Triple
T11411746
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Gelfand–Levitan theory |
E270386
|
entity |
| Predicate | relatedTo |
P37
|
FINISHED |
| Object |
Borg–Marchenko theorem
The Borg–Marchenko theorem is a fundamental result in inverse spectral theory that characterizes when a potential in a one-dimensional Schrödinger operator is uniquely determined by its spectral data.
|
E924204
|
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: Borg–Marchenko theorem | Statement: [Gelfand–Levitan theory, relatedTo, Borg–Marchenko theorem]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Borg–Marchenko theorem Context triple: [Gelfand–Levitan theory, relatedTo, Borg–Marchenko theorem]
-
A.
Gelfand–Levitan theory
Gelfand–Levitan theory is a foundational framework in inverse spectral theory that reconstructs differential operators or potentials from their spectral data using integral equations.
-
B.
Bohr–Courant theorem
The Bohr–Courant theorem is a classical result in analytic number theory describing the value distribution of Dirichlet series, particularly the Riemann zeta function, and serves as a precursor to modern universality theorems such as Voronin’s.
-
C.
Paley–Wiener theorem
The Paley–Wiener theorem is a fundamental result in harmonic analysis that characterizes which functions arise as Fourier transforms of compactly supported functions (or distributions), linking analytic properties of entire functions with support properties in the original domain.
-
D.
May–Wigner stability theorem
The May–Wigner stability theorem is a result in theoretical ecology and random matrix theory showing that large, complex systems with many random interactions are generically unstable beyond a critical level of complexity.
-
E.
Szegő limit theorem
The Szegő limit theorem is a fundamental result in analysis and operator theory that describes the asymptotic behavior of determinants of large Toeplitz matrices in terms of the symbol’s integral.
- 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: Borg–Marchenko theorem Triple: [Gelfand–Levitan theory, relatedTo, Borg–Marchenko theorem]
Generated description
The Borg–Marchenko theorem is a fundamental result in inverse spectral theory that characterizes when a potential in a one-dimensional Schrödinger operator is uniquely determined by its spectral data.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Borg–Marchenko theorem Target entity description: The Borg–Marchenko theorem is a fundamental result in inverse spectral theory that characterizes when a potential in a one-dimensional Schrödinger operator is uniquely determined by its spectral data.
-
A.
Gelfand–Levitan theory
Gelfand–Levitan theory is a foundational framework in inverse spectral theory that reconstructs differential operators or potentials from their spectral data using integral equations.
-
B.
Bohr–Courant theorem
The Bohr–Courant theorem is a classical result in analytic number theory describing the value distribution of Dirichlet series, particularly the Riemann zeta function, and serves as a precursor to modern universality theorems such as Voronin’s.
-
C.
Paley–Wiener theorem
The Paley–Wiener theorem is a fundamental result in harmonic analysis that characterizes which functions arise as Fourier transforms of compactly supported functions (or distributions), linking analytic properties of entire functions with support properties in the original domain.
-
D.
May–Wigner stability theorem
The May–Wigner stability theorem is a result in theoretical ecology and random matrix theory showing that large, complex systems with many random interactions are generically unstable beyond a critical level of complexity.
-
E.
Szegő limit theorem
The Szegő limit theorem is a fundamental result in analysis and operator theory that describes the asymptotic behavior of determinants of large Toeplitz matrices in terms of the symbol’s integral.
- 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_69d6aaddeaa8819088b30ef7b50598c9 |
completed | April 8, 2026, 7:22 p.m. |
| NER | Named-entity recognition | batch_69d8015017d08190b4020c76545556d6 |
completed | April 9, 2026, 7:43 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69e5b855f0508190a2e57ef9407ddb1a |
completed | April 20, 2026, 5:23 a.m. |
| NEDg | Description generation | batch_69e5c28d3824819097ff84cb4e13c923 |
completed | April 20, 2026, 6:07 a.m. |
| NED2 | Entity disambiguation (via description) | batch_69e5c451c6c88190bcbb1f54ede35d29 |
completed | April 20, 2026, 6:14 a.m. |
Created at: April 8, 2026, 9:34 p.m.