Triple
T7861129
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Adrien-Marie Legendre |
E182500
|
entity |
| Predicate | knownFor |
P22
|
FINISHED |
| Object |
Legendre transformation
The Legendre transformation is a mathematical operation that converts a function of one set of variables into a function of their conjugate variables, widely used in classical mechanics and thermodynamics to switch between different energy or potential formulations.
|
E695821
|
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: Legendre transformation | Statement: [Adrien-Marie Legendre, knownFor, Legendre transformation]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Legendre transformation Context triple: [Adrien-Marie Legendre, knownFor, Legendre transformation]
-
A.
Landen transformations
Landen transformations are classical iterative formulas in analysis that relate elliptic integrals (and associated means) at different moduli, enabling their efficient evaluation and simplification.
-
B.
Bogoliubov transformation
The Bogoliubov transformation is a mathematical change of basis used in quantum field theory and many-body physics to diagonalize Hamiltonians by mixing creation and annihilation operators, enabling the description of quasiparticles and phenomena like superconductivity.
-
C.
Laplace transform
The Laplace transform is an integral transform widely used in mathematics, physics, and engineering to convert functions of time into functions of a complex variable, simplifying the analysis and solution of differential equations and linear systems.
-
D.
Lagrangian function
The Lagrangian function is a mathematical construct that combines an objective function with its constraints, widely used in optimization and variational calculus to analyze and solve constrained problems.
-
E.
Sommerfeld-Watson transform
The Sommerfeld-Watson transform is a complex-analysis technique that converts discrete sums over angular momentum into contour integrals, widely used in scattering theory and Regge theory to study analytic properties of amplitudes.
- 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: Legendre transformation Triple: [Adrien-Marie Legendre, knownFor, Legendre transformation]
Generated description
The Legendre transformation is a mathematical operation that converts a function of one set of variables into a function of their conjugate variables, widely used in classical mechanics and thermodynamics to switch between different energy or potential formulations.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Legendre transformation Target entity description: The Legendre transformation is a mathematical operation that converts a function of one set of variables into a function of their conjugate variables, widely used in classical mechanics and thermodynamics to switch between different energy or potential formulations.
-
A.
Landen transformations
Landen transformations are classical iterative formulas in analysis that relate elliptic integrals (and associated means) at different moduli, enabling their efficient evaluation and simplification.
-
B.
Bogoliubov transformation
The Bogoliubov transformation is a mathematical change of basis used in quantum field theory and many-body physics to diagonalize Hamiltonians by mixing creation and annihilation operators, enabling the description of quasiparticles and phenomena like superconductivity.
-
C.
Laplace transform
The Laplace transform is an integral transform widely used in mathematics, physics, and engineering to convert functions of time into functions of a complex variable, simplifying the analysis and solution of differential equations and linear systems.
-
D.
Lagrangian function
The Lagrangian function is a mathematical construct that combines an objective function with its constraints, widely used in optimization and variational calculus to analyze and solve constrained problems.
-
E.
Sommerfeld-Watson transform
The Sommerfeld-Watson transform is a complex-analysis technique that converts discrete sums over angular momentum into contour integrals, widely used in scattering theory and Regge theory to study analytic properties of amplitudes.
- 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_69ca82887fd48190975896bf38c4596b |
completed | March 30, 2026, 2:02 p.m. |
| NER | Named-entity recognition | batch_69cb36bcb5cc8190a8a384ce0f020b9f |
completed | March 31, 2026, 2:51 a.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69cb5b4138d081908a5ff16b79f0a0c8 |
completed | March 31, 2026, 5:27 a.m. |
| NEDg | Description generation | batch_69cb5f1c9ef08190b1b79482f39966c7 |
completed | March 31, 2026, 5:43 a.m. |
| NED2 | Entity disambiguation (via description) | batch_69cb767b198481909cfc1f7a44e6f0d8 |
completed | March 31, 2026, 7:23 a.m. |
Created at: March 30, 2026, 4:53 p.m.