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.