Triple
T26254152
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | modular j-invariant |
E656674
|
entity |
| Predicate | hasFourierExpansion |
P90300
|
FINISHED |
| Object | j(τ) = q^{-1} + 744 + 196884 q + 21493760 q^2 + … |
—
|
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: j(τ) = q^{-1} + 744 + 196884 q + 21493760 q^2 + … | Statement: [modular j-invariant, hasFourierExpansion, j(τ) = q^{-1} + 744 + 196884 q + 21493760 q^2 + …]
PD
Predicate disambiguation
gpt-5-mini-2025-08-07
Target predicate: hasFourierExpansion
Context triple: [modular j-invariant, hasFourierExpansion, j(τ) = q^{-1} + 744 + 196884 q + 21493760 q^2 + …]
-
A.
isFourierTransformOf
Indicates that one mathematical function or signal is the Fourier transform representation of another, relating them via decomposition into frequency components.
-
B.
hasAsymptoticExpansion
Indicates that one mathematical object serves as the asymptotic expansion approximating another object in a specified limit or regime.
-
C.
hasSeriesExpansion
chosen
Indicates that a mathematical function or expression is associated with a specific series representation (such as a Taylor or power series) that expands it around a point or region.
-
D.
areEigenfunctionsOf
Indicates that certain functions serve as eigenfunctions corresponding to a specified operator or transformation.
-
E.
thetaSeriesIsModularFormFor
Indicates that a given theta series satisfies the defining properties of a modular form for a specified modular group or level.
- F. None of above.
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_69ee5b4d25ac819086acb51184602576 |
completed | April 26, 2026, 6:37 p.m. |
| NER | Named-entity recognition | batch_69f6978fe97081908fe568091ad9b159 |
completed | May 3, 2026, 12:32 a.m. |
| PD | Predicate disambiguation | batch_69f69661e6ec8190948251c7516a32ad |
completed | May 3, 2026, 12:27 a.m. |
Created at: April 26, 2026, 9:08 p.m.