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.