHED

How this triple was built (4 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: Griffiths transversality | Statement: [Hodge filtration, relatedConcept, Griffiths transversality]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Griffiths transversality
Context triple: [Hodge filtration, relatedConcept, Griffiths transversality]
  • A. 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.
  • B. 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.
  • 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. Hodge theory
    Hodge theory is a branch of mathematics that studies the relationship between differential forms, cohomology, and complex geometry, particularly on complex manifolds.
  • E. Lefschetz hyperplane theorem
    The Lefschetz hyperplane theorem is a fundamental result in algebraic geometry and topology that relates the topology (especially homology and homotopy groups) of a smooth projective variety to that of its hyperplane sections.
  • F. None of above. chosen
  • G. Unsure - the case is ambiguous/there is not enough information to decide.
NEDg Description generation gpt-5.1
Instruction
Generate a one-sentence description of the target entity. 
You are given a context triple in the form (subject, predicate, object), where the object is the target entity. 
# Instructions
Use the triple to infer relevant information about the entity. Describe the entity based on what is most defining, well-known. 
Avoid repeating the information from the triple, unless really essential.
# Response Format
Return only the sentence: "Description: [one-sentence description of the target entity]"
Input
Entity: Griffiths transversality
Triple: [Hodge filtration, relatedConcept, Griffiths transversality]
Generated description
Griffiths transversality is a fundamental condition in Hodge theory stating that the Gauss–Manin connection shifts the Hodge filtration by at most one step, governing how Hodge structures vary in families.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Griffiths transversality
Target entity description: Griffiths transversality is a fundamental condition in Hodge theory stating that the Gauss–Manin connection shifts the Hodge filtration by at most one step, governing how Hodge structures vary in families.
  • A. 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.
  • B. 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.
  • 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. Hodge theory
    Hodge theory is a branch of mathematics that studies the relationship between differential forms, cohomology, and complex geometry, particularly on complex manifolds.
  • E. Lefschetz hyperplane theorem
    The Lefschetz hyperplane theorem is a fundamental result in algebraic geometry and topology that relates the topology (especially homology and homotopy groups) of a smooth projective variety to that of its hyperplane sections.
  • F. None of above. chosen

Provenance (5 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.
NED1 Entity disambiguation (via context triple) batch_6a0ad523ecec8190a85eb932288965fb completed May 18, 2026, 9 a.m.
NEDg Description generation batch_6a0ad992b43c8190b0e409d64db83308 completed May 18, 2026, 9:19 a.m.
NED2 Entity disambiguation (via description) batch_6a0adac48bec8190989dd7c5e28d283a completed May 18, 2026, 9:24 a.m.
Created at: April 16, 2026, 8:43 p.m.