Triple
T5766809
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Regge theory |
E127234
|
entity |
| Predicate | hasMathematicalTool |
P4746
|
FINISHED |
| Object |
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.
|
E543033
|
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: Sommerfeld-Watson transform | Statement: [Regge theory, hasMathematicalTool, Sommerfeld-Watson transform]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Sommerfeld-Watson transform Context triple: [Regge theory, hasMathematicalTool, Sommerfeld-Watson transform]
-
A.
Poisson summation formula
The Poisson summation formula is a fundamental result in harmonic analysis that links sums of a function over the integers to sums of its Fourier transform, with deep applications in number theory, signal processing, and physics.
-
B.
Wightman functions
Wightman functions are vacuum expectation values of time-ordered products of quantum fields that rigorously encode the correlation structure and axiomatic foundations of relativistic quantum field theory.
-
C.
Mittag-Leffler function
The Mittag-Leffler function is a complex function that generalizes the exponential function and plays a central role in fractional calculus and the theory of differential and integral equations.
-
D.
Sommerfeld radiation condition
The Sommerfeld radiation condition is a mathematical criterion in wave and scattering theory that selects physically meaningful, outward-radiating solutions to the Helmholtz equation at infinity.
-
E.
The Fourier Integral and Certain of Its Applications
The Fourier Integral and Certain of Its Applications is a foundational mathematical work by Norbert Wiener that develops and applies Fourier analysis to problems in harmonic analysis and related areas.
- 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: Sommerfeld-Watson transform Triple: [Regge theory, hasMathematicalTool, Sommerfeld-Watson transform]
Generated description
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.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Sommerfeld-Watson transform Target entity description: 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.
-
A.
Poisson summation formula
The Poisson summation formula is a fundamental result in harmonic analysis that links sums of a function over the integers to sums of its Fourier transform, with deep applications in number theory, signal processing, and physics.
-
B.
Wightman functions
Wightman functions are vacuum expectation values of time-ordered products of quantum fields that rigorously encode the correlation structure and axiomatic foundations of relativistic quantum field theory.
-
C.
Mittag-Leffler function
The Mittag-Leffler function is a complex function that generalizes the exponential function and plays a central role in fractional calculus and the theory of differential and integral equations.
-
D.
Sommerfeld radiation condition
The Sommerfeld radiation condition is a mathematical criterion in wave and scattering theory that selects physically meaningful, outward-radiating solutions to the Helmholtz equation at infinity.
-
E.
The Fourier Integral and Certain of Its Applications
The Fourier Integral and Certain of Its Applications is a foundational mathematical work by Norbert Wiener that develops and applies Fourier analysis to problems in harmonic analysis and related areas.
- 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_69c00834f6308190851b0abeddd8ed7e |
completed | March 22, 2026, 3:18 p.m. |
| NER | Named-entity recognition | batch_69c0335f23c081909b35020801e3ef12 |
completed | March 22, 2026, 6:22 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69c07e5d8c8c819081067de808ac1b56 |
completed | March 22, 2026, 11:42 p.m. |
| NEDg | Description generation | batch_69c08bce3e808190af4e2f0e8591b2de |
completed | March 23, 2026, 12:39 a.m. |
| NED2 | Entity disambiguation (via description) | batch_69c08c6d1a788190acb7651a1f144d9d |
completed | March 23, 2026, 12:42 a.m. |
Created at: March 22, 2026, 3:49 p.m.