Triple

T23142462
Position Surface form Disambiguated ID Type / Status
Subject Hodge Laplacian E577497 entity
Predicate codifferentialDefinedAs P151070 FINISHED
Object δ = (−1)^{n(k+1)+1} * d * on k-forms in dimension n LITERAL 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: δ = (−1)^{n(k+1)+1} * d * on k-forms in dimension n | Statement: [Hodge Laplacian, codifferentialDefinedAs, δ = (−1)^{n(k+1)+1} * d * on k-forms in dimension n]
PD Predicate disambiguation gpt-5-mini-2025-08-07
Target predicate: codifferentialDefinedAs
Context triple: [Hodge Laplacian, codifferentialDefinedAs, δ = (−1)^{n(k+1)+1} * d * on k-forms in dimension n]
  • A. cochainComplex
    Indicates that one mathematical object is a cochain complex, i.e., a sequence of abelian groups or modules connected by homomorphisms whose composition of consecutive maps is zero.
  • B. differential
    Indicates a relationship where one quantity or state is defined as the infinitesimal change or difference relative to another variable or function.
  • C. hasDifferentialForm
    Indicates that one entity is associated with, or can be represented by, a specific differential form in a mathematical or geometric context.
  • D. differentials
    Indicates that there are measurable differences or distinctions between two or more related quantities, states, or conditions.
  • E. definesCohomologyClass
    Indicates that one mathematical object (such as a cocycle, form, or map) specifies or determines a particular cohomology class in a given cohomology group.
  • F. None of above. chosen

Provenance (4 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_69e245f8e6248190ba3d58e068b4dccb completed April 17, 2026, 2:38 p.m.
NER Named-entity recognition batch_69f18ecb72fc8190a24e8f5756217a36 completed April 29, 2026, 4:53 a.m.
PD Predicate disambiguation batch_69ef89f83b108190aaaa1db6221fc163 completed April 27, 2026, 4:08 p.m.
PDg Predicate description generation batch_69ef9b7494f4819088ae59ea3d0ae8ab completed April 27, 2026, 5:23 p.m.
Created at: April 17, 2026, 4 p.m.